On the Multiplexing Gain of K-user Partially Connected Interference Channel

The multiplexing gain (MUXG) of $K$-user interference channel (IC) with partially connected interfering links is analyzed. The motivation for the partially connected IC comes from the fact that not all interferences are equally strong in practice. The MUXG is characterized as a function of the number ($K$) of users and the number ($N \geq 1$) of interfering links. Our analysis is mainly based on the interference alignment (IA) technique to mitigate interference. Our main results are as follows: One may expect that higher MUXG can be attained when some of interfering links do not exist. However, when $N$ is odd and $K=N+2$, the MUXG is not increased beyond the optimal MUXG of fully connected IC, which is $\frac{KM}{2}$. The number of interfering links has no influence on the achievable MUXG using IA, but affects the efficiency in terms of the number of required channel realizations: When N=1 or 2, the optimal MUXG of the fully connected IC is achievable with a finite number of channel realizations. In case of $N \geq 3$, however, the MUXG of $\frac{KM}{2}$ can be achieved asymptotically as the number of channel realizations tends to infinity.