Exploring Data Compression for a Distributed Aerial Relay Application

85 Pages·2017·2.97 MB·English

Exploring Data Compression for a Distributed Aerial
Relay Application
by Joseph C. Griffin
S.B., Electrical Engineering M.I.T., 2016
Submitted to the
Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
at the
Massachusetts Institute of Technology
June 2017
○c 2017 Joseph C. Griffin. All rights reserved.
The author hereby grants to M.I.T. permission to reproduce and to distribute publicly
paper and electronic copies of this thesis document in whole or in part in any medium now
known or hereafter created.
Author:
Department of Electrical Engineering and Computer Science
May 26, 2017
Certified by:
James Ward, Lecturer for EECS, and Assistant Head Communication Systems
Division, MIT Lincoln Laboratory
May 26, 2017
Accepted by:
Christopher J. Terman, Chairman, Masters of Engineering Thesis Committee
Exploring Data Compression for a Distributed Aerial Relay
Application
by
Joseph C. Griffin
Submitted to the Department of Electrical Engineering and Computer Science
on May 26, 2017, in partial fulfillment of the
requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
Abstract
Beamforming systems typically involve arrays of antenna elements with controllable spac-
ing and little or no motion. However, a distributed beamforming system could leave array
geometry and motion largely unconstrained. This work considers an airborne relay commu-
nication concept with multiple balloons in which the individual array elements act as relays
to a receiver on the ground at a base station. The beamforming operation is performed at
the receiver. The link between the relays and receiver suffers from a high bandwidth re-
quirement. This thesis explores ways to reduce this bandwidth requirement by compressing
the signals across the relays. A distributed compression algorithm is proposed and applied
to both simulated and collected data. We conclude that a compression algorithm across the
relays offers a substantial decrease in bit rate requirement, and that a preprocessing step
can make the compression performance robust against differential delay and Doppler shifts
across the array.
2
Acknowledgments
The author thanks MIT Lincoln Laboratory for funding and guidance in developing this
thesis. In particular, the following people played important roles in the development of this
work:
1. Dr. James Ward
2. Dr. Zaid Towfic
3. Dr. Ameya Agaskar
4. Prof. Gregory Wornell
5. Dr. Or Ordentlich
6. Navid Yazdani
3
4
Contents
1 Introduction 11
2 System Model 19
2.1 Continuous-Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Discrete-Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Data Compressibility Without Noise . . . . . . . . . . . . . . . . . . 26
2.3.2 Noise Effects on Compressibility . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 Effects of Delay Spread on Compressibility . . . . . . . . . . . . . . . 31
2.3.4 Effects of Doppler Spread on Compressibility . . . . . . . . . . . . . . 35
3 Integer-Forcing Source Coding 39
3.0.1 Overload Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.0.2 IFSC Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.0.3 Performance and Bounds . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Simulation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Basic Problem Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 IFSC Modifications for Delay Spread 53
4.1 Delay Spread Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.1 Time Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.2 Joint Encoding Over Time . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.3 Channelization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5
5 IFSC Modifications for Doppler Spread 71
5.1 Fast Updating Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Conclusions 81
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.1 IFSC Vector Quantization . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.2 Asymmetric Wyner-Ziv Compression . . . . . . . . . . . . . . . . . . 83
6.2.3 Time Predictive IFSC . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.4 Covariance Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . 84
6
List of Figures
1-1 A diagram of the distributed beamforming setting for the proposed research.
The uplink transmission from User 1 is corrupted by an interference source,
and the corrupted signals are relayed to User 2, the base station. User 2 is
responsible for filtering out the interference and retrieving User 1’s transmission. 12
1-2 Ablockdiagramoftherelayanduserterminalreceivercomputation,including
the feedback link and compression steps. Each wireless transmission occurs
on a separate frequency, denoted 𝑓 , 𝑓 , and 𝑓 . . . . . . . . . . . . . . 16
up down,k FB
2-1 A diagram of the distributed beamforming system with differential and uni-
form delays between transmitters. 𝑇 is the sample period of the relays, and
𝑠
𝑐 is the speed of the transmission wave. . . . . . . . . . . . . . . . . . . . . . 21
3-1 A block diagram indicating the IFSC implementation. As applied to the
communications system of this thesis, ℰ would be implemented on relay 𝑘.
𝑘
The decoder 𝐷 would be on the ground station. Λ is the encoding bin size.
