Iterative Detection and Decoding for Wireless Matthew Valenti

Iterative Detection and Decoding for Wireless Matthew Valenti Communications Dissertation Defense July 8, 1999 Advisor: Dr. Brian D. Woerner VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY MPRG MOBILE & PORTABLE RADIO RESEARCH GROUP Mobile and Portable Radio Research Group Bradley Department of Electrical and Computer Engineering Virginia Tech Blacksburg, Virginia

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

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

Power Efficiency of Coding Standards d city Boun a p a C K BPS Uncoded BPSK ity B apa c Iridium 1998 n. C nno Sha Code Rate r Spectral Efficiency oun d 1. 0 0. 5 Pioneer 1968 -72 Turbo Code 1993 Globalstar 1999 Voyager 1977 Galileo: LGA 1996 -2 -1 0 1 Odenwalder Convolutional Codes 1976 Galileo: BVD 1992 Mariner 1969 2 3 4 Eb/No in d. B 5 6 7 8 9 10

Convolutional Codes n A convolutional encoder encodes a stream of data. u D D n The encoder is a Finite Impulse Response (FIR) filter. u Constraint Length Kc = 3 The size of the code word is unbounded. u u u k binary inputs n binary outputs Kc -1 delay elements All operations over GF(2) F F Addition: XOR Multiplier coefficients are either 1 or 0

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

Turbo Codes: Parallel Concatenated Codes with Nonuniform Interleaving n Turbo Codes n n n 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 Nonuniform Interleaver Encoder #2 Parity Output

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

Minimum-distance Asymptote n For convolutional code: n For turbo code:

Performance for various frame/interleaver sizes n n n Kc = 5 Rate r = 1/2 18 decoder iterations Log-MAP decoder AWGN Channel

The Turbo-Principle Iterative decoding n Turbo codes get their name because the decoder uses feedback, like a turbo engine.

Iterative Decoding Deinterleaver Extrinsic Information Iterative decoding systematic data parity data Decoder #1 Extrinsic Information Interleaver Decoder #2 De. MUX hard bit decisions Interleaver n There is one decoder for each elementary encoder. u u n n 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. u Obeys law of diminishing returns

Soft-Input Soft-Output (SISO) Decoding Algorithms Trellis-Based Estimation Algorithms Viterbi algorithm Iterative decoding 1967 Viterbi SOVA Viterbi Algorithm MAP Algorithm 1989 Hagenauer/Hoeher Improved SOVA 1996 Papke/Robertson/Villebrun SOVA max-log-MAP algorithm 1974 Bahl/Cocke/Jelinek/Raviv Improved SOVA log-MAP Sequence Estimation Symbol-by-symbol Estimation max-log-MAP 1990 Koch and Baier log-MAP 1994 Villebrun

Performance as a Function of Number of Iterations n n n Kc = 5 r = 1/2 K = 65, 536 Log-MAP algorithm AWGN

Summary of Performance Factors and Tradeoffs n Latency vs. performance Turbo Codes u n Complexity vs. performance u u u n Decoding algorithm Number of iterations Encoder constraint length Spectral efficiency vs. performance u n Frame/interleaver size Overall code rate Other factors u u u Interleaver design Puncture pattern Trellis termination

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

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

Fading Channel Types. n Fading channels u X(t), Y(t) are Gaussian random processes. F F u A is a constant. F n Represents the scattering component Autocorrelation: Rc( ) Represents the direct LOS component Types of channels u u u AWGN: A=constant and X(t)=Y(t)=0 Rayleigh fading: A=0 Rician fading: A > 0, =A 2/2 2 Correlated fading: Fully-interleaved fading:

Effect of Channel Correlation n Channel: u u u Rayleigh fading Correlated Channel interleaver F u n Perfect Estimates Turbo code: u u u n Depth = 32 symbols Rate 1/2 KC=3 K=1024 Decoder: u u Improved SOVA 8 iterations

Effect of Fading Distribution n Channel: u Correlated fading F fd Ts u Channel interleaving F u n =. 005 Depth = 32 symbols Perfect Estimates Turbo code: u u Rate 1/2 KC=4 K=1024 8 decoder iterations F F Log-MAP Improved SOVA

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

Case 1: Known Phase Fading channels n Assume that the receiver is able to obtain accurate estimates of the carrier phase n u u PLL: Phase locked loop Costas loop n The amplitude can be estimated using a Wiener filter: n The noise variance can be estimated as:

Channel Estimation with Known Phase n n AWGN Turbo Code Parameters: u n n u r=1/2, Kc=4, L=1024 8 decoder iterations Rayleigh flat-fading u n Fd. Ts =. 005 Channel interleaver depth 32 Wiener filter w/ Nc = 30

