Iterative%20Detection%20and%20Decoding%20for%20Wireless%20Communications

1
Iterative Detection and Decoding for Wireless
Communications

• Matthew Valenti
• Dissertation Defense
• July 8, 1999
• Advisor Dr. Brian D. Woerner
• Mobile and Portable Radio Research Group
• Bradley Department of Electrical and Computer
  Engineering
• Virginia Tech
• Blacksburg, Virginia

2
Outline

• Introduction and background
• Turbo codes
• Iterative decoding algorithms
• Turbo codes for the wireless channel
• Performance over fading channels
• Receiver/system design for time-varying channels
• Multiuser detection for coded multiple-access
  networks
• Distributed multiuser detection
• Turbo-MUD iterative multiuser detection and
  error correction
• Cooperative decoding for TDMA networks

3
Error Correction Coding

• Channel coding adds structured redundancy to a
  transmission.
• The input message m is composed of K info bits.
• The output code word x is composed of N code
  bits.
• Since N gt K there is redundancy in the output.
• The code rate is r K/N.
• (Hamming) weight
• Number of ones in the message m
• For linear codes, high weight code words are
  desired
• Minimum distance dmin limits performance

Channel Encoder
4
Power Efficiency of Coding Standards
BPSK Capacity Bound
1.0
Uncoded BPSK
Iridium 1998
Shannon Capacity Bound
Pioneer 1968-72
Spectral Efficiency
Code Rate r
Turbo Code 1993
0.5
Globalstar 1999
Odenwalder Convolutional Codes 1976
Voyager 1977
GalileoBVD 1992
GalileoLGA 1996
Mariner 1969
0
1
2
3
4
5
6
7
8
9
10
-1
-2
Eb/No in dB
5
Convolutional Codes

• A convolutional encoder encodes a stream of data.
• The size of the code word is unbounded.
• The encoder is a Finite Impulse Response (FIR)
  filter.
• k binary inputs
• n binary outputs
• Kc -1 delay elements
• All operations over GF(2)
• Addition XOR
• Multiplier coefficients are either 1 or 0

D
D
Constraint Length Kc 3
6
Recursive Systematic Convolutional Encoding

• An RSC encoder is constructed from a standard
  convolutional encoder by feeding back one of the
  outputs.
• An RSC code is systematic.
• The input bits appear directly in the output.
• An RSC encoder is an Infinite Impulse Response
  (IIR) Filter.
• Many low weight inputs produce high weight
  outputs.
• Some inputs will cause low weight outputs.

Systematic output
Input
D
D
Parity output
7
Turbo Codes Parallel Concatenated Codeswith
Nonuniform Interleaving

• A stronger code can be created by encoding in
  parallel.
• A nonuniform interleaver changes the ordering of
  bits at the input of the second encoder.
• It is very unlikely that both encoders produce
  low weight code words.
• MUX increases code rate from 1/3 to 1/2.

Systematic Output
Input
Encoder 1
MUX
Parity Output
Encoder 2
Nonuniform Interleaver
8
Turbo code performance

• Coding dilemma
• All codes are good, except those that we can
  think of.
• Random coding argument
• Truly random codes approach capacity, but are not
  feasible.
• Turbo codes appear random, yet have enough
  structure to allow practical decoding.
• Distance spectrum argument
• Traditional code design focused on maximizing the
  minimum distance.
• dmin determines performance at high SNR
• With turbo codes, the goal is to reduce the
  multiplicity of low weight code words.
• Even with small dmin, remarkable performance can
  be achieved at low SNR.

9
Minimum-distance Asymptote

• For convolutional code
• For turbo code

10
Performance for various frame/interleaver sizes

• Kc 5
• Rate r 1/2
• 18 decoder iterations
• Log-MAP decoder
• AWGN Channel

11
The Turbo-Principle

• Turbo codes get their name because the decoder
  uses feedback, like a turbo engine.

