A new approach for designing and implementing ADF equalization for 5G frequency selective channel based on two operating phases of LS and RLS algorithms

In this paper, a new approach is proposed for implementing an adaptive decision feedback equalizer (ADFE) for the 5G channel. The proposed equalizer works in two phases. In the first phase, a least-squares (LS) algorithm with a variable-length training sequence is used to estimate the coefficients of the channel and the equalizer. In the second phase, the recursive least-squares algorithm estimates the channel and adapts the equalizer, jointly. According to the channel quality, a variable-length training sequence is used to estimate the channel vector and the coefficients of the equalizer. The feed-forward equalizer (FFE) compensates the effects of the transmitting filter and the channel filter. No matched filter is used in the receiver. The noise samples at the input of the proposed FFE are independent. The noise enhancement of the proposed FFE is less than the noise enhancement of its corresponding one in the conventional ADFE. The overall filtering response (OFR) from the input of the transmitting filter to the output of the FFE is calculated and used to estimate the coefficients of the feedback equalizer (FBE). The channel model, the FFE coefficients, the OFR vector, and the FBE coefficients are continuously updated every symbol period. Using a variable training sequence increases the bandwidth efficiency of the transmitted signal. Simulation results and real-time implementation measurements show that the convergence time and the steady-state error at the output of the proposed equalizer are smaller than their corresponding values in the conventional ADFE.