Case 2: Unknown Phase n Now assume that the receiver is unable to obtain accurate estimates of the phase n. Fading channels u n 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. u Pilot tone F F u TTIB: Transparent Tone in Band 1984: Mc. Geehan and Bateman Pilot symbols F F PSAM: Pilot Symbol Assisted Modulation 1987: Lodge and Moher; 1991: Cavers

Pilot Symbol Assisted Modulation (PSAM) n Pilot symbols: Fading channels u u u 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 symbol #1 segment #2 symbol #Mp pilot symbol #1 symbol #Mp pilot symbols added here symbol #Mp

Pilot Symbol Assisted Decoding n Fading channels n 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. u n Decision-directed estimation. Channel estimator uses either a Wiener filter or Moving average. matched filter channel estimator channel interleaver symbol mapper symbol demapper channel deinterl. turbo decoder Tentative estimates of the code bits Final estimates of the data

Performance of Pilot Symbol Assisted Decoding n Simulation parameters: u u Rayleigh flat-fading F Correlated: fd. Ts =. 005 F channel interleaving depth 32 Turbo code F F F u u n r=1/2, Kc =4 1024 bit random interleaver 8 iterations of log-MAP Pilot symbol spacing: Mp = 8 Wiener filtering: Nc = 30 At Pb = 10 -5 u u u Noncoherent reception degrades performance by 4. 7 d. B. Estimation prior to decoding degrades performance by 1. 9 d. B. Estimation during decoding only degrades performance by 0. 8 d. B.

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

Improving the Bandwidth Efficiency of PSAM n Conventional PSAM requires a bandwidth expansion. u u u 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: F n u Rayleigh fading F u fd. Ts =. 005 Turbo code F F Kc = 4, r = 1/2 L=4140 bit iterleaver

Performance in Rapid Fading n Rayleigh fading channel u n fd. Ts =. 02 Turbo code u u Kc = 4, r = 1/2 L=4140 bit interleaver

Other Applications of the Turbo Principle Turbo principle n n The turbo-principle is more general than merely its application to the decoding of turbo codes. Other applications of the turbo principle include: u u 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.

Serial Concatenated Turbo Codes Serial Concatenated Codes Outer Data Convolution al Encoder interleaver Inner Decode r deinterleav er n(t) AWGN Extrinsic Information Outer Decoder Turbo Decoder Estimated Data

Turbo Equalization Turbo EQ Can model intersymbol interference channel as an FIR filter (Outer) Data Convolution al Encoder interleaver ISI Channel interleaver SISO Equaliz er deinterleav er n(t) AWGN Extrinsic Information (Outer) SISO Decoder Turbo Equalizer Estimated Data

Turbo Multiuser Detection Turbo MUD Convolution al Encoder #1 Convolution al Encoder #K Time-varying FIR filter “multiuser interleaver” interleaver #1 Parallel to Serial Channel MAI Channel Model n(t) AWGN interleaver #K multiuser interleaver SISO MUD multiuser deinterleav er Extrinsic Info Bank of K SISO Decoders Turbo MUD Estimated Data

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

Performance of Turbo-MUD for CDMA in AWGN n n n K = 5 users Spreading gain Ns = 7 Convolutional code: Kc = 3, r=1/2 n n Eb/No = 5 d. B 1 K 9

Performance of Turbo-MUD for CDMA in Rayleigh Flatfading n n K = 5 users Fully-interleaved fading n n Eb/No = 9 d. B 1 K 9

Time Division Multiple Access n TDMA: Time Division Multiple Access u Turbo MUD u u n n 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, gk(t) = g(t) for all cochannel k. MUD for TDMA u u Usually there is only one user per time-slot per cell. The interference comes from nearby cells. F u with Intercell interference. Observations from only one base station might not be sufficient. F Performance is improved by combining outputs from multiple base stations.

