Distributed spatial multiplexing with 1-bit feedback


Jatin Thukral and Helmut Bölcskei


Allerton Conference on Communication, Control, and Computing, Monticello, IL, pp. 502-509, Sept. 2007, (invited paper).

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We analyze the feasibility of distributed spatial multiplexing with limited feedback in a slow-fading interference network with MN non-cooperating single-antenna sources and M non-cooperating single-antenna destinations. In particular, we assume that the sources are divided into M mutually exclusive groups of N sources each, every group is dedicated to transmit a common message to a unique destination, all transmissions occur concurrently and in the same frequency band and a dedicated 1-bit broadcast feedback channel from each destination to its corresponding group of sources exists. We provide a feedback-based iterative distributed (multi-user) beamforming algorithm, which "learns'' the channels between each group of sources and its assigned destination. This algorithm is a straightforward generalization, to the multi-user case, of the feedback-based iterative distributed beamforming algorithm proposed recently by Mudumbai et al., IEEE Trans. IT, 2006, submitted, for networks with a single group of sources and a single destination. Putting the algorithm into a Markov chain context, we provide a simple convergence proof. We then show that, for M finite and N going to infinity, spatial multiplexing based on the beamforming weights produced by the algorithm achieves full spatial multiplexing gain of M and full per-stream array gain of N, provided the time spent "learning'' the channels scales linearly in N. The network is furthermore shown to "crystallize'' in the sense that, in the large-N limit, the M individual fading links not only decouple (as reflected by full spatial multiplexing gain) but also converge to non-fading links. Finally, we quantify the impact of the performance of the iterative distributed beamforming algorithm on the crystallization rate, and we show that the multi-user nature of the network leads to a significant reduction in the crystallization rate, when compared to the M=1 case.


Feedback, spatial multiplexing, crystallization, Markov chains

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Copyright Notice: © 2007 J. Thukral and H. Bölcskei.

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