12
Iterative Decoding
Deinterleaver
Extrinsic Information
Extrinsic Information
Interleaver
Decoder 1
Decoder 2
systematic data
hard bit decisions
parity data
DeMUX
Interleaver

• There is one decoder for each elementary encoder.
• Estimates the a posteriori probability (APP) of
  each data bit.
• Extrinsic Information is derived from the APP.
• The Extrinsic Information is used as a priori
  information by the other decoder.
• Decoding continues for a set number of
  iterations.
• Obeys law of diminishing returns

13
Soft-Input Soft-Output (SISO)Decoding Algorithms
Trellis-Based Estimation Algorithms

• Viterbi algorithm
• 1967 Viterbi
• SOVA
• 1989 Hagenauer/Hoeher
• Improved SOVA
• 1996 Papke/Robertson/Villebrun
• MAP algorithm
• 1974 Bahl/Cocke/Jelinek/Raviv
• max-log-MAP
• 1990 Koch and Baier
• log-MAP
• 1994 Villebrun

Viterbi Algorithm
MAP Algorithm
SOVA
max-log-MAP
Improved SOVA
log-MAP
Sequence Estimation
Symbol-by-symbol Estimation
14
Performance as a Function of Number of Iterations

• Kc 5
• r 1/2
• K 65,536
• Log-MAP algorithm
• AWGN

15
Summary of Performance Factors and Tradeoffs

• Latency vs. performance
• Frame/interleaver size
• Complexity vs. performance
• Decoding algorithm
• Number of iterations
• Encoder constraint length
• Spectral efficiency vs. performance
• Overall code rate
• Other factors
• Interleaver design
• Puncture pattern
• Trellis termination

16
Turbo Codes for Fading Channels

• Many channels of interest can be modeled as a
  frequency-flat fading channel.
• Fading channel is time-varying
• Flat all frequencies experience same attenuation
• Because of the time-varying nature of the
  channel, it is necessary to estimate and track
  the channel.
• Channel estimation is difficult for turbo codes
  because they operate at low SNR.
• Questions
• How do turbo codes perform over fading channels?
• How can the channel be estimated in a turbo coded
  system?
• Goal is to develop channel estimation techniques
  that take into account the iterative nature of
  the decoder.

17
System Model
turbo encoder
channel interleaver
symbol mapper
pulse shaping filter
Input data
transmitter
fading
AWGN
channel
matched filter
channel estimator
receiver
Decoded data
channel deinterl.
turbo decoder
symbol demapper
18
Fading Channel Types

• .
• X(t), Y(t) are Gaussian random processes.
• Represents the scattering component
• Autocorrelation Rc(?)
• A is a constant.
• Represents the direct LOS component
• Types of channels
• AWGN Aconstant and X(t)Y(t)0
• Rayleigh fading A0
• Rician fading A gt 0, ?A2/2?2
• Correlated fading
• Fully-interleaved fading

19
Effect of Channel Correlation

• Channel
• Rayleigh fading
• Correlated
• Channel interleaver
• Depth 32 symbols
• Perfect Estimates
• Turbo code
• Rate 1/2
• KC3
• K1024
• Decoder
• Improved SOVA
• 8 iterations

20
Effect of Fading Distribution

• Channel
• Correlated fading
• fdTs .005
• Channel interleaving
• Depth 32 symbols
• Perfect Estimates
• Turbo code
• Rate 1/2
• KC4
• K1024
• 8 decoder iterations
• Log-MAP
• Improved SOVA

21
Channel Estimationfor Turbo Codes

• The turbo decoding algorithm requires accurate
  estimates of channel parameters.
• Branch metric
• Noise variance
• Fading amplitude
• Phase (required for coherent
  detection)
• Because turbo codes operate at low SNR,
  conventional methods for channel estimation often
  fail.
• Therefore channel estimation and tracking is a
  critical issue with turbo codes.

