# Open-Source Software Radio Platform for Research on Cellular Networked UAVs
– It Works!

Aly Sabri Abdalla, Andrew Yingst, Keith Powell, Antoni Gelonch-Bosch, and Vuk
Marojevic

###### Abstract

Cellular network-connected unmanned aerial vehicles (UAVs) experience
different radio propagation conditions than radio nodes on the ground.
Therefore, it has become critical to investigate the performance of aerial
radios, both theoretically and through field trials. In this paper, we
consider low-altitude aerial nodes that are served by an experimental cellular
network. We provide a detailed description of the hardware and software
components needed for establishing a broadband wireless testbed for UAV
communications research using software radios. Results show that a testbed for
innovation in UAV communications and networking is feasible with commercial
off-the-shelf hardware, open-source software, and low-power signaling.

##  I Introduction

Unmanned aerial vehicles (UAVs) are increasingly popular in the commercial
sector and are considered one of the industrial verticals of the fifth
generation of mobile communications (5G). UAVs can support intelligent
transportation systems through traffic monitoring, accident reporting, and
aerial delivery of cargo and medication, among others. Among many
applications, UAVs can monitor crops, detect weeds, gather sensor data, and
assist with search and rescue and disaster recovery operations [1]. Fig. 1
illustrates this.

Figure 1: Emerging applications and use cases for networked UAVs.

The characteristics that make a UAV particularly suitable for the above-
mentioned applications are the strong line of sight (LOS) links, 3D mobility,
low cost, and ability to operate in a hostile environment. The cellular
network performance can be improved with UAVs by implementing stronger
security mechanisms [2], extending the coverage, and improving the capacity
[3]. This is being standardized by The Third Generation Partnership Project
(3GPP) [4].

The 3GPP Technical Report (TR) 36.777 and Technical Specification (TS) 22.125
define the essential requirements for providing unmanned aircraft system (UAS)
services through long-term evolution (LTE) networks. TR 23.754 and TR 23.755
identify the network infrastructure and the application architecture to
support UAV-enabled applications and use cases in 5G networks. TR 33.854
specifies the requirements and procedures to provide secure communications
services to UASs served by 3GPP networks. The International Telecommunication
Union (ITU) and the IEEE provide complementary standards for UAV applications
and use cases [5, 6].

UAVs are not only considered as user equipment (UEs) in the cellular network,
but also as network support nodes. They have the potential to facilitate
reliable, secure, and efficient wireless access [7]. A large number of
applications involving UAVs and advanced wireless communications are expected
to be developed in the coming years. To realize this vision, it is necessary
to have flexible research platforms and testbeds that are widely accessible.
This will accelerate research and development (R&D) that will provide
practical insights on the specific services that cellular networks should
offer to enable safe and efficient operation and cooperation among UASs. The
3GPP provides initial performance requirements for the network to support
command and control and video transmission from UAVs [4]. Cellular network
technology and procedures need to evolve to, among others, improve the 3D
coverage and effectively handle the challenging interference scenario between
UAV and terrestrial UEs.

Software defined radios (SDRs) can be used with a UAV for rapid radio
prototyping and experimentation. An SDR does the radio frequency (RF) data
acquisition/generation and data conversion for waveforms and protocols to be
processed in software [8]. Using a pair of Universal Software Radio
Peripherals (USRPs) and open-source LTE software srsRAN, [9] reports average
throughput and signal-to-noise ratio values at 10, 25, and 50 m UAV altitudes
from the ground SDR base station (BS) as 5.5, 2.0, 4.5 Mbps and 10.0, 7.5, 9.0
dB, respectively, for a 10 MHz frequency-division duplex (FDD) LTE system at
3.7 GHz. Those values are rather low, even without an external power amplifier
(PA). This may stem from choosing too high USRPs gains resulting in signal
distortion and self-interference from the design lacking isolation between the
transmit and receive antennas [9]. Another trial evaluates the performance of
the UAV as a relay between the ground BS and UE [10]. The open-source
OpenAirInterface (OAI) software with a USRP on board the UAV provides the
experimental LTE aerial relay (AR). The measurements show that the throughput
slightly improves when the signals are relayed through the AR, specifically
for non-LOS links between the BS and the UE. In another research project [11],
the UAV with a USRP and srsRAN is deployed as an aerial BS (ABS) that
positions itself to maximize network throughput for three ground UEs.
Throughput measurements were conducted in an outdoor drone cage over short
distances.

The published SDR platforms’ evaluation results often do not provide the
necessary performance because of poor design or operating decisions. The
difficulty is to select, integrate, and configure the hardware and the
software for providing a flexible and accessible platform that can provide
near commercial-grade performance and that can be scaled for enabling
cellular-connected UAV research in a production-like environment.

The purpose of this paper is to identify the requirements, the design
tradeoffs, the components and practical design and configuration choices for
building a reproducible open-source SDR platform that provides the necessary
interfaces and performance figures for enabling unlimited research
opportunities with cellular network-connected UAVs. The proposed platform is
the basis for the first SDR experiments offered through the Aerial
Experimentation and Research Platform for Advanced Wireless (AERPAW) [12].

The rest of the paper is organized as follows: Section II introduces the
platform requirements. Section III assesses the design options, tradeoffs, and
component choices. We show early results and offer guidelines for research in
this area. Section IV discusses the key challenges and directions for advanced
wireless R&D with UAVs. Section V provides the concluding remarks.

##  II Requirements of cellular network-connected UAV research platforms

The high demand for UAV integration into cellular networks requires a research
platform that can evolve with technology. Deploying a production-like 4G/5G
experimental cellular network requires implementing the radio access network
(RAN), the backhaul, and the core network (CN). This is the goal of AERPAW, a
public-private partnership project that is developing and operating a large-
scale testbed for advanced wireless research with UAVs. The requirements for
the open-source SDR research platform are

  * •

3GPP standard-compliant cellular communications system that performs according
to industry benchmarks,

  * •

Flexible and modular radio interface, supporting various cellular network-
connected UAV experiments,

  * •

Effective integration of the radio system with the UAV, subject to the UAV’s
space, weight and power constraints,

  * •

Open-source software that is maintained and that implements the RAN, the
backhaul, the CN, and the UEs,

  * •

Commercial off-the-shelf (COTS) hardware that is widely available and that is
popular among researchers,

  * •

Inter-operable and well-supported software and hardware,

  * •

Reproducible platform and experiments,

  * •

Open application programming interfaces (APIs),

  * •

Full control over the experiment (radio and vehicle), and

  * •

Scalable and portable platform that facilitates integration with other
testbeds, vehicles, or infrastructure.

The above requirements translate into specific requirements for the different
building blocks of the platform. These are summarized in Table I and
elaborated in continuation.

Data Conversion: The wireless transmission and reception of software-defined
waveforms requires data sampling and up/down conversion. These processes are
facilitated by commercial SDR hardware, which should support commercial 4G and
5G sampling rates, instantaneous bandwidths of at least 20 MHz, and frequency
agility. Moreover, it should allow multi-channel communications to support
transmit (Tx) and receive (Rx) diversity, multiple-input multiple-output
(MIMO) communications, and beamforming.

RF Front End: The goal is to have a modular and flexible RF front end for
supporting multiple bands, providing enough RF transmission power and
filtering to comply with spectrum regulations, Tx-Rx antenna isolation to
avoid receiver saturation, and enough gain to recover weak signals at the
limit of the coverage area, initially defined as 1 km from the BS. The choice
of RF components will eventually be driven by the experimenter needs and the
commercial availability of RF components for the desired frequency. Obtaining
a local license to radiate from the ground and air is also necessary.

Processing Unit: The baseband processing has the highest computing demand of a
cellular communications system. It can be executed on a general-purpose
processor with sufficient processing power. The processor also needs to
provide several network interfaces for data and control.

Power: Computers, SDRs, and active RF components need a power supply. The
power requirements are defined by the RF and processing units, experiment
configuration, and experiment duration.

SDR Software: AERPAW proposes to leverage popular open-source software
libraries that implement modern RANs, CNs, and UEs. The reason is that the
testbed is built for enabling global and cutting-edge research, which can be
excelled when the code is open, maintained, and easy to modify. This enables
rapid prototyping and experimenting variations to the RF signaling and
protocol processing. The main criteria for choosing a software library are its
user community, COTS hardware compatibility and portability, and
interoperability with other experimental or production radio equipment.

Experimental and Control Networks: The experimental network connects UEs to
the RAN via SDRs and the RAN to the CN via radio, fiber, or copper. All BSs
need IP connectivity to the CN to implement the S1 interface for
authentication, mobility management, and so forth. AERPAW users submit their
experiments and, when approved, the experiment runs in batch mode. However,
for initial platform development and during regular operation, experiments are
controlled by the testbed operator, who needs to be able to configure, start,
stop, or pause an experiment as needed, e.g. when undesired situations are
detected. Being able to connect to each SDR computer via secure shell (ssh) is
the goal for initial development, testing, and experiment control.

UAS: The UAS is the UAV and its remote controller (RC). Unless a UAV flight
waiver is obtained, a certified pilot must be in visual LOS with the UAV. The
UAV needs to be robust enough to lift the experimental radio system payload.
An experiment may encompass evaluating or choosing a UAV trajectory as a
function of the observed radio parameters. Timestamped and location-specific
data, typically provided by the onboard global positioning system receiver,
therefore need to be logged and provided to the experimenter after the
experiment.

