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In this paper, the transmission of an improper-complex second-orderstationary data sequence is considered over a strictly band-limitedfrequency-selective channel. It is assumed that the transmitter employs linearmodulation and that the channel output is corrupted by additive proper-complexcyclostationary noise. Under the average transmit power constraint, the problemof minimizing the mean-squared error at the output of a widely linear receiveris formulated in the time domain to find the optimal transmit and receivewaveforms. The optimization problem is converted into a frequency-domainproblem by using the vectorized Fourier transform technique and put into theform of a double minimization. First, the widely linear receiver is optimizedthat requires, unlike the linear receiver design with only one waveform, thedesign of two receive waveforms. Then, the optimal transmit waveform for thelinear modulator is derived by introducing the notion of the improprietyfrequency function of a discrete-time random process and by performing a linesearch combined with an iterative algorithm. The optimal solution shows thatboth the periodic spectral correlation due to the cyclostationarity and thesymmetric spectral correlation about the origin due to the impropriety are wellexploited.

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