22
Case 1Known Phase

• Assume that the receiver is able to obtain
  accurate estimates of the carrier phase ?n
• PLL Phase locked loop
• Costas loop
• The amplitude can be estimated using a Wiener
  filter
• The noise variance can be estimated as

23
Channel Estimation with Known Phase

• AWGN
• Turbo Code Parameters
• r1/2, Kc4, L1024
• 8 decoder iterations

• Rayleigh flat-fading
• FdTs .005
• Channel interleaver depth 32
• Wiener filter w/ Nc 30

24
Case 2Unknown Phase

• Now assume that the receiver is unable to obtain
  accurate estimates of the phase ?n.
• Because turbo codes operate at low SNR, the PLL
  often breaks down.
• Because of the phase ambiguity, we no longer can
  use the previous approach.
• Coherent detection over Rayleigh fading channels
  requires a pilot.
• Pilot tone
• TTIB Transparent Tone in Band
• 1984 McGeehan and Bateman
• Pilot symbols
• PSAM Pilot Symbol Assisted Modulation
• 1987 Lodge and Moher 1991 Cavers

25
Pilot Symbol Assisted Modulation (PSAM)

• Pilot symbols
• Known values that are periodically inserted into
  the transmitted code stream.
• Used to assist the operation of a channel
  estimator at the receiver.
• Allow for coherent detection over channels that
  are unknown and time varying.

segment 1
segment 2
symbol 1
symbol Mp
symbol 1
symbol Mp
pilot symbol
pilot symbol
symbol 1
symbol Mp
symbol 1
symbol Mp
pilot symbols added here
26
Pilot Symbol Assisted Decoding

• Pilot symbols are used to obtain initial channel
  estimates.
• After each iteration of turbo decoding, the bit
  estimates are used to obtain new channel
  estimates.
• Decision-directed estimation.
• Channel estimator uses either a Wiener filter or
  Moving average.

Tentative estimates of the code bits
channel estimator
matched filter
channel interleaver
symbol mapper
symbol demapper
channel deinterl.
turbo decoder
Final estimates of the data
27
Performance of Pilot Symbol Assisted Decoding

• Simulation parameters
• Rayleigh flat-fading
• Correlated fdTs .005
• channel interleaving depth 32
• Turbo code
• r1/2, Kc 4
• 1024 bit random interleaver
• 8 iterations of log-MAP
• Pilot symbol spacing Mp 8
• Wiener filtering Nc 30
• At Pb 10-5
• Noncoherent reception degrades performance by 4.7
  dB.
• Estimation prior to decoding degrades performance
  by 1.9 dB.
• Estimation during decoding only degrades
  performance by 0.8 dB.

28
Performance Factors for Pilot Symbol Assisted
Decoding

• Performance is more sensitive to errors in
  estimates of the fading process than estimates in
  noise variance.
• Pilot symbol spacing
• Want symbols close enough to track the channel.
• However, using pilot symbols reduces the energy
  available for the traffic bits.
• Type of channel estimation filter
• Wiener filter provides optimal solution.
• However, for small fd, a moving average is
  acceptable.
• Size of channel estimation filter
• Window size of filter should contain about 4
  pilot symbols.

29
Improving the Bandwidth Efficiency of PSAM

• Conventional PSAM requires a bandwidth expansion.
• Previous example required 12.5 more BW.
• This is because all code and pilot symbols are
  transmitted.
• Instead, could replace code symbols with pilot
  symbols.
• Parity-symbol stealing
• Simulation Parameters
• Rayleigh fading
• fdTs .005
• Turbo code
• Kc 4, r 1/2
• L4140 bit iterleaver

30
Performance in Rapid Fading

• Rayleigh fading channel
• fdTs .02
• Turbo code
• Kc 4, r 1/2
• L4140 bit interleaver

31
Other Applications of the Turbo Principle

• The turbo-principle is more general than merely
  its application to the decoding of turbo codes.
• Other applications of the turbo principle
  include
• Decoding serially concatenated codes.
• Combined equalization and error correction
  decoding.
• Combined multiuser detection and error correction
  decoding.
• (Spatial) diversity combining for coded systems
  in the presence of MAI or ISI.

