Optimal SIMO MLSE receivers for the detection of linear modulation corrupted by noncircular interference

Abstract

International audienceThis paper derives the optimal single input multiple output (SIMO) maximum likelihood sequence estimation (MLSE) receiver for the detection of quadrature amplitude modulations corrupted by potentially noncircular, stationary white or colored zero-mean Gaussian noise. It is proved that this receiver is composed by a widely linear (WL) filter followed by a modified version of the Viterbi algorithm. This WL linear filter is interpreted for complex-valued signal of interest (SOI) symbols as two WL multidimensional matched filter (WL MMF) that reduce to a single WL MMF for real-valued SOI symbols. The performance improvements of this receiver with respect to the standard SIMO MLSE are proved and illustrated

Enhanced Widely Linear Filtering to Make Quasi-Rectilinear Signals Almost Equivalent to Rectilinear Ones for SAIC/MAIC

“…In other words, it consists in computing the CT MLSE receiver from x(t) or x d (t), for R and QR signals respectively, assuming a Gaussian non-circular but stationary total noise n(t) or n d (t). It can be easily verified [53] that this approach is equivalent to computing the CT MLSE receiver from x(t) (R signals) or x d (t) (QR signals) in Gaussian circular stationary extended total noise n(t) or n d (t), respectively. To approximate the CT MLSE receiver in cyclostationary non-circular total noise, we adopt in the following the previous sub-optimal approach and we call it a CT two-input pseudo-MLSE approach.…”

“…For M = 2, these vectors correspond, for R signals, to x(t) and n(t), respectively, defined by (11), and for QR signals, to x d (t) and n d (t) respectively, defined by (15). Assuming a stationary, circular and Gaussian generic extended total noise n F (t), it is shown in [53], [54] that the sequence b ( b 1 , ..., b K ) which maximizes its likelihood from x F (t), is the one which minimizes the following criterion:…”

Reception filter impact on widely linear fresh receiver performance for SAIC/MAIC with frequency offsets

“…Assuming a stationary, circular and Gaussian generic FRESH total noise n p,F M (t), vector n p,F M ,δ (t) has the same properties. It is shown in [22], [23] that the sequence b (b 1 , ..., b K ) which maximizes its likelihood from x p,F M ,δ (t) is the one which minimizes the following criterion 1 :…”

Two and three inputs widely linear FRESH receivers for cancellation of a quasi-rectilinear interference with frequency offset

“…We assume that x EF1 (t) and n EF1 (t) correspond to x(t) and n(t) respectively. Assuming a stationary, circular and Gaussian generic extended FRESH total noise n EF M (t), it is shown in [22], [23] that the sequence b (b 1 , ..., b K ) which maximizes its likelihood from x EF M (t) is the one which minimizes the following criterion 1…”

“…Nevertheless, while its performance correspond to those of the conventional receiver for a spectral overlap which is less than 50%, it has better performance than the conventional receiver for a spectral overlap comprised between 50% and 75%. For a spectral overlap which is greater than 75% and for a strong CCI, (22) shows that the extended two-inputs WL FRESH receiver discriminates the sources spectrally and by phases and the output SINR depends on the differential phase of the sources and then on n. It completely cancels the CCI as long as there is at least one of the two discriminations (spectrum or phase) between the sources (∆ f , Ψ sI,n ) = (0, kπ). However (22) shows that the relative weight of the phase discrimination with respect to the spectral one increases with the spectral overlap.…”