Interference, information and performance in linear matrix modulation

The choice of basis for linear matrix modulation (linear space-time code with rotated and linearly combined constellation) is considered. Unitarily invariant polynomials of square matrices are discussed, the full spectrum of invariants interpolating between the well-known trace and determinant. These give the full spectrum of space-time code design criteria. The diagonal dominance (expansion around the trace) of these invariants is considered. Using this, it is shown that minimizing the self-interference, or equivalently, maximizing the second order expansion coefficient of the mutual information around SNR=0, is required when maximizing the mutual information and/or optimizing performance at any SNR. As an example, symbol rate 3 schemes for 4 transmit antennas are considered.