Channel Independent Viterbi Algorithm (CIVA) for Blind Sequence Detection with Near MLSE Performance Xiaohua(Edward) Li State Univ. of New York at Binghamton

Contents Introduction Basic idea of Probes and CIVA Practical Algorithms –Probes design –CIVA Simulations Conclusion

Analogy From DNA Array Probes: all possible DNA segments Probes are put on an array (chip) DNA sample binds to a unique probe

Basic Idea of CIVA: Testing Vector Communication System Model Testing vectors n v n H n x  sh

Basic Idea of CIVA: Noiseless Symbol Detection Find a testing vector for each possible symbol matrix Testing vector set: Determine testing vector sequence Detect symbols from

Construct Probe as Testing Vector Group Requirement on testing vectors not always satisfied Probe of : three cases – right null subspace different from – right null subspace in that of – and have the same right null subspace,

Blind Sequence Detection by Probes If are different in the right null subspace, then the corresponding probes are different Blind symbol detections: Do the probes sharing cases matter?

Sequence Identifiability Assumption 1: sequences begin or terminate with the same symbol matrix. Assumption 2: Proposition 1: Sequences can be determined uniquely from each other. Proposition 2: In noiseless case, symbols can be determined uniquely from data sequence and probes. If SNR is sufficiently high, then symbols can be determined uniquely with probability approaching one. Assumptions 1 and 2 can be relaxed in practice.

Trellis Search With Probes Metric calculation Trellis optimization

Trellis Search with Probes Metric updating along trellis An example:

Channel length Over-estimation in Noise For known channel length, Probe & trellis dim parameters: Use over-estimated channel length and for probe and trellis design Consider data matrix Choose proper

How to Determine Optimal N? In noiseless case, A large magnitude change in Optimal value can be determined.

Practical Algorithm I Probe Design Algorithm Many symbol matrices have more than one dim right null subspace: optimize testing vectors Select/combine testing vectors based on the trellis diagram: simplify probes design Further simplification: each probe contains at most three testing vectors. It is off-line! Probes are independent of channels.

Practical Algorithm II CIVA Algorithm Probes design with over-estimated channel length Form data matrix, determine the optimal Trellis updating Symbol determination Properties No channel and correlation estimation Fast, finite sample, global convergence –Symbol detection within samples –Tolerate faster time-variation index

Computational Complexity High computation complexity: trellis states May be practical for some wireless system Complexity reduction: desirable and possible –Parallel hardware implementation –Apply the complexity reduction techniques of VA –Integrated with channel decoder: promising complexity reduction, may even lower than MLSE. –Fast algorithms combining the repeated/redundant computations

Simulations: Experiment 1 Channel Symbol matrix, probe Testing vectors S1g1 S2g2, g4, g1 s3g3,g6, g4 s4g4, g5, g3

Simulations: Experiment 2 Random Channel Index Ratio Determine N independent of channel

Simulations: Experiment 2 Comparison –CIVA –MLSE –VA w/ training –MMSE training –Blind:VA+blind channel. est. 500 samples CIVA: 3 dB from MLSE

Simulations: Experiment 3 GSM like packets 3-tap random ch. 150 DQPSK samples/running CIVA: blind VA & MMSE: 30 training samples CIVA practically outperforms training methods.

Conclusions CIVA blind sequence detector using probes Properties Near ML optimal performance May practically outperform even training methods Fast global convergence Near future: complexity reductions Combining channel decoders Fast algorithm utilizing repeated structures