Nonparametric trellis equalization in the presence of non-gaussian interference

A PDF Estimation-Based Iterative MIMO Signal Detection With Unknown Interference

“…After upper bounding we obtain that , where . After some calculations it can be shown that (10) yielding a lower bound on (11) Note that the result shown in [6] is a special case of (11) for . The estimate of gives an asymptotically unbiased and consistent PDF estimator for chosen to be , since and .…”

“…Unlike that, the proposed receiver uses first samples , to make the estimate of PDF of and uses maximum likelihood (ML) detection to calculate extrinsic information (4) Assuming perfect soft-cancellation the true PDF is multimodal Gaussian, and it is given by (5) where , , and vectors depend on the entries of . Instead of estimating parameters and and using them in (5) to obtain estimate 1 , we use kernel-smoothing [5], [6] that approximates directly with (6) where is Gaussian kernel and is the smoothing parameter [5] to be optimized. It will be shown in the sequel that this choice of kernel gives an asymptotically unbiased and consistent PDF estimator [6].…”

“…Instead of estimating parameters and and using them in (5) to obtain estimate 1 , we use kernel-smoothing [5], [6] that approximates directly with (6) where is Gaussian kernel and is the smoothing parameter [5] to be optimized. It will be shown in the sequel that this choice of kernel gives an asymptotically unbiased and consistent PDF estimator [6]. It will also be shown that receiver based on (6) does not require knowledge of or , and that even no exact knowledge of is necessary for satisfactory performance in a variety of scenarios.…”

“…From (7) the optimal smoothing parameter is found to be (9) with . can be upper bounded by using Cauchy's inequality as it was done in [6] for the univariate case. After upper bounding we obtain that , where .…”

Noise benefits in joint detection and estimation problems

“…The mixture background noise is encountered in a variety of contexts [44] (and references therein) such as co-channel interference [45], ultra-wideband synthetic aperture radar (UWB SAR) imaging [46], and underwater noise modeling [47]. The standard deviation values are taken to be equal for all the mixture components just to simplify the analytical evaluation of this problem for K 41.…”