Opportunistic Interference Alignment in Poor Scattering Channels

Opportunistic interference alignment (OIA) is known to achieve the optimal degrees of freedom (DoF) in the interfering multiple-access channel (IMAC) with independent and identically distributed (i.i.d.) Rayleigh fading, provided that a certain user scaling condition is satisfied. We analyze the performance of OIA in a poor scattering
$K$
-cell single-input multiple-output IMAC, where there exist finite paths between the transmitter and receiver sides. Under the feasible model, we characterize a lower bound on the cumulative density function (cdf) of the leakage of interference (LIF) generated by each mobile station (MS) and then derive a new fundamental user scaling law that is, required to achieve a target DoF, which generalizes the existing achievability result shown for the i.i.d. Rayleigh fading case. Our main result indicates that
$KS$
DoF is achievable if the number of per-cell MSs scales at least as
$\mbox{SNR}^{(K-1)\min(L,S)}$
, where
$L$
denotes the number of paths and
$S$
denotes the number of simultaneously transmitting MSs per cell. We also show how to obtain the non-integer DoF when the above user scaling condition is not strictly satisfied for given system parameters. To verify our achievability result for finite system parameters, computer simulations are performed along with comparison to the i.i.d. Rayleigh channel case. The amount of LIF is first evaluated numerically and is shown to be consistent with our theoretical result. The achievable sum rates are also evaluated.