TABLE I: Requirements and proposed design for the SDR platform enabling 4G/5G cellular networked UAV research. System Features |  Requirements |  Components
---|---|---
SDR |  Data conversion |  \- COTS SDR hardware with drivers that support sampling rates of modern wireless systems, permit a wide range of RF, and have broad research community support. |  \- B205mini-i USRP: Up to 61.44 MHz sampling rate, 56 MHz instantaneous bandwidth, 0 dBm maximum Rx power, low Tx output power [13], $<$8 dB noise figure (NF), 70 MHz to 6 GHz.
|  Baseband/ protocol processing |  \- Multi-core x86 computer with 3 GHz or higher clock per core (at least 4 physical cores) with USB 3.0 or 10 Gbps NIC. |  \- Dell OptiPlex 7070 Micro (fixed node): Intel i9-9900 8-core processor, 32 GB RAM, USB3, two-port 10 Gbps NIC (SFP+), 1 Gbps NIC.
\- Intel NUC10 (NUC10i7FNK) (mobile node): Intel i7-10710U 4-core processor,
32 GB RAM, USB3, Thunderbolt 3, 1 Gbps NIC.
|  Software |  \- Supported open-source software libraries; closed source software can be useful, e.g. for baseline experiments. |  \- The latest USRP Hardware Driver (UHD) 4.0, srsRAN version 20.10.1, open5GS version 2.2.9, and OAI version 1.2.2, are installed on Ubuntu 18.04 in Docker containers.
RF Front End |  Amplifier |  \- Transmit PA for desired 1 km range; gain and other characteristics depend on the SDR and the output power it can cleanly produce for a wideband signal. \- Low power consumption, weight, size, and cooling for mobile node PA. \- Receiver LNA to improve reception range. |  \- Mini-Circuits (MC) ZHL-15W-422-S+PA: 15 W, 46 dB gain, 38-40 dBm output power at 1 dB compression, 49 dBm OIP3, 10 dB NF, 0.6-4.2 GHz.
\- MC ZVE-8G+ (mobile Tx) PA: 1 W, 34-36 dB gain, 32 dBm output power at 1 dB
compression, 40 dBm OIP3, 4-5 dB NF, 2-8 GHz.
\- MC ZX60-83LN12+ LNA (Rx): 22 dB gain, 13-20 dBm output power at 1 dB
compression, 30-35 dBm OIP3, 1.4-2.3 NF, 0.5-8 GHz.
|  Filters |  \- Eliminate harmonics and spurs in the transmitter. \- Limit the amount of undesired signals entering the receiver, yet provide frequency agility. |  \- MC VLF-4400+ (Tx): low pass filter DC-4400 MHz passband (PB), 3 dB loss at 5290 MHz.
\- MC VBFZ-3590+ (Rx): bandpass filter with 3000-4300 MHz PB.
|  Antennas |  \- Broad coverage and frequency agility. \- Small and lightweight for the UAV node. |  \- Mobile Mark RM-WB1-DN-B1K (fixed node): 617-960 and 1700-6000 MHz, 3 dBi peak gain, up to 10 W.
\- Octane Wireless SA-1400-5900 (mobile node): 1400-5900 MHz, up to 500 mW.
Net-work |  Experimen-tal network |  \- Reliable interface between the RAN and the CN. |  \- Ethernet or WiFi6 (AX4800 router) for the backhaul and BS-BS links (X2 interface).
|  Experiment control |  \- Reliable wireless side channel for aerial SDR experiment control. |  \- Private IP network using ssh via WiFi6.
UAS |  UAV |  \- Easy takeoff and landing, hovering capability, and 5 kg payload capacity. |  \- DJI Matrice 600: Hexacopter with 5.5 kg maximum payload and 6 x 5,700 mAh battery capacity (TB48S battery pack).
|  UAV control |  \- Certified UAV pilot with RC and visual line of sight to the UAV due to current regulations. |  \- DJI Matrice 600 manufacturer supplied RC. On-site operator, one per UAV.
Power |  Ground node |  \- Direct AC, if available, or a generator for powering computers, SDRs and RF components. |  \- 2000 W portable gasoline generator with grounding rod collocated with each fixed node at the test location.
|  Aerial node |  \- Autonomous (battery-powered) operation. |  \- Separate power sources for UAV and SDR payload. \- The UAV comes with high-capacity batteries (30 minute flight). \- 5S 3000 mAh LiPo battery for NUC10 + SDR, PA, and LNA.

##  III Software and hardware options and the system design tradeoffs to make
it all work

The selection of components depends on their compatibility, ease of
integration, flexibility, scalability, performance, and availability. While we
organize this section similar to the previous, the software (SW) and hardware
(HW) interactions are critical for the choice of components to prototype an
efficient platform that meets the outlined requirements. Table I lists the
specific components of the proposed platform.

Fig. 2 shows the minimum necessary system components and the logical
interfaces. Defining the components and interfaces facilitate scalability and
portability.

Figure 2: Testbed interfaces (E/C-RF – experiment/control RF; NIC – network
interface card).

###  III-A Radio Network Hardware

Data Conversion: Among the examined options, USRPs offer several advantages: a
wide set of board and RF module options, 56+ MHz instantaneous bandwidth per
channel, and a single open-source hardware driver. There are lightweight and
small form factor devices that fit well on a UAV. We chose USRPs mainly
because of their flexibility and openness, their popularity among the broader
R&D community, and their compatibility with advanced SDR software, the popular
GNU Radio framework, and Matlab. USRPs have their limitations, including low
Tx power, especially for wideband multicarrier waveforms, limited analog
filtering, and interoperability issues among certain driver versions, devices,
software, and frequencies. These can be overcome by careful hardware and
software design, configuration, and systematic laboratory and outdoor testing.
We use auxiliary SDR hardware, RF instruments, and open-source tools, such as
iPerf, ping, Wireshark, and SDR-specific tools for signal and network
analysis.

Figure 3: Transmit signal spectrum at the BS antenna port, measured with
spectrum analyzer through a splitter and attenuator.

RF Front End: The output power of the USRPs alone is insufficient for
establishing reliable communications links over more than a few 10s of meters;
hence, a PA in the transmit chain is necessary. Given our goal to communicate
over 1 km, our calculations have shown that a high linearity PA with a gain of
30-45 dB is needed. The 15 W PA from Table I requires a heavy heatsink and
dedicated power supply and is recommended for the fixed node. The UAV imposes
constraints on size, weight, and power. The smaller and lighter 1 W PA can be
mounted directly to the payload chassis for cooling. Based on the maximum
output power of the USRP and any signal distortion, appropriate input power
backoff to provide a clean transmission.

Our experimental license prohibits out-of-band transmissions. A well-specified
low-pass filter in the transmit chain provides simplicity and frequency
agility while mitigating potential RF harmonics. A wide bandpass filter
(preselector) in the receive chain helps with minimizing interference while
allowing frequency agility. The specific filters for the band of interest are
provided in Table I and were selected because of their specifications and
availability.

In the receive chain, a low noise amplifier (LNA) was anticipated, and
experimentally verified, to improve the communications range. The power supply
voltage for the LNA and 1 W PA are identical, thus saving weight on the UAV.

The USRP has internal variable gain amplifiers in the transmit and receive
paths. They allow for a range of linear amplification [13], but these gains
need to be carefully adjusted to optimize the connection depending on the PA
and LNA specifications, the Tx-Rx antenna isolation, and the desired range. In
general, the USRP Tx gain is set to the highest value to provide maximum
signal strength while accounting for sufficient backoff to not damage the PA
and avoid signal distortion, as shown in Fig. 3. The USRP Rx gain is set to be
able to receive weak signals while avoiding receiver saturation from the
desired signal, its own Tx signal, and any other signals falling into the
passband of the preselector.

Because a duplexer would limit frequency agility, we choose to minimize self-
interference by physically isolating the antennas both on the UAV and at the
BS (Fig. 4). In order to ensure good aerial coverage and simplify deployment,
we chose wideband omnidirectional antennas.

Processing Unit: Selecting the processing unit and SDR should be done jointly
and as a function of the SDR software. Because of the need for a small form
factor, lightweight, and low power consuming processing unit for the UAV, we
had to compromise the 10 Gbit network interface card (NIC). This left us with
USB-driven USRPs and the powerful and compact Intel NUC10 computer (Table I),
which has many USB 3.0 ports for driving multiple such USRPs. The NUC10 also
has a modern WiFi chip, leveraged for experiment control. For the SDR BS, a
multicore processor with highest per-core clock rates, a WiFi chip, and a 10
Gbit NIC are essential to support the necessary network interfaces of Fig. 2.
A high-end Intel i7 or i9 processor offers a high clock rate per core, can be
packaged in a small form factor, and has a lower power consumption compared to
high-end processors used for servers or workstations, easing field deployment.

Power: The choice of the power supply source for the mobile radio node will
impact the UAV flight duration. Although it is possible to power the payload
from the UAV power system, an additional battery will limit flight time loss
in spite of the increased weight [14]. This payload battery is sized by
calculating the maximum power requirements of the system from the component
data sheets and multiplying by the desired flight time of 0.5 h. Recognizing
that the maximum power case is a worst-case scenario, no additional safety
margin is incorporated. This calculation yields a 3000 mAh battery as optimum.
Payload and UAV batteries are swapped and recharged at the same time. A 2000 W
gasoline generator using 0.5 gallon of fuel can supply the ground node
equipment plus displays shown in Fig. 4 for about 7 h.

###  III-B Radio Network Software

Both OAI and srsRAN have a fully functional 4G LTE protocol stack and are
developing 5G systems in software. They support multiple SDRs and are popular
among researchers and developers. OAI is built using scripts for creating the
appropriate executables, whereas srsRAN uses a standard process for building
from source. Both libraries run on Ubuntu, are well maintained, and new
versions are regularly released.

