Downlink Average User Rate with Linear Precoding

　

In a multi-user cellular system, the downlink rate performance of each user is crucially determined by the precoding strategy. In the single-cell case, [Wang-Dai'15] presented a comparative study of the asymptotic rate performance of downlink multi-user systems with multiple BS antennas either co-located or uniformly distributed within a circular cell. Two representative linear precoding schemes, maximum ratio transmission (MRT), and zero-forcing beamforming (ZFBF), are considered, with which the effect of BS antenna layout on the rate performance is characterized. The analysis shows that as the number of BS antennas L and the number of users K grow infinitely while L/K → υ, the asymptotic average user rates with the co-located antenna (CA) layout for both MRT and ZFBF are logarithmic functions of the ratio υ. With the distributed antenna (DA) layout, in contrast, the scaling behavior of the average user rate closely depends on the precoding schemes. With ZFBF, for instance, the average user rate grows unboundedly as L,K →∞ and L/K → υ > 1, which indicates that substantial rate gains over the CA layout can be achieved when the number of BS antennas L is large. The gain, nevertheless, becomes marginal when MRT is adopted.

For the multi-cell case, a 1-tier (7-cell) cellular system was considered in [Liu-Dai'14] with K>>1 uniformly distributed users each equipped with N co-located antennas in each cell, and M BS antennas either co-located at the center of each cell or grouped into M/N uniformly distributed clusters. By assuming M,N →∞ and M/N → L>>K, an asymptotic lower-bound of the average per-antenna rate with block diagonalization (BD) in the DA layout is derived, and compared with the asymptotic average rate in the CA layout. It is shown that in contrast to the CA case where the asymptotic average per-antenna rate increases in the order of log2{L/K}, the asymptotic lower-bound of the average per-antenna rate with the DA layout has a larger scaling order of log2{ (L-K+1)^{α/2}/K}, where α > 2 is the path-loss factor. Simulation results verify that the average per-antenna rate in the DA layout has the same scaling order as its asymptotic lower-bound, and is much higher than that with the CA layout when L is large.