32
Serial Concatenated Codes
n(t) AWGN
Inner Convolutional Encoder
Outer Convolutional Encoder
Data
interleaver
Extrinsic Information
Turbo Decoder
interleaver
Inner Decoder
Outer Decoder
Estimated Data
deinterleaver
33
Turbo Equalization
Can model intersymbol interference channel as an
FIR filter
n(t) AWGN
(Outer) Convolutional Encoder
Data
ISI Channel
interleaver
Extrinsic Information
Turbo Equalizer
interleaver
(Outer) SISO Decoder
SISO Equalizer
Estimated Data
deinterleaver
34
Turbo Multiuser Detection
Time-varying FIR filter
multiuser interleaver
Convolutional Encoder 1
Channel
interleaver 1
MAI Channel Model
Parallel to Serial
n(t) AWGN
Convolutional Encoder K
interleaver K
Turbo MUD
Extrinsic Info
multiuser interleaver
Bank of K SISO Decoders
SISO MUD
multiuser deinterleaver
Estimated Data
35
Direct Sequence CDMA

• CDMA Code Division Multiple Access
• The users are assigned distinct waveforms.
• Spreading/signature sequences
• All users transmit at same time/frequency.
• Use a wide bandwidth signal
• Processing gain Ns
• Ratio of bandwidth after spreading to bandwidth
  before
• MUD for CDMA
• The resolvable MAI originates from the same cell.
• Intracell interference.
• MUD uses observations from only one base station.

36
Performance of Turbo-MUD for CDMA in AWGN

• Eb/No 5 dB
• 1 ? K ? 9

• K 5 users
• Spreading gain Ns 7
• Convolutional code Kc 3, r1/2

37
Performance of Turbo-MUD for CDMA in Rayleigh
Flat-fading

• K 5 users
• Fully-interleaved fading

• Eb/No 9 dB
• 1 ? K ? 9

38
Time Division Multiple Access

• TDMA Time Division Multiple Access
• Users are assigned unique time slots
• All users transmit at same frequency
• All users have the same waveform, g(t)
• TDMA can be considered a special case of CDMA,
  with gk(t) g(t) for all cochannel k.
• MUD for TDMA
• Usually there is only one user per time-slot per
  cell.
• The interference comes from nearby cells.
• Intercell interference.
• Observations from only one base station might
  not be sufficient.
• Performance is improved by combining outputs from
  multiple base stations.

39
Performance of Turbo-MUD for TDMA in AWGN

• K 3 users
• Convolutional code Kc 3, r1/2
• Observations at 1 base station

• Eb/No 5 dB
• 1 ? K ? 9

40
Performance of Turbo-MUD for TDMA in Rayleigh
Flat-Fading

• K 3 users
• Fully-interleaved fading

• Eb/No 9 dB
• 1 ? K ? 9

41
Extension Multiuser Detection for TDMA Networks

• Each base station has a multiuser detector.
• Sum the LLR outputs from M base stations.
• Pass through a bank of SISO channel decoder.
• Feed back LLR outputs of the decoders to the
  MUDs.

Extrinsic Info
Multiuser Detector 1
Bank of K SISO Channel Decoders
Estimated Data
Multiuser Detector M
42
Distributed Multiuser Detection

• First, consider the case where each user is
  uncoded.
• Each base station has a multiuser detector.
• Implemented with the Log-MAP algorithm.
• Produces LLR estimates of the users symbols.
• Sum the LLR outputs of each MUD.

Multiuser Detector 1
Multiuser Detector M
43
Cellular Network Topology
F3
F4
F2
F1
F5
F7
F6

• Alternative layout
• 120 degree sectorized antennas
• Located in 3 corners of cell
• Frequency reuse factor 3

• Conventional layout
• Isotropic antennas in cell center
• Frequency reuse factor 7

44
Performance of Distributed MUD

• With diversity combining.
• M3 base stations
• Mobiles randomly placed in cell.
• Exponential path loss, ne 3.

• Without diversity combining.
• Fully-interleaved Rayleigh fading
• Output from BS closest to the mobile used to make
  decision.

45
Performance of Distributed MUD

• Eb/No 20 dB
• 1 ? K ? 9
• For conventional receiver
• Performance degrades quickly with increasing K.
• Only small benefit to using observations from
  multiple BS.
• With multiuser detection
• Performance degrades very slowly with increasing
  K.
• Order of magnitude decrease in BER by using
  multiple observations.
• Now multiple cochannel users per cell are
  allowed.

46
Cooperative Decoding for the TDMA Uplink

• Now consider the coded case.
• The outputs of the MUDs are summed and passed
  through a bank of decoders.
• The SISO decoder outputs are fed back to the
  multiuser detectors to be used as a priori
  information.