Each software has advantages and disadvantages that make them useful for
different experiments. Different modules of each software may be used to take
advantage of their features. But this poses compatibility and interoperability
challenges that may include incompatible interfaces or parameters. We analyzed
the options and found that srsEPC is compatible with either the OAI BS (eNB)
or srsENB and either combination supports the srsUE. Open5GS is compatible
with srsENB and srsUE and supports handover.

When using different eNBs, the key parameters are those relating to the EPC
connection, such as the mobility management entity IP address, tracking area,
mobile country and network codes. Those parameters must match the EPC in order
for proper communication to occur between them. Using an EPC from a different
project, e.g. Open5GS with srsENB, requires that the UE information is entered
into its database. RAN settings include LTE band or frequency and USRP gain.

###  III-C Network Interfaces

Experimental Network: The experimental cellular network uses the wireless
interface and networked computers for implementing the RAN and CN. The CN can
be integrated with one BS but other BSs need to connect to it through a wired
or wireless link. When deploying multiple BSs, the backhaul is ideally
implemented via fiber. For flexibility, simplicity, and to not have to rely on
costly infrastructure, we recommend setting up a dedicated WiFi network with
directional antennas for higher range. A potential future solution is the
integrated access and backhaul, which is an emerging 3GPP technology that
future ground and ABSs will likely leverage [15].

Experiment Control: For the experiment control interface, a cellular control
link is a viable option for most places, but requires a data plan and
lightweight yet quality LTE USB dongles. This is AERPAW’s choice. Below we
present an alternative that works well with minimum dependencies and no
additional payload.

WiFi6, or IEEE 802.11ax, is widely available. It can be configured to operate
in the 2.4 or 5 GHz unlicensed band and implements multi-user (MU)-MIMO for
improving range and capacity. The BSs and UEs need to be within the range of
the WiFi access point (AP) for continuous experiment control. COTS directional
antennas are widely available for these bands and one can be collocated with
each ground node for interconnecting BSs and implementing the required
interfaces. The NUC10 has an integrated WiFi6 chip and antennas, and it is
therefore mounted upside down on the outside of the UAV payload cage (Fig. 4).

Figure 4: Experiment with UAV and radio payload, directional 5 GHz antenna
(bottom left), which communicates with the WiFi6 AP 700 m away from it in the
field over which the UAV flies, SDR BS (middle), spectrum monitoring (right).

###  III-D UAS

The weight of the payload and desired length of flight are the dominant
factors determining UAV selection. Our platform (including payload battery)
weighs 2.2 kg and we desire approximately 30 minutes of airborne experiment
time. These requirements drive the need for a medium lift vehicle like the DJI
Matrice 600. For flexibility and exploratory research, we recommend manual
control of the UAV flight during the experiment as opposed to waypoint-based
flight path navigation. The control link is established through the standard
RC provided by the UAV manufacturer and is independent of the previously
discussed interfaces. Fig. 4 shows our aerial node.

Figure 5: UL/DL throughput for 20 MHz FD-LTE using srsRAN at 3.5 GHz. The BS
is at the origin and the UAV at (distance, height) with respect to it.

###  III-E Experimental Results

Here we present initial 3D coverage measurements in a rural environment. We
operate an LTE experiment in FDD mode (FD-LTE) in 3GPP Band 22 (C-Band), where
we have a license and where 5G systems will operate. The fixed BS is 2.5 m
above ground. The UAV flight is over an agricultural field with LOS to the BS
(Fig. 4). We implement the eNB and UE with srsRAN and the EPC with open5GS.
The USRP Tx and Rx gains are 72 and 47 for the eNB and 75 and 35 for the UE.
Fig. 3 shows the spectrum of the eNB Tx signal, the LTE downlink (DL), at full
DL resource allocation at the output of the 15 W PA for the above gains
settings. After correcting for the splitter and attenuator losses in the
spectrum analyzer path we obtain the average output power of 21 dBm at the eNB
Tx antenna port. Equivalent measurements at the mobile node yield about 15 dBm
average UE Tx power for the proposed configuration. The differences in Tx
gains are due to the higher PA distortion at the eNB, whereas the differences
in the Rx gains are due to the lower Tx-Rx antenna isolation at the UE.

Fig. 5 presents our uplink (UL) and DL throughput measurements. A UAV position
close to the eNB at low altitude prove the successful attachment of the aerial
UE (AUE) with the eNB and achieves nearly the highest theoretical rates for
the UL and DL of 50 and 60 Mbps, respectively. About 25% of the LTE frame is
for control signaling which makes the theoretical maximum 50 and 75 Mbps,
respectively. The throughput remains very high for more than 400 m horizontal
distance from the BS at different UAV heights. The performance starts to
degrade when the distance increases further as a result of the increased path
loss, but is still well above 10 Mbps even beyond 1 km.

These results satisfy our goals to provide flexibility, performance, and
enable scalable experiments. Compared to existing open-source SDR platforms
and reported results, our platform offers high performance, range, and allows
agility in frequency and flight trajectory. The platform can operate between
3.0 and 4.3 GHz, which can be further extended by changing the filters. All
the deployed software is available for free download and use and is well
maintained. All the hardware is widely available. The radio software and
hardware choices are compliant with AERPAW and will be available through it
for global researchers to use. One has still many choices, e.g. which UAV and
frequency to use or how to implement the backhaul. This allows portability of
our SDR platform with many customization and extension options for R&D.

###  III-F Guidelines

A few important guidelines for interested researchers are provided below.

  * •

COTS SDR Tx power levels are low and there is often little isolation between
the Tx and Rx signal paths. This requires signal, gain, and interference
analysis, especially when using PAs.

  * •

The RF environment on the ground and in the air needs to be understood from
the perspectives of the interference to and from the planned experiment.
Adjacent channel signals passing the preselector of the SDR can cause aliasing
or receiver saturation. Filters should therefore be used.

  * •

Processors, interfaces, the software environment, the SDR software processes,
and the SDR and RF hardware need to be examined in concert and tested
exhaustively to identify and eliminate bottlenecks. Baseline performance
metrics and benchmarks need to be defined and RF and system testing processes
established to verify and calibrate the system configuration before each
experiment.

##  IV Challenges and Research Directions

The proposed platform has been developed to enable advanced research and help
solving the challenges identified by industry and academia, including those
described below.
Interference: The deployment of an aerial radio platform comes with various
types of interference problems that can affect the network performance. In
addition, the RF footprint of AUEs which typically have LOS channels with
multiple ground BSs can severely degrade the capacity of the cellular network.
Managing inter-cell interference (ICI) will be critical to enable coexistence
between aerial and ground users. The air-to-ground (A2G) ICI will exist
between a UAV in one cell and cochannel interference between terrestrial and
AUEs associated with nearby cells. The conventional ICI that has been studied
for terrestrial communications will not be valid for solving the A2G ICI
problem. Therefore, interference management is a critical research direction
for UAV integration into cellular networks.
Cell Association and Handover: Because antennas have specific RF patterns and
there is typically no signal blockage in the sky as there is on the ground
that is leveraged to deploy cell towers and define cells boundaries for
terrestrial users, the traditional cell association and handover procedures
will need to be revised to avoid frequent handovers and complex resource
management. Aerial and terrestrial users may need to be treated differently.
Advanced wireless technology, specifically beam-based access, can be leveraged
for this.
Limited Airtime: Battery-powered multi-rotor UAVs have an airtime of about
thirty minutes. Different solutions can be conceived to address this
limitation: (1) Design and deploy tethered UAVs where high endurance is needed
and low mobility is possible. Research needs to make drone tethers more
available, flexible, and safer to use [14]. (2) Coordinate UAVs to accomplish
a mission, where one UAV can carry on the mission of another that needs a
recharge. (3) Design and develop a combination of energy storage and charging
technologies, as well as more energy-efficient UAV operation.
UxNB: UxNB is The 3GPP’s term for UAVs taking on different roles in a cellular
network. This includes the AUE, the ABS and the AR [4]. As we have flown the
UE, we can fly the BS as well. In fact, the SDR software installed on all
radio nodes implements the BS, CN, and UE. It is then a matter of executing
the desired processes on the aerial or ground nodes. ABSs and ARs are popular
concepts, but their gains and limitations need to be investigated. The
coverage of ABSs will depend on the antennas used and the UAV height, among
others. Research on deployment and radio resource management is much-needed
for practical use cases in production-like environments. This is what the
proposed SDR platform and the AERPAW testbed enable.

##  V Conclusions

This paper has introduced the requirements and enabling technologies for
implementing a modern cellular communications testbed for research on cellular
networked UAVs. We provide detailed information about the SDR hardware and
software, the RF front ends, the network, the UAS, and the power supply to
successfully establish an open-source, software-defined broadband cellular
network for R&D. Our measurement results show that the introduced platform can
provide high throughput and the desired range between an AUE and a ground BS.
These results offer early insights and will lead to more research on enhancing
aerial 3D communications performance. The AERPAW testbed, deploying the SDRs
presented here, provides an at-scale research platform featuring multiple
cells, micro and mm-wave radio transceivers, and multiple aerial and ground
vehicles. It enables collecting data and evaluating different network
configurations for serving future UAS communications and networking needs. The
open-source software-driven platform enables implementing the emerging open
RAN architecture/interfaces and introducing network intelligence for research
on 6G wireless.

## Acknowledgments

This work was in part supported by NSF award CNS-1939334. We would like to
thank Roshan KC, Joshua Moore, and Ajaya Dahal for their contributions to
integration and testing.

