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Register a new userBlind Unwrapping of Modulo Reduced Gaussian Vectors: Recovering MSBs from LSBs
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We consider the problem of recovering $n$ i.i.d samples from a zero mean multivariate Gaussian distribution with an unknown covariance matrix, from their modulo wrapped measurements, i.e., measurement where each coordinate is reduced modulo $Delta$, for some $Delta>0$. For this setup, which is motivated by quantization and analog-to-digital conversion, we develop a low-complexity iterative decoding algorithm. We show that if a benchmark informed decoder that knows the covariance matrix can recover each sample with small error probability, and $n$ is large enough, the performance of the proposed blind recovery algorithm closely follows that of the informed one. We complement the analysis with numeric results that show that the algorithm performs well even in non-asymptotic conditions.
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We consider the problem of recovering a continuous-time bandlimited signal from the discrete-time signal obtained from sampling it every $T_s$ seconds and reducing the result modulo $Delta$, for some $Delta>0$. For $Delta=infty$ the celebrated Shannon-Nyquist sampling theorem guarantees that perfect recovery is possible provided that the sampling rate $1/T_s$ exceeds the so-called Nyquist rate. Recent work by Bhandari et al. has shown that for any $Delta>0$ perfect reconstruction is still possible if the sampling rate exceeds the Nyquist rate by a factor of $pi e$. In this letter we improve upon this result and show that for finite energy signals, perfect recovery is possible for any $Delta>0$ and any sampling rate above the Nyquist rate. Thus, modulo folding does not degrade the signal, provided that the sampling rate exceeds the Nyquist rate. This claim is proved by establishing a connection between the recovery problem of a discrete-time signal from its modulo reduced version and the problem of predicting the next sample of a discrete-time signal from its past, and leveraging the fact that for a bandlimited signal the prediction error can be made arbitrarily small.
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution.
This paper studies a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrary signal distribution, and forward error control (FEC) coding. We develop a universal Gram-Schmidt orthogonalization for orthogonal approximate message passing (OAMP). Numerous area properties are established based on the state evolution and minimum mean squared error (MMSE) property of OAMP in an un-coded LUIS. As a byproduct, we provide an alternative derivation for the constrained capacity of a LUIS. Under the assumption that the state evolution for OAMP is correct for the coded system, the achievable rate of OAMP is analyzed. We prove that OAMP achieves the constrained capacity of the LUIS with an arbitrary signal distribution provided that a matching condition is satisfied. Meanwhile, we elaborate a capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the numerical results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, capacity-approaching bit error rate (BER) performances are observed under various channel conditions.
Although the hardware complexity of the analog self-interference canceller in full duplex Multiple Input Multiple Output (MIMO) designs does not necessarily scale with the number of transceiver antennas, exploiting the benefits of analog cancellation in massive MIMO systems with hundreds of antenna elements is still quite impractical. Hybrid Analog and Digital (A/D) beamforming architectures have been lately considered as a candidate technology for realizing massive MIMO transceivers with very large number of antenna elements, but with much fewer numbers of Radio Frequency (RF) chains. In this paper, we present a novel architecture for full duplex hybrid A/D beamforming transceivers including multi-tap analog cancellation with reduced number of taps and simple multiplexers for efficient signal routing among the transceiver RF chains. Capitalizing on the proposed transceiver architecture, we present a joint design of analog cancellation and A/D beamforming with the objective to maximize the achievable full duplex rate performance. Representative millimeter wave simulation results demonstrate the effectiveness of the proposed architecture and algorithmic framework for enabling simultaneous uplink and downlink communications with reduced complexity analog self-interference cancellation.
In this paper, we study Full Duplex (FD) Multiple-Input Multiple-Output (MIMO) radios for simultaneous data communication and control information exchange. Capitalizing on a recently proposed FD MIMO architecture combining digital transmit and receive beamforming with reduced complexity multi-tap analog Self-Interference (SI) cancellation, we propose a novel transmission scheme exploiting channel reciprocity for joint downlink beamformed information data communication and uplink channel estimation through training data transmission. We adopt a general model for pilot-assisted channel estimation and present a unified optimization framework for all involved FD MIMO design parameters. Our representative Monte Carlo simulation results for an example algorithmic solution for the beamformers as well as for the analog and digital SI cancellation demonstrate that the proposed FD-based joint communication and control scheme provides 1.4x the downlink rate of its half duplex counterpart. This performance improvement is achieved with 50% reduction in the hardware complexity for the analog canceller than conventional FD MIMO architectures with fully connected analog cancellation.
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