Extrinsic Info
Multiuser Detector 1
Bank of K SISO Channel Decoders
Estimated Data
Multiuser Detector M
47
Performance of Cooperative Decoding

• K 3 transmitters
• Randomly placed in cell.
• M 3 receivers (BSs)
• Corners of cell
• path loss ne 3
• Fully-interleaved Rayleigh flat-fading
• Convolutional code
• Kc 3, r 1/2

48
Performance of Cooperative Decoding

• Eb/No 5 dB
• 1 ? K ? 9
• Randomly placed in cell.
• M 3 receivers
• For conventional receiver
• Performance degrades quickly with increasing K.
• Only small benefit to using observations from
  multiple BS.
• With multiuser detection
• Performance degrades gracefully with increasing
  K.
• No benefit after third iteration.
• Could allow an increase in TDMA system capacity.

49
Conclusion

• Turbo code advantages
• Remarkable power efficiency in AWGN and
  flat-fading channels for moderately low BER.
• Turbo code disadvantages
• Long latency due to large frame sizes.
• Less beneficial at high SNR.
• Because turbo codes operate at very low SNR,
  channel estimation and tracking is a critical
  issue.
• The principle of iterative or turbo processing
  can be applied to other problems.
• Turbo-multiuser detection can improve performance
  of coded multiple-access systems.
• When applied to TDMA networks, can allow multiple
  users per time/frequency slot.

50
Future Work

• Turbo codes for wireless communications.
• We have addressed the issue of carrier
  synchronization.
• Multiple-symbol DPSK could be a viable
  alternative.
• Symbol and frame synchronization should also be
  considered.
• Adaptive turbo codes
• ARQ schemes for turbo codes.
• Distributed multiuser detection.
• Reduced complexity implementations.
• Methods for performing channel estimation.
• Study the impact on network architecture/control.
• Multiuser detection at a network level.

51
Contributions/Publications

• Turbo codes for the wireless channel
• Use of pilot symbols for channel estimation
• Combined pilot symbol-assisted and
  decision-directed decoding
• Performance curves for Rician channels
• Wireless multimedia applications
• Valenti and Woerner, Refined channel estimation
  for coherent detection of turbo codes over
  flat-fading channels, IEE Electronics Letters,
  Aug. 1998.
• Valenti and Woerner, Pilot symbol assisted
  detection of turbo codes over flat-fading
  channels," IEEE Journal on Selected Areas in
  Communications, in review.
• Valenti and Woerner, A bandwidth efficient pilot
  symbol technique for coherent detection of turbo
  codes over fading channels, in Proc. MILCOM,
  Atlantic City, Oct./Nov. 1999, to appear.
• Valenti, Turbo codes and iterative processing,
  in Proc. IEEE New Zealand Wireless Communications
  Symposium, Auckland, New Zealand, Nov. 1998,
  invited paper.
• Valenti and Woerner, Performance of turbo codes
  in interleaved flat fading channels with
  estimated channel state information, in Proc.,
  IEEE VTC, Ottawa, Canada, May 1998.
• Valenti and Woerner, Variable latency
  Turbo-codes for wireless multimedia
  applications, in Proc. International Symposium
  of Turbo Codes and Related Topics, Brest, France,
  Sept. 1997.

52
Contributions/Publications

• Multiuser detection for coded multiple-access
  networks
• Log-MAP multiuser detection algorithm.
• Distributed multiuser detection using
  observations from multiple receivers.
• Application to TDMA networks.
• Valenti and Woerner, Distributed multiuser
  detection for the TDMA cellular uplink, IEE
  Electronics Letters, in review.
• Valenti and Woerner, Combined multiuser
  detection and channel decoding with receiver
  diversity, in Proc. GLOBECOM, Communications
  Theory Mini-conference, Sydney, Australia, Nov.
  1998.
• M.C. Valenti and Woerner, Multiuser detection
  with base station diversity, in Proc. ICUPC,
  Florence, Italy, Oct. 1998.
• M.C. Valenti and Woerner, Iterative multiuser
  detection for convolutionally coded asynchronous
  DS-CDMA, in Proc. PIMRC, Boston, MA, Sept. 1998.
  
