Ergodic interference alignment for the SIMO/MIMO interference channel

Ergodic interference alignment (IA) is a simple yet powerful tool that not only achieves the optimal K/2 degrees of freedom (DoF) of the K-user single-input single-output (SISO) interference channel (IC), but also allows each user to achieve at least half of its interference-free capacity at any SNR. By considering more general message sets, Nazer et al. also covered the MISO case. In this paper, we consider first the SIMO interference channel and extend ergodic IA techniques to this setting with N_r receive antennas. Our scheme achieves KN_r/(N_r + 1), which is the DoF yielded by (standard) IA and is also the DoF of the channel when K > N_r. Moreover, this technique exhibits spatial scale invariance. By combining the existing MISO and the new SIMO results, we can also cover MIMO with N_t transmit antennas for the cases where either N_t/N_r or N_r/N_t is an integer R, yielding DoF =3D min(N_t, N_r)KR/(R + 1) which is optimal for K > R.