2011/09/20 by Chenwei Wang, Wang, Chenwei, Tiangao Gou +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #Antenna Design and Analysis #Antenna Design and Optimization #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1109.4350
84 pages, 19 figures, 1 table
arxiv created 2011/09/20 · openalex publication_date 2011/09/20 · arxiv updated 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the 3 user MT x MR MIMO interference channel has d(M,N)=min(M/(2-1/k),N/(2+1/k)) degrees of freedom (DoF) normalized by time, frequency, and space dimensions, where M=min(MT,MR), N=max(MT,MR), k=ceilM/(N-M). While the DoF outer bound is established for every MT, MR value, the achievability is established in general subject to normalization with respect to spatial-extensions. Given spatial-extensions, the achievability relies only on linear beamforming based interference alignment schemes with no need for time/frequency extensions. In the absence of spatial extensions, we show through examples how essentially the same scheme may be applied over time/frequency extensions. The central new insight to emerge from this work is the notion of subspace alignment chains as DoF bottlenecks. The DoF value d(M,N) is a piecewise linear function of M,N, with either M or N being the bottleneck within each linear segment. The corner points of these piecewise linear segments correspond to A=1/2,2/3,3/4,... and B=1/3,3/5,5/7,.... The set A contains all values of M/N and only those for which there is redundancy in both M and N. The set B contains all values of M/N and only those for which there is no redundancy in either M or N. Our results settle the feasibility of linear interference alignment, introduced by Cenk et al., for the 3 user MT x MR MIMO interference channel, completely for all values of MT, MR. Specifically, the linear interference alignment problem (MT x MR, d)3 (as defined in previous work by Cenk et al.) is feasible if and only if d<=floord(M,N). With and only with the exception of the values M/N∈ B, we show that for every M/N value there are proper systems that are not feasible. Our results show that M/N∈ A are the only values for which there is no DoF benefit of joint processing among co-located antennas at the transmitters or receivers.