## References

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  * [2] A. S. Abdalla, K. Powell, V. Marojevic, and G. Geraci, “UAV-assisted attack prevention, detection, and recovery of 5G networks,” _IEEE Wireless Commun._ , vol. 27, no. 4, pp. 40–47, 2020.
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  * [6] “IEEE Draft Standard for Aerial Communications and Networking Standards,” _IEEE P1920.1/D4_ , pp. 1–85, Aug. 2020.
  * [7] A. S. Abdalla and V. Marojevic, “Securing mobile multiuser transmissions with UAVs in the presence of multiple eavesdroppers,” _IEEE Trans. Veh. Techn._ , vol. 70, no. 10, pp. 11 011–11 016, 2021.
  * [8] A. M. Wyglinski, D. P. Orofino, M. N. Ettus, and T. W. Rondeau, “Revolutionizing software defined radio: case studies in hardware, software, and education,” _IEEE Commun. Mag._ , vol. 54, no. 1, pp. 68–75, 2016.
  * [9] A. E. Garcia, et al., “Direct air to ground communications for flying vehicles: Measurement and scaling study for 5G,” in _IEEE 5G-WF_ , 2019, pp. 310–315.
  * [10] R. Gangula, et al., “Flying rebots: First results on an autonomous UAV-based LTE relay using Open Airinterface,” in _IEEE SPAWC_ , 2018, pp. 1–5.
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## Biographies

Aly Sabri Abdalla<EMAIL_ADDRESS>is a PhD candidate in the Electrical
and Computer Engineering (ECE) Department at Mississippi State University,
Starkville, MS, USA. His research interests are on scheduling, congestion
control and wireless security for vehicular ad-hoc and UAV networks.

Andrew Yingst<EMAIL_ADDRESS>is pursuing a PhD degree in the ECE
Department at Mississippi State University, Starkville, MS, USA. His research
interests include long-range UAV communications and tethered UAV power
systems.

Keith Powell<EMAIL_ADDRESS>is pursuing a PhD degree in the ECE
Department at Mississippi State University, Starkville, MS, USA. His research
interests include software radio platforms, UAV communications, and embedded
systems.

Antoni Gelonch-Bosch<EMAIL_ADDRESS>is an associate professor in the
Department of Signal Theory and Communications at Barcelona Tech,
Castelldefels, Spain. His research interests include wireless communications,
SDR systems, real-time processing, software abstraction, resource
virtualization, and associated management.

Vuk Marojevic<EMAIL_ADDRESS>is an associate professor in ECE at
Mississippi State University, Starkville, MS, USA. His research interests
include mobile communications and wireless security with application to
mission-critical networks and UAS.


# Dynamic Gradient Reactivation for Backward Compatible Person Re-
identification

Xiao Pan<EMAIL_ADDRESS>Hao Luo<EMAIL_ADDRESS>Weihua Chen
<EMAIL_ADDRESS>Fan Wang<EMAIL_ADDRESS>Hao Li
<EMAIL_ADDRESS>Wei Jiang<EMAIL_ADDRESS>Jianming Zhang
<EMAIL_ADDRESS>Jianyang Gu<EMAIL_ADDRESS>Peike Li
<EMAIL_ADDRESS>Zhejiang University, Hangzhou, China  Alibaba
Group, Hangzhou, China  University of Technology Sydney, Sydney, Australia

###### Abstract

We study the backward compatible problem for person re-identification (Re-ID),
which aims to constrain the features of an updated new model to be comparable
with the existing features from the old model in galleries. Most of the
existing works adopt distillation-based methods, which focus on pushing new
features to imitate the distribution of the old ones. However, the
distillation-based methods are intrinsically sub-optimal since it forces the
new feature space to imitate the inferior old feature space. To address this
issue, we propose the Ranking-based Backward Compatible Learning (RBCL), which
directly optimizes the ranking metric between new features and old features.
Different from previous methods, RBCL only pushes the new features to find
best-ranking positions in the old feature space instead of strictly alignment,
and is in line with the ultimate goal of backward retrieval. However, the
sharp sigmoid function used to make the ranking metric differentiable also
incurs the gradient vanish issue, therefore stems the ranking refinement
during the later period of training. To address this issue, we propose the
Dynamic Gradient Reactivation (DGR), which can reactivate the suppressed
gradients by adding dynamic computed constant during forward step. To further
help targeting the best-ranking positions, we include the Neighbor Context
Agents (NCAs) to approximate the entire old feature space during training.
Unlike previous works which only test on the in-domain settings, we make the
first attempt to introduce the cross-domain settings (including both
supervised and unsupervised), which are more meaningful and difficult. The
experimental results on all five settings show that the proposed RBCL
outperforms previous state-of-the-art methods by large margins under all
settings.

###### keywords:

Person re-identification , Backward compatible training , Deep learning

††journal: Pattern Recognition

##  1 Introduction

Given an query image of a person, person re-identification (Re-ID) retrieves
images of the same person from a large gallery of images collected across
multiple cameras. In real-world applications, such a gallery is often
accumulated over time through pedestrian detection in real-time video streams,
with person images represented by learned high-dimensional features. In
practice, as the performance of old model becomes worse due to the enlarged
gallery, model update is needed. However, it is intractable to recompute the
features for all existing images given the sheer size of galleries (billions
of images at least), while without recomputing the features, features from
different versions of model are in different feature spaces, leading to poor
retrieval performance.

Figure 1: Illustration of the difference between the previous distillation-
based methods and RBCL (ours). Squares and circles represent the new features
and the old features, respectively. Different colors represent different IDs
and the arrows represent the optimization direction. The distillation-based
methods lead to some mis-ranked new features after BCT due to the entangled
old feature clusters. With the help of RBCL, the new features are pushed into
proper ranking positions.

To tackle this problem, the ideal solution is to perform Backward Compatible
Training (BCT) [1] for the new model, which targets at making the new features
comparable with the existing old features via adding specially designed losses
during the training of new model. There has been some works along this
direction [1, 2, 3]. For example, the Influence Loss [1] conducts the
distillation between the new features and the old ones with the help of the
old classifier. RBT [2] first maps new features and old ones into a common
feature space and then conduct distillation. R3AN [3] transforms the new
features into the old feature spaces with the reconstruction of the face
image.

To our best knowledge, the existing methods are mainly distillation-based.
Such methods aim to imitate the distribution of the old model that is less
discriminative. However, we argue that they are intrinsically sub-optimal for
BCT Re-ID due to the following two disadvantages: (1) Forcing the new model to
imitate the old model would be harmful to the performance of new model itself,
especially for the cross-domain setting where the performance of old model on
new domain is extremely poor. (2) Due to the low performance of old model,
there may exist _entangled clusters_ in the old feature space. The roughly
alignment will lead to mis-ranked new features, which will damage the ultimate
cross-model retrieval performance.

To address these issues, we propose the Ranking-based Backward Compatible
Lraining (RBCL), which directly optimizes the ranking metric between new
features and old features. As illustrated in Fig. 1, RBCL aims to push new
features into best-ranking positions in the old feature space, instead of
aligned strictly with it. In this case, the new feature space will not be
damaged too much, and the optimization is consistent with the optimal goal of
BCT Re-ID, which is to perform retrieval between new features and old
features. However, to make the discrete ranking metric differentiable, the
sharp sigmoid function is needed to smooth the indication function, yet also
incurs the gradient vanish issue of triplets due to its narrow gradient-
effective interval, and therefore stems the refinement of ranking positions
during the later period of training. To relieve this issue, we propose the
Dynamic Gradient Reactivation (DGR), which can reactivate the suppressed
gradients via adding dynamic computed compensate constant during the forward
step. With DGR, the gradients for ranking optimization are exponentially
enlarged, so that the new features are refined to better-ranking positions. To
further target the best-ranking positions, we propose to include the _Neighbor
Context Agents (NCAs)_ during optimization. NCAs can approximate the entire
old feature space with several representative samples, and can provide more
triplets for DGR to reactivate.

We evaluate our method under five challenging settings. In contrast to
previous works which only test on in-domain settings,  we make the first
attempt to study BCT under cross-domain settings, including supervised and
unsupervised for Re-ID. We emphasize that cross-domain Re-ID [4, 5, 6, 7, 8]
is important for real-world applications but has not been taken into
discussion in previous BCT works due to its challenging nature. The
experimental results show that our method can achieve superior performance
than the existing methods under both in-domain and cross-domain settings.

The main contributions of this paper can be summarized into the following
aspects:

  * 1.

To the best of our knowledge, we are the first work to study the backward
compatible training for person Re-ID under both in-domain and cross-domain
settings (including both supervised and unsupervised).

  * 2.

Unlike previous distillation-based methods, we propose the RBCL to fully
optimize the ranking metric between new features and old features, which
leverages DGR to reactivate the suppressed gradients and includes NCAs to
further target the best-ranking positions.

  * 3.

We perform extensive experiments to demonstrate the effectiveness and
superiority of our proposed RBCL.

Figure 2:  The training pipeline of RBCL. The fixed old features space is pre-
computed before iteration. Then, during each iteration, the mini-batch is sent
to the new model to get the corresponding new features. After that, the new
features are taken as query features and their corresponding NCAs are taken as
gallery features for ranking metric optimization. DGR is added during ranking
metric optimization to refine the ranking positions. During inference stage,
the query features extracted by the new model are retrieved directly with the
gallery features from the old model.

##  2 Related Work

###  2.1 Optimizing Ranking for Re-ID

Multiple works in this community [9, 10, 11, 12] have proved that ranking
information is important for Re-ID as a retrieval task. The typical methods
for optimizing the ranking for Re-ID are Deep Metric Learning (DML) methods,
which intend to optimize the distance metric. Generally, the DML methods can
be further divided into pairwise [13, 14] and triplet-wise methods [10, 15,
16, 17, 11, 12]. To better exploit the information when comparing features in
a mini-batch, hard example mining is first combined with Triplet loss by [10]
and achieves significant improvement. To get richer pairwise information
beyond a mini-batch, Wang et al. [12] propose the cross-batch memory (XBM)
mechanism which memorizes the features of the past iterations.

