Shmuel Saadi-Blind equalization of moving average channels over Galois fields

Electrical Engineering Systems Seminar

Speaker: Shmuel Saadi

M.Sc. student under the supervision of Prof. Arie Yeredor

Sunday, 11^th February 2024, at 15:00

Room 011, Kitot Building, Faculty of Engineering

Blind equalization of moving average channels over Galois fields

Abstract

This work presents three different approaches for the estimation (or equalization) of the blind moving average (MA) channel over finite fields. In this framework, the channel's input signal, output signal, and coefficients all belong to a Galois (finite) field of prime order, and all the arithmetics (additions and multiplications) are calculated modulo the field's order.

The source signal is assumed to be a sequence of independent and identically distributed (iid) samples with an unknown distribution. The goal is to estimate the channel's coefficients from the output signal alone.

In the first approach, we try to maximize the source's implied probability vector's norm (with respect to the channel's coefficients) and based on new theories and insight that we present in this work, we show that this maximization process yields a consistent estimate of the channel's coefficients that define the MA channel (and thus solve the equalization problem).

The second approach attempts to factorize the empirical characteristic tensor of the output, where the factors are the unknown characteristic vectors of the channel's source at different indices, which depend on the channel's coefficients. Applying a logarithmic operator, we obtain a set of linear equations that leads us to solve a least-squares (LS) problem, whose solution is an implied estimate of the second characteristic vector of the channel's source that yields the minimum squared error (MSE) for a specific hypothesized set of channel coefficients.

Repeating this process for every possible set of channel coefficients (out of a finite number of possibilities) leads us to the true set as explained in detail in this work.

The last approach is based on a sequential identification of the polynomial factors of the channel's associated polynomial (the Z-transform of its impulse response). By using this sequential approach, we "break" the problem into smaller problems (with smaller channel orders) that are easier to solve. Once we identify all the factors, we can easily compose the original associated polynomial and extract the channel's coefficients.

For each approach, we explain the advantages and disadvantages, demonstrate their performance by simulations with different parameter settings, and compare them to each other. Note that since, to the best of our knowledge, this work is the first attempt to solve this problem, there are no other known approaches to compare to.

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