In this paper, we present a maximum a posteriori probability (MAP) approach to the problem of blind estimation of single-input, multiple-output (SIMO), finite impulse response (FIR) channels. A number of methods have been developed to date for this blind estimation problem. Some of those utilize prior knowledge on input signal statistics. However, there are very few that utilize channel statistics too. In this paper, the unknown channel to be estimated is assumed as the frequency-selective Rayleigh fading channel, and we incorporate the channel prior distributions (and hyperprior distributions) into our model in two different ways. Then for each case an iterative MAP estimator is derived approximately. Performance comparisons over existing methods are conducted via numerical simulation on randomly generated channel coefficients according to the Rayleigh fading channel model. It is shown that improved estimation performance can be achieved through the MAP approaches, especially for such channel realizations that have resulted in large estimation error with existing methods.

In this paper, time-difference estimation of filtered random signals passed through multipath channels is discussed. First, we reformulate the approach based on innovation-rate sampling (IRS) to fit our random signal model, then use the IRS results to drive the nonlinear least-squares (NLS) minimization algorithm. This hybrid approach (referred to as the IRS-NLS method) provides consistent estimates even for cases with sub-Nyquist sampling assuming the use of compactly-supported sampling kernels that satisfies the recently-developed nonaliasing condition in the frequency domain. Numerical simulations show that the proposed NLS-IRS method can improve performance over the straight-forward IRS method, and provides approximately the same performance as the NLS method with reduced sampling rate, even for closely-spaced time delays. This enables, given a fixed observation time, significant reduction in the required number of samples, while maintaining the same level of estimation performance.

In this paper, a new approach to channel order selection of single-input multiple-output (SIMO), finite impulse response (FIR) channels is proposed for blind channel estimation. The approach utilizes cross spectral density (CSD) of the channel outputs, and minimizes the distance between two CSD's, one calculated non-parametrically from the observed output data, and the other calculated from the blindly estimated channel parameters. The CSD criterion is numerically tested on randomly generated SIMO-FIR channels, and shown to be very effective compared to existing channel order selection methods especially under low SNR settings. Blind estimates of the channels with the selected channel order also show superiority of the CSD criterion.