Another line of works for the ranking optimization is to directly optimize the
Average Precision (AP), which belongs to the ranking metric optimization.
Average Precision (AP) is an important metric for person Re-ID. The main
problem for directly optimizing AP is that the calculation of AP includes a
discrete ranking function, which is neither differentiable nor decomposable.
Brown et al. [18] propose the Smooth-AP which optimizes a smoothed
approximation of AP and show its satisfactory performance on large-scale
datasets.

The improvement from these ranking-motivated loss functions shows that
exploiting the ranking is crucial for the Re-ID task. Our proposed RBCL also
takes the ranking into consideration, which has been ignored in previous works
for BCT. We follow the ranking metric optimization [18] since the distance
metric optimization is sub-optimal when evaluating using a ranking metric.

###  2.2 Backward Compatible Training

Chen et al. [3] first formalize the cross-model face recognition task and
propose the R3AN to transfer the features of the query model to the feature
space of the gallery model. R3AN is specialized for the face recognition task
and requires the two models to be similar, which is not applicable in some
real-world model upgrade scenario. Wang et al. [2] propose to map the features
of the two models into a unified feature space through the proposed Residual
Bottleneck Transformation (RBT) blocks. Then, several distillation
(imitation)-style losses are applied in the unified feature space. Both R3AN
and RBT require extra transformations on features, which brings about extra
computation and is intractable in real-world applications. Shen et al. [1]
bring up the term of Backward Compatible Training (BCT) for the first time,
which focus more on the model upgrade scenario compared with the above
mentioned two methods. They propose the Influence Loss, which performs
distillation between the logits of new features and old ones through the
classifier of the old model, and the classification loss of the new model is
combined with the Influence Loss when training the new model. This form of
combination is similar to Learning Without Forgetting (LWF) [19] which is the
typical solution of incremental learning, but differs in that the classifier
of the old model is fixed here. Meng et al. [20] propose LCE, which aligns the
centers between new features and old features, and then restrict more compact
intra-class distributions for new features. Although LCE won’t distill the new
feature distribution to the old one strictly in instance-level, it still
aligns these two distributions, which is ineffective for handling the
entangled old clusters. Different from the previous methods, our proposed RBCL
directly optimizes the ranking metric between new features and old features.

##  3 Methodology

In this section, we first introduce the backward compatible training in
formula and then introduce our proposed Ranking-based Backward Compatible
Learning (RBCL).

###  3.1 Problem Formalization

Assuming that a new model trained without any consideration of BCT is denoted
as $\phi_{new}$, and the fixed old model is denoted as $\phi_{old}$. To
improve the backward compatibility, we design a method $L$ and integrate it
into the training process of $\phi_{new}$. We then name the new model trained
with the help of method $L$ as $\phi_{new-L}$.

For a test set $\mathcal{D}_{test}$, its evaluation metric (e.g., mAP or
Rank-1) is represented as $M(\phi_{q},\phi_{g};\mathcal{D}_{test})$, where the
query features are extracted by $\phi_{q}$, and gallery features are extracted
by $\phi_{g}$. Since $\phi_{new}$ and $\phi_{old}$ are in different feature
spaces, directly evaluating between $\phi_{new}$ and $\phi_{old}$, i.e.,
$M(\phi_{new},\phi_{old};\mathcal{D}_{test})$, gives unsatisfactory
performance. Therefore, our goal is to design a method $L$, which can make
$M(\phi_{new-L},\phi_{old};\mathcal{D}_{test})>M(\phi_{old},\phi_{old};\mathcal{D}_{test})$
as much as possible.

###  3.2 Ranking-based Backward Compatible Learning

The pipeline of our RBCL is illustrated in Fig. 2. Before iteration, the
training set of the new model is first sent to the old model to get the fixed
old feature space. Then, during each iteration, a mini-batch is sampled from
the training set, and then sent to the new model to get the corresponding new
features. After that, the new features are taken as the query features and
their corresponding NCAs (indexed by IDs from the pre-computed old feature
space) are taken as the gallery features. Finally, the metric optimization is
conducted between query features and gallery features with the help of DGR,
and the new features are sent to Re-ID losses for discriminative learning.
During inference, the the query features are extracted by the new model, and
then directly retrieved (cosine similarity) with the old gallery features.

####  3.2.1 Ranking Metric Optimization

Inspired by [18], we use the smoothed mean Average Precision (mAP) metric to
optimize the ranking between new features and old features during training.
Given a query feature $f_{i}$ from query feature set $F_{q}$, which is
extracted by the new model, the gallery feature set $F_{g}$ extracted by the
old model is split into positive set $\mathbbm{P_{i}}$ and negative set
$\mathbbm{N_{i}}$, which are formed by all instances of the same class and of
different classes, respectively. Then, the smoothed AP for query $i$ becomes:

$\small
AP_{i}\\!=\\!\frac{1}{|\mathbbm{P}_{i}|}\\!\sum_{j\in\mathbbm{P}_{i}}\\!\frac{1\\!+\\!\sum_{p\in\mathbbm{P}_{i}\backslash\\{j\\}}\sigma(d_{pj}^{i})}{1+\sum_{p\in\mathbbm{P}_{i}\backslash\\{j\\}}\sigma(d_{pj}^{i})\\!+\\!\sum_{n\in\mathbbm{N}_{i}}\sigma(d_{nj}^{i})},$
(1)

where $d_{pj}^{i}=s_{ip}-s_{ij}$ and $d_{nj}^{i}=s_{in}-s_{ij}$, in which
$s_{ij}$ represents for the cosine similarity between $f_{i}$ and $f_{j}$; and
$\sigma(\cdot)$ represents for the sigmoid function:

$\sigma=\frac{1}{1+e^{-x/\tau}}.$ (2)

which is the relaxed form of indication function to make AP differentiable
[18]. Then, the final smoothed mean Average Precision (mAP) loss is:

$\mathcal{L}_{m}=1-\frac{1}{|F_{q}|}\sum_{i\in|F_{q}|}AP_{i}.$ (3)

####  3.2.2 Dynamic Gradient Reactivation

(a)

(b)

Figure 3:  (a) The derivative of $\sigma(\cdot)$ when $\tau=0.01$. (b) The
influence of $\alpha$ to the compression function (Eq. 5).

The main goal of optimizing $\mathcal{L}_{m}$ is to make $AP_{i}$ close to 1,
thus, although not completely equivalent, the key is to minimize the
$\sum_{n\in\mathbbm{N}_{i}}\sigma(d_{nj}^{i})$ term in the denominator of Eq.
1. $d_{nj}^{i}=s_{in}-s_{ij}$ is a triplet composed of an anchor $i$, a
positive sample $j$, and a negative sample $n$. Minimizing
$\sum_{n\in\mathbbm{N}_{i}}\sigma(d_{nj}^{i})$ means to decrease the
similarity of negative pairs and increase the similarity of positive pairs,
i.e., to optimize the ranking. Therefore, the gradient of each triplet
$d_{nj}^{i}$ plays an important role in the ranking optimization. However,
$d_{nj}^{i}$ is wrapped by the sigmoid function $\sigma^{\prime}(\cdot)$,
whose gradient-effective interval is quite narrow since the derivative
decreases exponentially as the distance from $0$ becomes larger (see Fig. 3a),
especially when $\tau$ is small ($\tau=0.01$ performs best as mentioned in
[18]). In this case, only the triplets close to $0$ can achieve effective
gradients, while for those away from $0$ with certain distance, the gradients
are extremely small, i.e., vanished.

On the other hand, during the later period of training, we have two
observations about the distribution of $d_{nj}^{i}$ (see the green line in the
upper right corner of Fig. 2): (1) Most of the triplets are in proper ranking
order after considerable time of optimization, i.e., the majority of
$d_{nj}^{i}$ are smaller than $0$ with certain distance, and therefore achieve
extremely small gradients. However, we propose that there still exists
valuable information among them which can further help refining the ranking
positions. Intuitively, the best-ranking positions in the fixed old feature
space are more likely to be achieved when more triplets (ranking relations)
are considered. (2) There still exist several extremely hard negative samples
which are closer to the anchors than the positive samples with certain
distance due to the entangled clusters in the old feature space, i.e., several
$d_{nj}^{i}$ are still larger than $0$ with certain distance. However, such
extremely hard negative samples can hardly be optimized due to the vanished
gradients. Therefore, their gradients should also be enhanced. Based on (1)
and (2), we conclude that the gradient vanish issue stems the further ranking
optimization during the later period of training.

To address this issue, we propose to reactivate these triplets by compressing
their distribution toward the gradient-effective interval of
$\sigma^{\prime}(\cdot)$ via adding a reactivation constant $c_{nj}^{i}$
during the forward step:

$\displaystyle d_{nj}^{i}$
$\displaystyle\xleftarrow[]{}{}d_{nj}^{i}+c_{nj}^{i},$ (4) $\displaystyle
c_{nj}^{i}$ $\displaystyle=f(d_{nj}^{i};\alpha)-d_{nj}^{i},$

where $f(d_{nj}^{i};\alpha)$ is a compression function, and $\alpha$ controls
the degree of compression. Specifically, we choose $f(d_{nj}^{i};\alpha)$ as:

$f(d_{nj}^{i};\alpha)=\sigma(d_{nj}^{i};\alpha)-0.5,$ (5)

where $\alpha$ is the anneal of sigmoid function. The influence of $\alpha$ is
illustrated in Fig. 3b. The larger the $\alpha$ is, the greater compression
is. Note that $c_{nj}^{i}$ is a constant without gradient, and is customized
for each $d_{nj}^{i}$, therefore we term it as “dynamic”.

