A Bandwidth Efficient Pilot Symbol Technique for Coherent Detection of Turbo Codes over Fading Channels Matthew C. Valenti Dept. of Comp. Sci. & Elect. Eng. West Virginia University Brian D. Woerner Mobile and Portable Radio Research Group Bradley Dept. of Elect. & Comp. Eng. Virginia Tech

Overview Turbo codes. Practical problems over fading channels. Methods for detecting turbo codes over fading channels. DPSK-based Pilot-based Improved pilot-symbol techniques Iterative channel estimation parity-symbol stealing

Turbo Codes Features: Parallel Code Concatenation Can also use a serial concatenation Nonuniform interleaving Recursive systematic encoding Usually RSC convolutional codes are used. Can use block codes. Iterative decoding algorithm. Max-log-MAP log-MAP SOVA

Recursive Systematic Convolutional Turbo Encoder The data is encoded twice by two identical RSC encoders A nonuniform interleaver changes the ordering of bits at the input of the second encoder. MUX increases code rate from 1/3 to 1/2. Systematic Output Input Encoder #1 MUX Parity Output Encoder #2 Nonuniform Interleaver Length L Constraint length K Recursive Systematic Convolutional (RSC) Encoder

Iterative Decoding One decoder for each elementary encoder. Deinterleaver Extrinsic Information Extrinsic Information Interleaver systematic data Decoder #1 Decoder #2 hard bit decisions parity data DeMUX Interleaver One decoder for each elementary encoder. Estimates the a posteriori probability (APP) of each data bit. Extrinsic Information is derived from the APP. Each decoder uses the Log-MAP algorithm. The Extrinsic Information is used as a priori information by the other decoder. Decoding continues for a set number of iterations.

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.

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

Fading Channel Types Types of channels 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: A=constant and X(t)=Y(t)=0 Rayleigh fading: A=0 Rician fading: A > 0, =A2/22 Correlated fading: Fully-interleaved fading:

Channel Estimation for 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.

The Phase Ambiguity Problem If the receiver is operating at low SNR, accurate estimates of the phase n will not be available. A proactive solution to the phase ambiguity problem is required. Use DPSK. Differential detection Multiple-symbol differential detection. Use a pilot. Pilot tone. Pilot symbol.

DPSK for Turbo Codes One solution is to use DPSK. When differential detection is used, a severe loss in performance is noted. ~ 4.5 dB loss for turbo codes in Rayleigh fading Called the noncoherent combining loss. Not a viable option. However, multiple-symbol differential detection can be used to approach coherent performance. Considered for convolutional codes in: P. Hoeher and J. Lodge, “Iterative encoding/demodulation of coded DPSK systems,” Globecom 98.

Multiple-symbol Differential Detection Can think of a differential encoder as a recursive convolutional code. Any coded system that uses DPSK can be thought of as a turbo code. Serially concatenated. Inner code = the differential encoder. Outer code = the channel code itself. Systems using DPSK don’t need pilot symbols. The decoder can use per-survivor processing to estimate the channel. However, this is still a differential technique…

Coherent Detection using Pilot Symbols 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 PSAM has been shown to be more power efficient than TTIB for turbo codes. L.-D. Jeng, Y.-T. Su, and J.-T. Chiang, “Performance of turbo codes in multipath fading channels,” VTC 98.

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 symbol #1 pilot symbol symbol #Mp symbol #1 pilot symbol symbol #Mp pilot symbols added here

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. channel estimator Tentative estimates of the code bits matched filter symbol mapper channel interleaver symbol demapper channel deinterl. turbo decoder Final estimates of the data

Performance of Pilot Symbol Assisted Decoding Simulation parameters: Rayleigh flat-fading Correlated: fdTs = .005 channel interleaving depth 32 Turbo code r=1/2, Kc =4 1024 bit random interleaver 8 iterations of log-MAP Pilot symbol spacing: Mp = 8 Wiener filtering: Nc = 30

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.

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 Puncture parity bits at the same rate that pilot symbols are inserted. Must be careful about how this puncturing is done.

Simulation Results for Slow Fading Simulation Parameters: Rayleigh fading fdTs = .005 Turbo code constraint length K = 4 rate r = 1/2 L = 4140 bit interleaver

Performance in Rapid Fading Rayleigh fading channel fdTs = .02 Turbo code K = 4, r = 1/2 L= 4140 bit interleaver

Future Work Compare coherent PSAM technique with multiple-symbol DSPK technique. In terms of performance and complexity. Soft vs. hard decision feedback. Incorporate adaptability Adaptive estimation filters. Adaptive pilot-symbol spacing. Extend the results to higher order modulation and trellis coded modulation. Extend the results to the problems of symbol-timing estimation and frame synchronization.

Conclusions Pilot symbol assisted decoding can be used to achieve nearly coherent detection/decoding of turbo codes. Iterative estimation/decoding improves performance. Good performance even with just hard-decision feedback. Iterative estimation can also be used for other types of codes. Main disadvantage of PSAM is loss of bandwidth efficiency. BW efficiency can be recovered by overwriting parity bits with pilot symbols