  We propose a method for MIMO decoding when channel state information (CSI) is
unknown to both the transmitter and receiver. The proposed method requires some
structure in the transmitted signal for the decoding to be effective, in
particular that the underlying sources are drawn from a hypercubic space. Our
proposed technique fits a minimum volume parallelepiped to the received
samples. This problem can be expressed as a non-convex optimization problem
that can be solved with high probability by gradient descent. Our blind
decoding algorithm can be used when communicating over unknown MIMO wireless
channels using either BPSK or MPAM modulation. We apply our technique to
jointly estimate MIMO channel gain matrices and decode the underlying
transmissions with only knowledge of the transmitted constellation and without
the use of pilot symbols. Our results provide theoretical guarantees that the
proposed algorithm is correct when applied to small MIMO systems. Empirical
results show small sample size requirements, making this algorithm suitable for
block-fading channels with coherence times typically seen in practice. Our
approach has a loss of less than 3dB compared to zero-forcing with perfect CSI,
imposing a similar performance penalty as space-time coding techniques without
the loss of rate incurred by those techniques.