As illustrated in the bottom right corner of Fig. 2, the distribution of the
triplets (${d_{nj}^{i}}$) is compressed toward $0$ after adding DGR, therefore
their gradients are exponentially enhanced in general, which promotes refining
the ranking positions.

####  3.2.3 Neighbor Context Agents

Although DGR can refine the ranking positions by enhancing gradients, the
ranking optimization still lacks the global perspective for targeting the
best-ranking positions. Intuitively, the global best-ranking positions can be
achieved only when the model sees the entire old feature space. However, the
computation overhead will be extremely expensive, especially when the training
set is large. Thus, we propose to include Neighbor Context Agents (NCAs)
during training to approximate the entire old feature space. As illustrated in
the middle of Fig. 2, NCAs are composed of random agents from each class in
the neighbor area of current mini-batch. More concretely, we pre-compute the
old features of the training set, and then build an adjacency matrix based on
the euclidean distance between cluster centroids. Then, during each iteration,
given the samples from the $c$-th class in the mini-batch, we choose the $K$
classes closest to the $c$-th class in the old feature space as its neighbor
set $\mathcal{N}_{c}$. For each class in $\mathcal{N}_{c}\cup\\{c\\}$, we
randomly pick one sample as the agent at each iteration:

$A_{old}^{c}=\\{Rand(F_{old}^{k})|k\in\mathcal{N}_{c}\cup\\{c\\}\\},$ (6)

where $Rand(\cdot)$ represents for the operation of randomly selecting one
feature, $F_{old}^{k}$ represents the set of old features for $k$-th class,
and $A_{old}^{c}$ represents the set of the selected agents for $c$-th class.
Assuming that there are totally $B$ classes in a mini-batch ({$k_{1}$,
$k_{2}$, …, $k_{B}\\}$), all the gallery features picked at each iteration
are:

$F_{g}=A_{old}^{k_{1}}\cup A_{old}^{k_{2}}\cup...\cup A_{old}^{k_{B}}.$ (7)

After training with abundant iterations, the NCAs will walk through the entire
old feature space, which can help targeting the best-ranking positions. Also,
NCAs can provide more triplets for DGR to reactivate.

####  3.2.4 Overall Losses

We train $\mathcal{L}_{m}$ together with the Re-ID losses. Formally, the final
loss function for backward compatible training is:

$\mathcal{L}_{total}=\mathcal{L}_{tri}+\mathcal{L}_{id}+\mathcal{L}_{m},$ (8)

where $\mathcal{L}_{tri}$ and $\mathcal{L}_{id}$ represent for the Hard Mining
Triplet Loss [10] and ID Loss [21], which are commonly used losses in Re-ID
for discriminative learning.

##  4 Experimental Setting Formalization

| $\mathcal{T}_{old}$ | $\mathcal{B}_{old}$ | $\mathcal{T}_{new}$ | $\mathcal{B}_{new}$ | $\mathcal{D}_{test}$ | Sup | CD | NS |
---|---|---|---|---|---|---|---|---|---
ID-S-1 | M2M | $\mathcal{T}_{M0.1}$ | $R_{50}$ | $\mathcal{T}_{M}$ | $R_{50}$ | $\mathcal{D}_{M}$ | ✓ | ✕ | ✕ |
D2D | $\mathcal{T}_{D0.1}$ | $R_{50}$ | $\mathcal{T}_{D}$ | $R_{50}$ | $\mathcal{D}_{D}$ |
ID-S-2 | M2M | $\mathcal{T}_{M0.1}$ | $R_{50}$ | $\mathcal{T}_{M}$ | $R_{101ibn}$ | $\mathcal{D}_{M}$ | ✓ | ✕ | ✓ |
D2D | $\mathcal{T}_{D0.1}$ | $R_{50}$ | $\mathcal{T}_{D}$ | $R_{101ibn}$ | $\mathcal{D}_{D}$ |
CD-S-1 | M2D | $\mathcal{T}_{M}$ | $R_{50}$ | $\mathcal{T}_{D}$ | $R_{50}$ | $\mathcal{D}_{D}$ | ✓ | ✓ | ✕ |
D2M | $\mathcal{T}_{D}$ | $R_{50}$ | $\mathcal{T}_{M}$ | $R_{50}$ | $\mathcal{D}_{M}$ |
CD-S-2 | M2D | $\mathcal{T}_{M}$ | $R_{50}$ | $\mathcal{T}_{D}$ | $R_{101ibn}$ | $\mathcal{D}_{D}$ | ✓ | ✓ | ✓ |
D2M | $\mathcal{T}_{D}$ | $R_{50}$ | $\mathcal{T}_{M}$ | $R_{101ibn}$ | $\mathcal{D}_{M}$ |
CD-US | M2D | $\mathcal{T}_{M}$ | $R_{50}$ | $\mathcal{T}_{D}^{u}$ | $R_{50}$ | $\mathcal{D}_{D}$ | ✕ | ✓ | ✕ |
D2M | $\mathcal{T}_{D}$ | $R_{50}$ | $\mathcal{T}_{M}^{u}$ | $R_{50}$ | $\mathcal{D}_{M}$ |
Table 1:  The detailed configurations of each setting. “Sup”, “CD”, and “NS”
represent for “Supervised”, “Cross Domain”, and “New Structure”, separately.
$\mathcal{T}_{M0.1}$ and $\mathcal{T}_{D0.1}$ represent for 10% of the
training set (randomly split by identities). $\mathcal{T}_{M}^{u}$ and
$\mathcal{T}_{D}^{u}$ represent for the unlabelled training set.

As the backward compatible training for person Re-ID is a relatively new
topic, we would like to first formalize the experimental setup in this section
before describing the details of experimental results.

###  4.1 Datasets and Backbones

We conduct experiments on Market-1501 [22] and DukeMTMC-reID [23, 24].
Market-1501 contains 12,936 images from 751 identities for training and 19,732
images from 750 identities for testing. The images are captured from 6
cameras. DukeMTMC-reID contains 16,522 images from 702 identities for training
and the rest images from 702 identities for testing. ResNet-50 [25] and IBN-
ResNet-101 [26] are used as the backbones.

###  4.2 Setting Types

Notations. Formally, we represent the different backbones as
$\mathcal{B}=\\{R_{50},R_{101ibn}\\}$, where $R_{50}$ and $R_{101ibn}$
represent for ResNet-50 and IBN-ResNet-101, respectively. The training sets
are represented as $\mathcal{T}=\\{\mathcal{T}_{M},\mathcal{T}_{D}\\}$, where
$\mathcal{T}_{M}$ represents for the training set of Market1501, and
$\mathcal{T}_{D}$ for DukeMTMC-reID. Similarly, their test sets are denoted as
$\mathcal{D}=\\{\mathcal{D}_{M},\mathcal{D}_{D}\\}$. The detailed
configurations of all the settings below are illustrated in Table. 1.

####  4.2.1 In-Domain Settings

We first test the BCT performance under the basic in-domain settings. For each
in-domain setting, we test on both Market1501 (M2M) and DukeMTMC-reID (D2D).

In-Domain Supervised Setting 1 (ID-S-1): Under this setting, we randomly split
10% IDs from the original training set for the training of old model, and
train the new model with the entire training set.

In-Domain Supervised Setting 2 (ID-S-2): To verify the robustness of the
methods to the structure variance, under this setting, we replace the backbone
of the new model in ID-S-1 with IBN-ResNet-101.

####  4.2.2 Cross-Domain Settings

Aside from the basic in-domain settings, we also test our methods under
challenging cross-domain settings targeting several real-world scenarios. For
each cross-domain setting, we test on two directions, i.e., from Market1501 to
DukeMTMC-reID (M2D) and from DukeMTMC-reID to Market1501 (D2M).

Cross-Domain Supervised Setting 1 (CD-S-1): In real-world applications, the
poor performance of the old model may be caused by the domain bias between the
training set and the application scenario (test set). To improve the
performance, new training set from the target domain is collected for model
upgrade. Moreover, training set for the old model is not accessible any more
due to the expensive storage overhead and privacy issue. This setup is
challenging due to the domain gap and the poor performance of the old model.

Cross-Domain Supervised Setting 2 (CD-S-2): Similar to ID-S-2, we use IBN-
ResNet-101 as the backbone of new model, while ResNet-50 for the old model
under this setting.

