Joint Transmitter and Receiver Optimization for Improper-Complex Second-Order Stationary Data Sequence

TL;DR

This paper develops a joint optimization framework for transmit and receive waveforms to minimize mean-squared error when transmitting improper-complex second-order stationary data over band-limited channels with cyclostationary noise.

Contribution

It introduces a novel frequency-domain optimization method for joint transmitter and receiver design considering impropriety and cyclostationarity.

Findings

Optimal waveforms exploit spectral correlation and impropriety.

The method achieves lower mean-squared error compared to traditional designs.

Iterative algorithm effectively finds the optimal transmit waveform.

Abstract

In this paper, the transmission of an improper-complex second-order stationary data sequence is considered over a strictly band-limited frequency-selective channel. It is assumed that the transmitter employs linear modulation and that the channel output is corrupted by additive proper-complex cyclostationary noise. Under the average transmit power constraint, the problem of minimizing the mean-squared error at the output of a widely linear receiver is formulated in the time domain to find the optimal transmit and receive waveforms. The optimization problem is converted into a frequency-domain problem by using the vectorized Fourier transform technique and put into the form of a double minimization. First, the widely linear receiver is optimized that requires, unlike the linear receiver design with only one waveform, the design of two receive waveforms. Then, the optimal transmit waveform for the linear modulator is derived by introducing the notion of the impropriety frequency function of a discrete-time random process and by performing a line search combined with an iterative algorithm. The optimal solution shows that both the periodic spectral correlation due to the cyclostationarity and the symmetric spectral correlation about the origin due to the impropriety are well exploited.