Effect of Window Size on the Performance of a Turbo Equalizer Using a SWMAP Algorithm

The excellent performance exhibited by the turbo codes is attributed, partly to the use of soft-in soft-out algorithms (SISO) and iterating the soft output between the constituent signal processors in the turbo decoder. The maximum a posteriori probability (MAP) and soft output Viterbi algorithm (SOVA) have been used as the workhorse of receivers that employ turbo principle. The MAP is preferred to SOVA because of its inherent ability to produce the log likelihood ratio (LLR) on each bit. However, it suffers from huge computational complexity, storage requirements. A sliding window MAP (SWMAP) algorithm addresses these two issues. Our objective in this paper is to investigate the effect of different window sizes on the average bit error rate (BER) performance of a turbo equalizer that uses this SWMAP as the equalizer and a SW SOVA algorithm as the decoder. This study is important as it establishes a lower limit on the window size that is acceptable without sacrificing much performance at a reasonable complexity. We evaluate the performance of this receiver by computer simulations. The results obtained for 3 different window sizes establish that, a window of size three times the length of the ISI channel is adequate to ensure a desirable performance with reduced complexity and storage.