Performance of Turbo-MUD for TDMA in AWGN n n n K = 3 users Convolutional code: Kc = 3, r=1/2 Observations at 1 base station n n Eb/No = 5 d. B 1 K 9

Performance of Turbo-MUD for TDMA in Rayleigh Flat. Fading n n K = 3 users Fully-interleaved fading n n Eb/No = 9 d. B 1 K 9

n n Turbo MUD n n 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 MUD’s. Extrinsic Info Multiuser Detector #1 Bank of K SISO Channel Decoders Multiuser Detector #M Estimated Data

Distributed Multiuser Detection n n First, consider the case where each user is uncoded. Each base station has a multiuser detector. Turbo MUD u u n 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

Cellular Network Topology F 3 F 4 F 2 F 1 F 3 F 5 F 7 F 4 F 2 F 1 F 5 F 7 F 6 F 3 F 6 F 4 F 2 F 1 F 5 F 7 F 6 n Conventional layout u u Isotropic antennas in cell center Frequency reuse factor 7 n Alternative layout u 120 degree sectorized antennas F u Located in 3 corners of cell Frequency reuse factor 3

Performance of Distributed MUD n n n Without diversity combining. Fully-interleaved Rayleigh fading Output from BS closest to the mobile used to make decision. n n With diversity combining. M=3 base stations Mobiles randomly placed in cell. Exponential path loss, ne = 3.

Performance of Distributed MUD n Eb/No = 20 d. B 1 K 9 n For conventional receiver: n u u n With multiuser detection: u u n Performance degrades quickly with increasing K. Only small benefit to using observations from multiple BS. 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.

Cooperative Decoding for the TDMA Uplink n Turbo MUD n n Now consider the coded case. The outputs of the MUD’s 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 Multiuser Detector #M Estimated Data

Performance of Cooperative Decoding n K = 3 transmitters u n M = 3 receivers (BS’s) u u n n Randomly placed in cell. Corners of cell path loss ne = 3 Fully-interleaved Rayleigh flat-fading Convolutional code u Kc = 3, r = 1/2

Performance of Cooperative Decoding n n Eb/No = 5 d. B 1 K 9 u n n M = 3 receivers For conventional receiver: u u n Performance degrades quickly with increasing K. Only small benefit to using observations from multiple BS. With multiuser detection: u u n Randomly placed in cell. Performance degrades gracefully with increasing K. No benefit after third iteration. Could allow an increase in TDMA system capacity.

Conclusion n Turbo code advantages: u Conclusion n Turbo code disadvantages: u u u n Remarkable power efficiency in AWGN and flat-fading channels for moderately low BER. 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. u u Turbo-multiuser detection can improve performance of coded multiple-access systems. When applied to TDMA networks, can allow multiple users per time/frequency slot.

Future Work n Turbo codes for wireless communications. u We have addressed the issue of carrier synchronization. Conclusion F F u u n 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. u u u Reduced complexity implementations. Methods for performing channel estimation. Study the impact on network architecture/control. F Multiuser detection at a network level.

Contributions/Publications n Turbo codes for the wireless channel u Use of pilot symbols for channel estimation F Performance curves for Rician channels u 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 flatfading 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. u Publications n n n Combined pilot symbol-assisted and decision-directed decoding

Contributions/Publications n Multiuser detection for coded multiple-access networks Log-MAP multiuser detection algorithm. u Distributed multiuser detection using observations from multiple receivers. u 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 Miniconference, 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. Publications u n n n

Web Page n For more information visit: u http: /www. ee. vt. edu/valenti/turbo. html

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

Turbo Multiuser Detection n The “inner code” of a serial concatenation could be a multiple-access interference (MAI) channel. Turbo MUD u u 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.

Low Power Communications n Goal for modern communication system design: Introduction u n Reduce the minimum signal-to-noise power ratio (SNR) required by the receiver Benefits: u Allows more design flexibility F The transmitted signal can be less powerful • • F F F 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

How to Achieve Low Power Communications n Introduction n P = E b. R b Lower the data rate Rb u Source coding: F F F n Compression Compaction Vocoding Lower the energy per bit Eb required at the receiver u Signal processing: F F F u Equalization Multiuser detection “Smart” antennas Channel coding

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

Turbo Codes n Background: Turbo Codes u u n Turbo codes were proposed by Berrou and Glavieux in the 1993 International Conference in Communications. Performance within 0. 5 d. B of the channel capacity limit for BPSK was demonstrated. Features of turbo codes: u u Recursive convolutional encoders Parallel code concatenation Nonuniform or “Pseudo-random” interleaving Iterative decoding

Performance Bounds for Linear Block Codes Turbo Codes n n n Union bound for maximum likelihood soft-decision decoding: Or: The minimum-distance asymptote is the first term of the sum:

Performance of Turbo Equalizer n M=5 independent multipaths u u u n Convolutional code: u n Symbol spaced paths Stationary channel Perfectly known channel. Kc=5 r=1/2 u C. Douillard, et al “Iterative Correction of Intersymbol Interference: Turbo. Equalization”, European Transactions on Telecommuications, Sept. /Oct. 97.

Performance of Serial Concatenated Turbo Code n n n Rate r=1/3 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.

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