Broadcast approach for the sparse-input random-sampled MIMO Gaussian channel

We consider a MIMO (linear Gaussian) channel where the inputs are turned on and off at random, and the outputs are sampled at random with probability p. In particular, for a given probability of 'on' input q (input sparsity), we consider a scenario where the transmitter wishes to send information to a family of possible receivers characterized by different random sampling rates p ∈ [0,1]. For this setting, we focus on the broadcast approach, i.e., a coding technique where the transmitter sends information encoded into superposition layers, such that the number of decoded layers depends on the receiver sampling rate p. We obtain a method for calculating the power allocation across the layers for given statistics of the MIMO channel matrix in order to maximize the system weighted sum rate for arbitrary non-negative weighting function w(p). In particular, we provide analytical solutions both for iid and Haar distributed MIMO channel matrices. The latter case accounts also for DFT matrices (see [1]), with application to sparse spectrum signals with random sub-Nyquist sampling.