Some of the more commonly used blind separation and deconvolution adaptation rules are constrained to only handling square matrices of filters [1]. For our experiment, we used the multichannel blind least-mean-square algorithm (MBLMS) described by Lambert [8].
The MBLMS algorithm attempts to minimize the cost function J where u is the estimated output and g is the Bussgang nonlinearity that uses prior knowledge of the probability density function (pdf) of the sources.
The weight update equation is determined from the cost function, where x is the mixture of sources:
We ran the algorithm on the four different filter configurations used in the previous section, using truncated and windowed room impulse responses as our mixing filters. Figure 6 shows one of these responses. We set the algorithm to learn 512-tap filters, and we used 200,000 gamma-distributed (speech-like) random samples.
Figure 6: A shortened room impulse response used in MBLMS
algorithm. The sampling rate was 11.025kHz.
We used a Multichannel Intersymbol Interference (ISI) performance metric to determine how close the learned unmixing filters were to a scaled and/or permuted identity FIR matrix [8]:
where 
are the filter elements of the mixing matrix, W
convolved with the separating matrix, A. The ISI converges to zero
for a perfectly learned unmixing matrix. Figure 7 shows
a comparison plot of the ISI measurements as the algorithm ran through
all the sample points for each configuration.
Figure 7: ISI measurements obtained from the MBLMS algorithm for
four different filter configurations.
The plots show that the MBLMS algorithm performs significantly better when the number of sensors are increased.