Cross-Domain Unsupervised Setting (CD-US): In real-world applications,
achieving the large-scale labelled training set is expensive, thus
unsupervised domain adaption (UDA) is extensively studied [4, 5, 6, 7, 8]. We
also prove the effectiveness of our method under this challenging setting. We
conduct UDA from the domain of old model to the domain of new model.

| ID-S-1 | ID-S-2 | CD-S-1 | CD-S-2 | CD-US
---|---|---|---|---|---
Method | M2M | D2D | M2M | D2D | M2D | D2M | M2D | D2M | M2D | D2M
mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1
Direct | 37.5 | 61.0 | 36.5 | 56.4 | 37.5 | 61.0 | 36.5 | 56.4 | 17.9 | 31.9 | 22.4 | 49.2 | 17.9 | 31.9 | 22.4 | 49.2 | 28.7 | 44.5 | 30.0 | 58.8
LB | 50.0 | 74.1 | 43.6 | 66.2 | 0.2 | 0.1 | 0.2 | 0.1 | 32.2 | 54.5 | 33.0 | 57.5 | 0.2 | 0.0 | 0.2 | 0.1 | 0.4 | 0.3 | 0.2 | 0.1
UB | 85.8 | 93.8 | 76.6 | 86.3 | 89.1 | 95.7 | 81.0 | 90.6 | 76.6 | 86.3 | 85.8 | 93.8 | 81.0 | 90.6 | 89.1 | 95.7 | 58.7 | 74.5 | 67.6 | 85.0
Table 2:  The primary experiments of BCT under all the settings. No additional loss for improving the backward compatibility is used. “Direct”, “LB” and “UB” represent for $M(\phi_{old},\phi_{old})$, $M(\phi_{new},\phi_{old})$, and $M(\phi_{new},\phi_{new})$ (defined in Sec. 3.1), separately. | ID-S-1 | ID-S-2 | CD-S-1 | CD-S-2 | CD-US
---|---|---|---|---|---
Method | M2M | D2D | M2M | D2D | M2D | D2M | M2D | D2M | M2D | D2M
mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1
baseline | 50.0 | 74.1 | 43.6 | 66.2 | 0.2 | 0.1 | 0.2 | 0.1 | 32.2 | 54.5 | 33.0 | 57.5 | 0.2 | 0.0 | 0.2 | 0.1 | 0.4 | 0.3 | 0.2 | 0.1
L2 |  | 51.1
---
(77.0)
| 74.8
---
(89.5)
| 46.1
---
(68.9)
| 67.3
---
(80.7)
| 49.8
---
(81.4)
| 73.9
---
(92.0)
| 45.9
---
(73.9)
| 67.6
---
(86.1)
| 29.8
---
(64.2)
| 47.9
---
(75.7)
| 40.1
---
(79.6)
| 69.1
---
(90.6)
| 23.0
---
(64.6)
| 39.5
---
(76.9)
| 31.7
---
(83.0)
| 58.0
---
(92.4)
| 24.3
---
(47.1)
| 40.2
---
(63.0)
| 22.2
---
(50.1)
| 41.0
---
(74.0)
Influence [1] |  | 46.7
---
(81.9)
| 71.8
---
(92.8)
| 41.7
---
(70.9)
| 64.8
---
(83.7)
| 32.5
---
(82.3)
| 53.8
---
(92.6)
| 25.9
---
(64.8)
| 48.4
---
(85.4)
| 32.9
---
(70.8)
| 56.8
---
(82.0)
| 39.5
---
(79.9)
| 67.5
---
(91.9)
| 28.5
---
(75.6)
| 52.0
---
(87.2)
| 35.3
---
(85.3)
| 61.7
---
(94.4)
| 34.5
---
(55.8)
| 53.9
---
(71.0)
| 34.5
---
(59.9)
| 56.7
---
(79.4)
MMD [27] |  | 42.5
---
(59.8)
| 74.6
---
(78.5)
| 42.9
---
(36.2)
| 66.0
---
(52.3)
| 49.0
---
(57.5)
| 73.1
---
(74.6)
| 42.9
---
(37.7)
| 66.1
---
(55.0)
| 37.7
---
(46.6)
| 64.0
---
(60.7)
| 42.5
---
(61.7)
| 74.6
---
(79.9)
| 36.6
---
(48.3)
| 64.1
---
(64.8)
| 37.4
---
(59.1)
| 67.4
---
(77.7)
| 16.2
---
(38.0)
| 27.4
---
(52.9)
| 15.5
---
(35.1)
| 27.0
---
(59.6)
Triplet [10] |  | 53.1
---
(82.6)
| 75.4
---
(92.8)
| 44.2
---
(71.9)
| 64.8
---
(84.4)
| 51.4
---
(86.1)
| 73.8
---
(93.9)
| 44.8
---
(76.4)
| 66.2
---
(87.5)
| 40.5
---
(71.8)
| 62.1
---
(83.9)
| 48.6
---
(84.5)
| 70.5
---
(93.5)
| 39.8
---
(77.6)
| 61.1
---
(88.6)
| 46.1
---
(87.8)
| 67.1
---
(94.8)
| 29.0
---
(48.8)
| 47.3
---
(65.2)
| 27.5
---
(50.3)
| 50.1
---
(74.6)
RBCL (ours) |  | 61.3
---
(85.0)
| 82.7
---
(93.7)
| 53.2
---
(74.3)
| 75.0
---
(85.5)
| 60.8
---
(88.0)
| 82.8
---
(95.0)
| 54.0
---
(79.5)
| 75.3
---
(89.8)
| 51.2
---
(75.6)
| 73.5
---
(86.4)
| 58.4
---
(85.4)
| 81.6
---
(93.8)
| 50.6
---
(79.7)
| 73.7
---
(90.2)
| 58.0
---
(88.5)
| 80.2
---
(95.4)
| 40.5
---
(60.6)
| 63.0
---
(75.5)
| 39.5
---
(64.9)
| 64.8
---
(83.6)
UB | 85.8 | 93.8 | 76.6 | 86.3 | 89.1 | 95.7 | 81.0 | 90.6 | 76.6 | 86.3 | 85.8 | 93.8 | 81.0 | 90.6 | 89.1 | 95.7 | 58.7 | 74.5 | 67.6 | 85.0
Table 3: The experimental results for the comparison between our proposed RBCL and other methods. The gray number in between “()” is the performance of the self-test retrieval. Our RBCL outperforms others in both cross-model and self-test retrieval by large margins. The best and second best performance for cross-model and self-test retrieval are in bold and underlined, respectively.  | ID-S-1 | ID-S-2 | CD-S-1 | CD-S-2 | CD-US
---|---|---|---|---|---
Method | M2M | D2D | M2M | D2D | M2D | D2M | M2D | D2M | M2D | D2M
mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1 | mAP | R-1
baseline | 57.0 | 79.5 | 50.2 | 72.0 | 53.4 | 77.1 | 46.7 | 69.1 | 44.6 | 67.0 | 52.4 | 76.2 | 42.8 | 65.8 | 50.1 | 73.5 | 36.5 | 57.6 | 35.0 | 59.6
\+ DGR | 57.5 | 79.9 | 50.6 | 72.9 | 55.2 | 78.5 | 48.8 | 71.3 | 45.2 | 67.7 | 52.8 | 76.6 | 44.0 | 66.8 | 51.6 | 75.3 | 37.8 | 58.9 | 36.8 | 62.7
\+ NCAs | 60.4 | 81.9 | 52.1 | 73.7 | 59.4 | 81.7 | 52.2 | 73.6 | 49.7 | 72.0 | 57.6 | 80.3 | 49.4 | 71.6 | 56.6 | 79.1 | 39.6 | 62.0 | 38.9 | 63.4
\+ NCAs + DGR (ours) | 61.3 | 82.7 | 53.2 | 75.0 | 60.8 | 82.8 | 54.0 | 75.3 | 51.2 | 73.5 | 58.4 | 81.6 | 50.6 | 73.7 | 58.0 | 80.2 | 40.5 | 63.0 | 39.5 | 64.8
Table 4: The ablation of NCAs and DGR in RBCL. Cross-model retrieval
performance is reported.

##  5 Experimental Results

In this section, we first complement some experimental details. Then, we
conduct primary experiments for all the settings. After that, we compare RBCL
with baseline methods in the above mentioned five setting types. Finally, we
analyze the effectiveness of RBCL with the ablation study and visualization.

###  5.1 Experimental Details

For all the supervised learning settings, we conduct experiments based on BoT
baseline [28, 29], and all the tricks and hyper-parameters are kept except
that we remove the Center Loss [30].

For the unsupervised setting (CD-US), we use the baseline modified based on
the open sourced UDA strong baseline
111https://github.com/zkcys001/UDAStrongBaseline. To be consistent with BoT,
we remove the non-local block and generalized mean pooling from the default
setting and use the basic ResNet-50 as the backbone. We conduct the backward
compatible training together with the UDA iteration. We update the labels of
old features with the pseudo labels after each time of clustering.

The new model is initialized with the parameters of old model by default for
all the reported results, except when the network structure changes (i.e.,
ID-S-2 and CD-S-2). We calculate $\mathcal{L}_{m}$ on the features before
classifier with cosine similarity. We add the DGR after the convergence of
training loss. The mAP and Rank-1 accuracy are reported as evaluation metrics.
Considering the variance between supervised and unsupervised learning, we set
$K=100,\alpha=0.5$ for supervised settings and $K=40,\alpha=0.3$ for the
unsupervised setting.

###  5.2 Primary Experiment

We first conduct primary experiments under all the settings without adding any
loss for improving the backward compatibility. The results are illustrated in
Table. 2. By observing the table, we summarize the conclusions as follows:

(1) The extended cross-domain settings are more challenging than the in-domain
settings. The performance of Direct under the cross-domain settings is
significantly lower than that of the in-domain settings. For example, the mAP
of Direct in ID-S-1-M2M is 37.5%, whilst only 17.9% for CD-S-1-M2D. This is
caused by the domain gap between source domain and target domain, and
achieving backward compatibility in such a chaos old feature space is rather
challenging.

(2) The unsupervised setting is more difficult than the supervised settings.
This can be observed by comparing between the LB of CD-US and CD-S-1. For the
supervised setting CD-S-1-M2D, it can achieve 32.2% mAP in LB, whilst the
unsupervised setting CD-US-M2D only achieves 0.4% mAP. This decrement may be
caused by the unstable pseudo labeling process in UDA iterations. The label
space is different after each time of clustering, therefore the current
feature space is gradually shifted away from the old feature space.

