H. Bölcskei | Searcharxiv

arXiv2021

Beurling-type density criteria for system identification

This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delay-Doppler shifts without a lattice (or other geometry-discretizing) constraint on the support set. Concretely, we show that a class of such LTV systems is identifiable whenever the upper uniform Beurling density of the delay-Doppler support sets, measured uniformly over the class, is strictly less than 1/2. The proof of this result reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Moreover, we show that this density condition is also necessary for classes of systems invariant under time-frequency shifts and closed under a natural topology on the support sets. We furthermore show that identifiability guarantees robust recovery of the delay-Doppler support set, as well as the weights of the individual delay-Doppler shifts, both in the sense of asymptotically vanishing reconstruction error for vanishing measurement error.

cs.IT↗

arXiv2007

Distributed spatial multiplexing with 1-bit feedback

We analyze 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., in IEEE Trans. Inf. Th. (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 approaching 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''. Finally, we characterize the corresponding crystallization rate.

cs.IT↗