Asymptotic Spectral Efficiency of MIMO Ad hoc Networks

In this correspondence, we present an asymptotic analysis of spectral efficiency of MIMO ad hoc networks. We consider a MIMO ad hoc network where
L
links, each consisting of a transmitter/receiver pair, communicate independent information over the network, simultaneously. Each transmitter node has
Nt
antennas and each receiver node is equipped with
Nr
antennas. It is assumed that for each user, perfect channel state information (CSI) is available at its transmitter and receiver. The exact asymptotic spectral efficiency of large MIMO ad hoc networks has been considered to be an unsolved problem until now. A lower bound has been found by Chen and Gans based on using beamforming as a sub-optimal transmission scheme. In this work, we show that the previously presented lower bound is also an upper bound when L goes to infinity, all links use full power and single-user decoding is used; hence, it represents the exact asymptotic spectral efficiency (ASE) of the network. Therefore, the network ASE is equal to the mean value of the largest eigenvalue of the channel covariance matrix which is upper bounded by (¿{
Nt
}+¿{
Nr
})
²
for large values of
Nt
and
Nr
.