The performance of Fano-multiple symbol differential detection

Multiple-symbol differential detection (MSDD) is a robust maximum-likelihood (ML) receiver technique for frequency-nonselective fast Rayleigh fading channels. However, its complexity grows exponentially with the block size N and that makes it impractical to implement. Recently, multiple-symbol differential sphere decoder (MSDSD) is developed to alleviate this problem but its complexity at low signal-to-noise ratio (SNR) grows exponentially with decreasing SNR. In this paper, we explore the potential of the Fano algorithm as an efficient MSDD receiver. The bit-error performance and the complexity of the Fano-MSDD are evaluated and compared with other reduced complexity techniques. Our preliminary results indicate that Fano-MSDD is more attractive than decision-feedback differential detection (P.Y. Kam and CH Teh, 1983) and (R Schober and WH Gerstacker, 2000) from both the error performance and the complexity points of view. When compared to the MSDSD, the Fano-MSDD suffers a moderate degradation in power efficiency. However, its computational complexity is very steady even at low SNR. This translates into a dramatic saving in complexity over the MSDSD when SNR is low. Even at large SNR, the Fano-MSDD still provides a small edge over the MSDSD in terms of complexity. We believe that with some fine tuning of the decoder parameters, such as the bias and the threshold´s step size, it is possible to extract better performance from the Fano decoder than it is now.