The encoders quantize the data 𝑦 , reduce mod Λ, and transmit. The decoder
𝑘
decouples the data streams, reduces mod Λ, and re-couples them. Note the
lack of interaction between encoder blocks. Only the decoder needs access to
all the data streams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3-2 A block diagram of the base station in uncompressed mode. . . . . . . . . . 44
3-3 A graph of distortion introduced by compression in the absence of delay and
Doppler spread. The Berger-Tung benchmark is denoted 𝑅 , and plain
𝑏𝑒𝑛𝑐ℎ
quantization without compression is denoted 𝑅 . . . . . . . . . . . . . . . 50
𝑛𝑎𝑖𝑣𝑒
7
3-4 A basic-case rate-distortion curve that includes implemented compression al-
gorithms. The plain quantization with a bit buffer and without compression is
denoted𝑅 +𝛿. Wesee, inthisbasiccase, thattheimplementedalgorithms
𝑛𝑎𝑖𝑣𝑒
effectively match their counterparts without the bit buffer. . . . . . . . . . . 51
4-1 A comparison of rate-distortion benchmark curves both with and without
delay spread effects. Curves generated in cases with delay spread are denoted
"delayed," and other curves labeled without modification are generated in the
absence of delay spread. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4-2 A graph indicating the effectsof delay spread on IFSC1Dand IFSCHD perfor-
mance. IFSC1D in the presence of delay spread offers almost no improvement
over plain quantization with a buffer. IFSCHD offers some improvement, even
in the presence of delay spread, but it is much more computationally intensive
to redesign the parameters each time the channel measurements are updated. 55
4-3 A comparison of Berger-Tung performance with the use of relay signal time-
alignment. Each relay experienced a uniform delay across its received signals.
This can happen if the transmitters are located near each other. . . . . . . . 57
4-4 A comparison of IFSC1D performance with the use of relay signal time-
alignment. Each relay experienced a uniform delay across its received signals.
A plot of 𝑅 +𝛿 is provided to indicate how time-aligned IFSC1D improves
𝑛𝑎𝑖𝑣𝑒
over plain quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4-5 A comparison of Berger-Tung performance with the use of relay signal time-
alignment in the presence of differential delays. . . . . . . . . . . . . . . . . . 59
4-6 IFSC1D performance with time-alignment in the presence of differential de-
lays. Thiscanhappenifthetransmittersarelocatedfarawayfromeachother.
IFSCHD performance is provided as a visual reference. . . . . . . . . . . . . 60
4-7 A plot of 𝑅 with a joint encoding strategy for mitigating delay spread.
𝑏𝑒𝑛𝑐ℎ
The unaddressed delay and delay-free cases are plotted for reference. . . . . . 62
8
4-8 A plot of 𝑅 performance with joint encoding. Joint encoding does not
𝐼𝐹
improve IFSC as much as it does Berger-Tung. About half the compression
performance is reintroduced with a joint encoding scheme. 𝑅 is provided
𝑛𝑎𝑖𝑣𝑒
for visual reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4-9 A plot of IFSC1D performance with joint encoding. The unaddressed delay
and delay-free cases are plotted for reference. The high overload rate causes
IFSC1D with joint decoding to perform even worse than a plain quantization
scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4-10 A graph of the Berger-Tung benchmark and 𝑅 . In addition to the delay-free
𝐼𝐹
case, a rate-distortion curve is provided to show the performance of channel-
ization schemes with 𝑁 = 16 and 𝑁 = 128. The delayless gap between 𝑅
𝐼𝐹
and 𝑅 matches the gaps for the channelized cases, so we know that IFSC
𝑏𝑒𝑛𝑐ℎ
is compatible with channelization. . . . . . . . . . . . . . . . . . . . . . . . . 67
4-11 A graph of the Berger-Tung benchmark for different frequency resolutions.
Thefigurefeaturesonly𝑅 fordifferentscenarios,sowechangetheplotting
𝑏𝑒𝑛𝑐ℎ
format in this figure. Curves with no channelization are indicated with data
markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4-12 A graph of the Berger-Tung benchmark for different frequency resolutions.
Thefigurefeaturesonly𝑅 fordifferentscenarios,sowechangetheplotting
𝑏𝑒𝑛𝑐ℎ
format in this figure. Curves with no channelization are indicated with data
markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5-1 AdiagramoftheBerger-TungbenchmarkinthepresenceofdelayandDoppler
spread, with different look times for fast updating. In addition to a basic-case
performance curve, the graph features a rate-distortion curve for the Berger-
Tung benchmark in the presence of delay spread without Doppler spread,
channelizing at 𝑁 = 32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
9
5-2 AdiagramoftheBerger-TungbenchmarkinthepresenceofdelayandDoppler
spread,withdifferentlooktimesforfastupdating. Thealgorithmshows𝑅
𝑏𝑒𝑛𝑐ℎ
for look times that are so short that the covariance measurements for each
channel begin to appear degenerate. . . . . . . . . . . . . . . . . . . . . . . . 76
5-3 A diagram of IFSC1D performance with fast updating in the presence of delay
and Doppler spread. The look times shown indicate how IFSC1D performs
with bad covariance measurements. . . . . . . . . . . . . . . . . . . . . . . . 77
5-4 IFSC1Dperformancewith128frequencychannels,indicatingthattheDoppler-
free case cannot be reached for high 𝑁. . . . . . . . . . . . . . . . . . . . . . 78
5-5 IFSC1D performance with 8 frequency channels, indicating that the Doppler-
free case acts as a lower bound for Doppler affected cases with short look
times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
10