The effect of poor scattering on the degrees-of-freedom in interfering multiple-access 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 derive a new fundamental user scaling law, 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 mobile stations (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. 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 leakage of interference is numerically evaluated and is shown to be consistent with our theoretical result. The achievable sum-rates are also evaluated.