Algorithms for Wireless Channel Equalization with Joint Coding and Soft Decizion Feedback

Abstract

The paper proposes a new approach based on Joint Entropy Maximisation (JEM) using a soft decision feedback equalizer (S-DE) to suppress error propagation. In its first section, the paper presents the principle of the solution and the theoretical framework based on entropy maximisation, which allows introducing the soft decision device without assuming that the channel distortion is Gaussian. Because JE is a nonlinear function, a gradient descent algorithm is used for maximising. Then an equivalence of JEM and ISIC (Inter-Symbol Interference Cancellation) is proved in order to establish that an equalised single carrier system using coded modulation (8- phase shift keying associated with a convolution code) offers similar performances when compared with multicarrier modulation. In the second section the paper develop an adequate receiver model for joint convolution coding and S-DFE. The error correction decoder uses a standard Viterbi algorithm. The DFE consists of a feedforward finite impulse response (FIR) filter (FFF) and a feedback filter (FBF) implemented as a transversal FIR filter. FFF eliminates the precursor ISI, while FBF minimise the effect of residual ISI using soft decisions by the joint coding and equalisation process. The third main section of the paper describes the proposed method for estimating optimum soft feedback using a maximum a posteriori probability (MAP) algorithm. Then, performances of the soft decision device in a simulated environment are analysed on a structure with 8 taps for FFF and 5 taps for FBF. Since the purpose of the evaluation was to compare the proposed S-DFE with a former HEFE, the coded packet error rate was estimated in a two-path and in a six- path channel. We have shown that in some case the proposed algorithm offers better convergence rate and robustness when compared with the corresponding existing algorithm. Some conclusions on the extension of the S-DFE techniques in vary applications are finally presented.