Opportunistic interference alignment for MIMO IMAC: Effect of user scaling over degrees-of-freedom

We consider a new opportunistic interference alignment (OIA) for the K-cell multiple-input multiple-output (MIMO) interfering multiple-access channel (IMAC) with time-invariant channel coefficients, where each cell consists of a base station (BS) with M antennas and N mobile stations (MSs) having L antennas each. In this paper, we propose three OIA techniques: antenna selection-based OIA, singular value decomposition (SVD)-based OIA, and vector-quantized (codebook-based) OIA. Then, their performance is analyzed in terms of user scaling law required to achieve KS degrees-of-freedom (DoF), where S(≤ M) denotes the number of simultaneously transmitting MSs per cell. As our main result, it is shown that the antenna selection-based OIA does not fundamentally change the user scaling required to achieve KS DoF if L is fixed, compared with the single-input multiple-output (SIMO) IMAC case. In contrast, it is shown that the SVD-based OIA can greatly reduce the required user scaling to SNR^{(K-1) S-L+1} through optimizing weight vectors at each MS. Furthermore, we show that the vector-quantized OIA can achieve the same user scaling as the SVD-based OIA case if the codebook size is beyond a certain value. For the vector-quantized OIA, we analyze a fundamental tradeoff between the quantization level (i.e., codebook size) and the required user scaling.