Closed-Form Capacity Result for Interference-Limited Environments With Mixed Fading

We study a multinode network, where a multi-antenna transmitter Tx communicates with its desired receiver Rx, whereas a cluster P ≡̂ {P
_x,n
, n = 1, . .. ,N} of unintended nodes is disturbed by the Tx-Rx (TR) communication. To prevent severe performance degradation, we impose a constraint on the total interference that is inflicted at the nodes of P. The TR link contains a line-of-sight component, whereas the propagation environment for each Tx-Px,n link is shadowed. The Tx node is preprocessing the information sequence by means of a precoding matrix that is optimized to achieve the ergodic capacity under a constraint on the maximum admissible ergodic interference power, arriving on P. In this paper, we show that the optimum precoding strategy involves the transmission of a single stream over the precoding direction, i.e., the eigenvector of the precoding matrix, which corresponds to beamforming along the instantaneous direction of the TR-link channel. The solution of the remaining power allocation problem yields the optimal precoding matrix. For this setup, we provide an efficient stochastic characterization of the network, which allows us to obtain an analytical expression for the TR-link ergodic capacity; this problem has been previously open, even for the case of a single-antenna node Tx and a single-element set P. We complement the analysis by deriving the TR-link signal-to-noise ratio and the average bit error rate, which are associated with our transmission scheme. Numerical results corroborate the theoretical analysis and reveal an interplay between the network parameters and their impact on the TR-link performance.