Generalized Framework for the Analysis of Linear MIMO Transmission Schemes in Decentralized Wireless Ad Hoc Networks

Asymptotic data rates of limited-rank transmissions in wireless networks with interferers at correlated locations

“…h = r T and α = 4 and M = 2 or 4 were considered. Figure 3 shows simulated mean spectral efficiencies along with (12). For N ≥ 8 antennas, in both the simulated cases, the mean spectral efficiency and the asymptotic prediction are within 3% of each other which validates the approximation.…”

“…Moreover, (12) indicates that the mean spectral efficiency can be kept approximately constant with increasing ρ if N is increased linearly, which suggests that to the extent that the system assumptions hold (in particular the independent fading), a higher density of active transmissions can be accommodated by using a larger number of antennas. Moreover (12) indicates that to the extent that the approximations above hold, there is an optimum value for M which trades off the multiplexing gain with the increased interference as each interferer appears like M interferers from the perspective of the representative receiver. This optimization can be performed using steps similar to Problem of 14.6 of [14] in which an equation of a similar form is maximized.…”

“…An additional mobile (the representative transmitter) is then placed at random in the cell at the origin and is assumed to be active. Conditioned on the distance between the representative transmitter and the base-station at the origin r T , the spectral efficiency of the representative link assuming large numbers of antennas at the base station is given by (12) with an appropriate value for the density of active mobiles ρ.…”

“…Combining (13) and (12) yields an approximation to the spectral efficiency conditioned on the link-length r T . Assuming that the representative transmitter is located with uniform probability in the cell at the origin, we can approximate the CDF of the spectral efficiency using the CDF of the length of a random link for the hexagonal-cell model F r (r), which can be found in Lemma 2 of [18].…”

“…We limit the rank of transmit covariance matrices which has been shown to increase the network-wide spectral efficiencies in a wide range of networks with spatially independent transmitters (e.g. [8], [9], [10], [11], [12]). Such a limitation results directly if the number of transmitter antennas is small or can be imposed by a protocol in order to increase network-wide performance.…”