Adaptive Step-size Iterative Equalization for Underwater Communication

Abstract

This paper presents a fully adaptive Minimum Mean Square Error (MMSE) iterative equalization with a joint phase estimation, using various adaptive step-sizes scheme. To meet the requirement of fast convergence and low MSE over time-varying channels, we propose an original self-optimized algorithm whose step-sizes are updated adaptively and assisted by soft-information provided by the channel decoder in an iterative manner. Simulation results show that our proposal achieves better performance over various multipath time-varying channels, compared to the conventional equalizer using a fixed step-size.

Turbo Equalization for Underwater Communication Systems using Rotated Constellations

“…This section compares the performance of the proposed algorithm with that of the Turbo equalization method proposed for conventional constellations [8]. In our simulations, each block of 1024 bits is encoded with a turbo code of rate 1/3.…”

“…We first tested our proposal on a synthetic channel. Similar to [8], [9], [14], the channel response is modeled as follows:…”

“…where the Doppler shift is characterized by ϵ, P l denotes the average power of the l-th path, ψ l,i and ζ l,i are uniform random variables on [0, 2π[; I is set to 10, and (15) includes three paths of equal average power, with ϵ set to 0.002. Figure 3 compares the Bit Error Rate (BER) performance of the conventional QPSK with the Turbo equalization algorithm [8], the rotated QPSK with the conventional Turbo equalization algorithm [8], and the rotated QPSK with the proposed equalization algorithm on the channel (15). We can observe that, on this channel and with the chosen coding rate, rotated constellations provide significantly better performance in terms of BER, with a gain of about 0.7 dB compared to conventional QPSK when the same Turbo equalization algorithm is used.…”

“…where ∂J ∂µ and ∂J ∂γ can be easily obtained with some basic mathematical derivations. Note that, unlike conventional methods, the proposed step-size optimization can be carried out over all received symbols, not just over the preamble thanks to chosen definition of the mean square error (8).…”

“…In particular, the frequency selectivity of the UWA channel induces inter-symbol interference (ISI) that can seriously limit system performance. Following the discovery of turbo codes, turbo equalization was proposed: it allows a significant improvement in Bit Error Rate (BER) compared to previous classical approaches by iteratively considering the correlations between bits introduced by channel coding through exchange of information between the equalizer and channel decoder [8]- [14].…”