where is a sequence of matrices containing the impulse responses of the mixing channels, and the operator "*" denotes matrix convolution.
where is the source vector, is the observed vector, is a sequence of matrices containing the impulse responses of the mixing channels, and the operator "*" denotes matrix convolution.
where is the beamforming output vector, is the observed vector, is a sequence of matrices containing the impulse responses of beamformer, is the global impulse response by combining and, and the operator "*" denotes matrix convolution.
where is a sequence of matrices containing the impulse responses of the beamformer, is length of the beamforming filter, and is the beamformed output vector.
However, in the aforementioned two literatures, the sparsifying matrix constructed using the impulse response for voiced speech is impractical for its dependence on the currently reconstructed signal itself.
Here H i) denotes the q × p real constant matrix corresponding to the impulse response of the channel at time i and S(n−i) is the source vector at time (n−i).
where is the identity matrix, vector,, ; and are both convolution matrices by cascading the impulse response, that is, (25).
where n is the discrete-time sample index, x j [n] is the discrete-time OFDM signal transmitted by user j, H ij [n] is the matrix impulse response of the frequency-selective MIMO channel between transmitter j and receiver i, μ ij denotes the delay between transmitter j and receiver i, and ∗ denotes convolution.
p ̂ y, PD is an estimate of the joint probability density function (pdf) of dimension PD over all P (here, P = 2) output channels, and p ̂ y q, D is the estimated multivariate pdf for channel q of dimension D. Matrix W captures all the impulse response coefficients of the demixing filters, with a detailed description of its structure given in [31, 32].
In a first step, the matrix impulse responses are measured with a channel sounder.