(3) The structure variation will increase the difficulty of achieving backward
compatibility. By comparing the performance between ID-S-1 and ID-S-2, CD-S-1
and CD-S-2, we find that the performance of new model itself (UB) is improved,
while the cross-model retrieval performance (LB) is decreased a lot, e.g., the
mAP decreases from 50.0% in ID-S-1-M2M to 0.2% in ID-S-2-M2M. Intuitively,
different structures have different capacities and parameters, thus the final
feature spaces are different.

(a)

(b)

Figure 4: (a) The influence of hyper-parameter $K$ in NCAs under CD-S-1-M2D.
(b) The influence of hyper-parameter $\alpha$ in DGR under CD-S-1-M2D.

(a) Distribution of triplets ($d_{nj}^{i}$).

(b) Gradient of triplets ($d_{nj}^{i}$).

(c) Loss curve of $\mathcal{L}_{m}$ after adding DGR.

Figure 5:  The visualization of distribution and gradient change of triplets
($d_{nj}^{i}$) in a mini-batch, and the loss curve of $\mathcal{L}_{m}$ (with
NCAs) after adding DGR. We add DGR after the convergence of $\mathcal{L}_{m}$
under the CD-S-1-M2D setting and $\alpha$ is set as $0.5$. (a) The
distribution of triplets before (red) and after (blue) adding DGR, and the
derivative of sigmoid function when $\tau=0.01$. (b) The average gradients in
each interval before (red) and after (blue) adding DGR. We split the range of
$d_{nj}^{i}$ into several intervals, and then report the average gradients for
each interval. Note that the y axis is logarithmic. (c) The loss curve of
$\mathcal{L}_{m}$ under CD-S-1-M2D. DGR is added after epoch 80.

(a) Influence Loss

(b) RBCL (ours)

Figure 6: The visualization of feature distributions for different methods
under CD-US-M2D by t-SNE. The features of the first $10$ IDs of
$\mathcal{D}_{D}$ are illustrated. Triangles and circles represent for new
query features and old gallery features, separately. Different colors denote
for different IDs. Best view in color and zoom in.

###  5.3 Comparison with Baseline Methods

####  5.3.1 Baseline Methods

The comparison between RBCL and baseline methods under all the settings is
illustrated in Table. 3. The performance of cross-model retrieval without
additional loss for improving the backward compatibility is reported as the
baseline. Aside from the cross-model retrieval performance, we also report the
self-test performance of new model to illustrate the superiority of our RBCL.

We compare our proposed RBCL with three distillation-based methods and one .
The first one is to optimize the $L_{2}$ Loss between new features and the
corresponding old ones in a mini-batch. The second one is the Influence Loss
proposed in [1]. The third one is the Maximum Mean Discrepancy (MMD) loss
proposed in [27] which can make the distribution of new and old features in a
mini-batch close to each other. The last one is Hard Mining Triplet Loss [10],
which is also a typical ranking-based loss but belongs to the distance metric
optimization.

####  5.3.2 Analysis of Cross-model Performance

The cross-model retrieval performance of our RBCL outperforms other methods by
large margins under all the settings.

Compared with the distillation-based losses, in ID-S-1-D2D, RBCL outperforms
Influence Loss by 11.7% and 10.2% in mAP and Rank-1, separately. For Influence
Loss and MMD Loss, their performance in ID-S-1 is even lower than the
baseline, which significantly shows the inferiority of the distillation-based
methods. They only push the new features to be close the old features, which
will lead to mis-ranked new features, therefore the cross-model retrieval
performance is inferior.

Compared with another ranking-based method, in ID-S-2-M2M, RBCL surpasses
Triplet Loss by 9.4% and 9.0% in mAP and Rank-1, respectively. In CD-S-1-M2D,
RBCL surpasses it by 10.7% and 11.3% in mAP and Rank-1, respectively. The
significant improvement shows that optimizing ranking metric is better than
distance metric for BCT, and the proposed DGR and NCAs can help the new
features achieve better ranking positions than the basic Triplet Loss.

####  5.3.3 Analysis of Self-test Performance

The self-test performance of RBCL is the closest one to the upper bound. By
comparing the self-test performance of RBCL with the upper bound, we find that
the backward compatible training process of RBCL has little impact on the
performance of new model itself. For example, the Rank-1 in ID-S-1-M2M only
decreases from 93.8% to 93.7%, and the mAP and Rank-1 in CD-US-M2D even
outperform the upper bound by 1.9% and 1.0%, respectively. This superiority is
attributed to that RBCL only adjust the absolute position of each cluster
toward a best-ranking position, whilst the relative distribution between
clusters are maintained, therefore the self-test performance will not decrease
too much.

####  5.3.4 Robustness to Structure Variation

By comparing the performance between ID-S-1 and ID-S-2, CD-S-1 and CD-S-2, we
observe that the performance of RBCL is both high and robust in self-test and
cross-model performance. For the cross-model performance, the mAP difference
and Rank-1 difference of RBCL between CD-S-1-M2D and CD-S-2-M2D are 0.6% and
0.2%, while for L2 Loss, the differences become 6.8% and 8.4%. As to the self-
test performance, the difference between RBCL and upper bound is consistently
small. For example, the Rank-1 difference in CD-S-1-D2M is 0.0%. After the
change of new model structure in CD-S-2-D2M, the difference merely increases
by 0.3%. When the structure changes, the gap between the new feature space and
the old one becomes larger. Distillation-based methods intend to roughly
diminish the gap, whilst RBCL only tries to find better ranking order of
samples, therefore the impact on self-test performance is smaller.

###  5.4 Effectiveness of RBCL

####  5.4.1 Influence of $K$ and $\alpha$

For supervised settings, we choose the hyper-parameters under CD-S-1-M2D, then
adopt it for all the supervised settings.

For the choice of $K$ (Fig. 4a), we change $K$ sequentially from $10$ to $120$
with $10$ as the step size. In general, the performance increases as $K$
becomes larger (with slight oscillation), which proves the effectiveness of
NCAs. We set $K=100$ for all the supervised settings due to its best
performance.

For the ablation of $\alpha$ (Fig. 4b), we add DGR after the convergence of
using NCAs ($K=100$), and then adjust $\alpha$ from $0.3$ to $0.9$ with $0.1$
as the step size. Obviously, $\alpha=0.5$ gives the best performance because
it provides the moderate gradients.

The similar ablation for unsupervised settings is conducted the same way, and
we find that $K=40,\alpha=0.3$ works well.

####  5.4.2 Ablation of DGR and NCAs

The ablation of DGR and NCAs is illustrated in Table. 4. The ranking metric
optimization between new features and the corresponding old features without
DGR and NCAs is used as the baseline. We have the following important
observations:

(1) DGR can boost the performance of both baseline method and the
baseline+NCAs method under all the challenging settings. For example, for the
unsupervised setting CD-US-D2M, the Rank-1 increments are 3.1% and 2.4%,
respectively. DGR solves the gradient vanish issue, which can refine the
ranking positions and optimize the extremely hard negative samples, thus the
performance is improved.

(2) With the help of NCAs, the performance is largely boosted. After adding
the NCAs to the baseline, for the in-domain setting ID-S-2-M2M, the mAP is
increased by 6.0%. For the cross-domain settings CD-S-2-M2D and CD-S-2-D2M,
the mAP are increased by 6.6% and 6.5%, separately. This strongly proves the
effectiveness of our proposed NCAs, which successfully approximates the entire
ole features space and brings the optimization with global perspective.

(3) The combination of NCAs and DGR gives the best performance. For example,
the mAP and Rank-1 achieve increments of 7.8% and 7.9% in CD-S-2-M2D,
separately. For the challenging unsupervised setting CD-US-M2D, the mAP and
Rank-1 are also increased by 4.0% and 5.4%, separately.

In summary, both NCAs and DGR can boost the performance for all the
challenging settings.

####  5.4.3 Visualization of DGR

We visualize the distribution and gradient changes in a mini-batch in Fig. 5a
and Fig. 5b. After adding DGR, the distribution is closer to the gradient-
effective interval of sigmoid function (Fig. 5a), therefore the gradients of
the majority of triplets are exponentially enhanced (Fig. 5b). We also
illustrate the loss curve of $\mathcal{L}_{m}$ during the training of
CD-S-1-M2D in Fig. 5c. We add DGR after epoch $80$. Obviously, the loss is
enlarged after adding DGR, which means more ranking information is mined.

####  5.4.4 Visualization of Feature Space

To intuitively illustrate the principle difference between our RBCL and the
existing distillation-based methods, we visualize the feature distributions in
Fig. 6. We choose the Influence Loss as the representation of the
distillation-based methods. We can easily observe that: (1) The old feature
clusters are highly entangled with each other, which is due to the poor
representation ability of the old model. (2) For the Influence Loss, there
exist quite a lot of mis-ranked new query features, while for our RBCL, most
of the new query features are in proper-ranking positions.

##  6 Conclusion

In this paper, we propose the effective RBCL for BCT task in person Re-ID.
Different from the existing distillation-based methods, our proposed RBCL
optimizes the ranking metric between new features and old features, which is
superior in principle. To relieve the gradient vanish issue incurred by the
sharp sigmoid function, we propose the DGR, which can reactivate the
suppressed gradients. To further help targeting the global best-ranking
positions, we propose to include NCAs during training, which can approximate
the entire old feature space. RBCL outperforms other methods by a large margin
under both in-domain and challenging cross-domain settings. In the future, we
will study this problem on more retrieval tasks.

## Acknowledgment

This work was supported by the National Natural Science Foundation of China
(No.62173302), the National Key Research and Development Program of China
(2018YFE0119000) and the Fundamental Research Funds for the Central
Universities (2021XZZX022).

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