• Valenti and Woerner, Performance of turbo codes
  in interleaved flat fading channels with
  estimated channel state information, in Proc.
  VTC, Ottawa, Canada, May 1998.

53
Web Page

• For more information visit
• http/www.ee.vt.edu/valenti/turbo.html

54
Goals of Error Correction Coding

• When the channel induces an error, the decoder
  chooses the closest code word.
• Therefore distinct code words are desired.
• Hamming distance the number of bit positions
  that two code words differ.
• The Hamming distance between two code words
  should be as large as possible.
• Minimum distance smallest Hamming distance
  between two code words.
• Traditional code design seeks to maximize the
  minimum distance.
• (Hamming) weight the number of ones in a code
  word.
• In a linear code the minimum distance is the
  smallest Hamming weight of all non-zero code
  words.

55
Turbo Multiuser Detection

• The inner code of a serial concatenation could
  be a multiple-access interference (MAI) channel.
• MAI channel describes the interaction between K
  nonorthogonal users sharing the same channel.
• MAI channel can be interpreted as a time varying
  ISI channel.
• MAI channel is a rate 1 code with time-varying
  coefficients over the field of real numbers.
• The input to the MAI channel consists of the
  encoded and interleaved sequences of all K users
  in the system.

56
Low Power Communications

• Goal for modern communication system design
• Reduce the minimum signal-to-noise power ratio
  (SNR) required by the receiver
• Benefits
• Allows more design flexibility
• The transmitted signal can be less powerful
• Extended battery life
• Allows use of smaller transmit antennas
• Produces less interference
• Reduced adverse biological effects
• More robust against noise, fading, and
  interference
• Increased range of transmission
• Allows use of smaller receive antennas

57
How to Achieve Low Power Communications

• P EbRb
• Lower the data rate Rb
• Source coding
• Compression
• Compaction
• Vocoding
• Lower the energy per bit Eb required at the
  receiver
• Signal processing
• Equalization
• Multiuser detection
• Smart antennas
• Channel coding

58
Random Codes

• Random codes achieve the best performance.
• Shannon showed that as N approaches infinity,
  random codes require the theoretical minimum SNR.
• However, random codes are not feasible.
• The code must contain enough structure so that
  decoding can be realized with actual hardware.
• Coding dilemma
• All codes are good, except those that we can
  think of.
• With turbo codes
• The codes appear random to the channel.
• Yet, they contain enough structure so that
  decoding is feasible.

59
Turbo Codes

• Background
• Turbo codes were proposed by Berrou and Glavieux
  in the 1993 International Conference in
  Communications.
• Performance within 0.5 dB of the channel capacity
  limit for BPSK was demonstrated.
• Features of turbo codes
• Recursive convolutional encoders
• Parallel code concatenation
• Nonuniform or Pseudo-random interleaving
• Iterative decoding

60
Performance Bounds for Linear Block Codes

• Union bound for maximum likelihood soft-decision
  decoding
• Or
• The minimum-distance asymptote is the first term
  of the sum

61
Performance of Turbo Equalizer

• M5 independent multipaths
• Symbol spaced paths
• Stationary channel
• Perfectly known channel.
• Convolutional code
• Kc5
• r1/2
• C. Douillard,et al Iterative Correction of
  Intersymbol Interference Turbo-Equalization,
  European Transactions on Telecommuications,
  Sept./Oct. 97.

62
Performance of Serial Concatenated Turbo Code

• Rate r1/3
• Interleaver size K 16,384
• Kc 3 encoders
• Serial concatenated codes do not seem to have a
  bit error rate floor
• S. Benedetto, et al Serial Concatenation of
  Interleaved Codes Performance Analysis, Design,
  and Iterative Decoding Proc., Int. Symp. on
  Info. Theory, 1997.

63
Performance of Turbo MUD

• Generic MAI system
• Ku 3 asynchronous users
• Identical pulse shapes
• Each user has its own interleaver
• Convolutionally coded
• Kc 3
• r 1/2
• Iterative decoder
• M. Moher, An iterative algorithm for
  asynchronous coded multiuser detection, IEEE
  Comm. Letters, Aug.1998.