Randomly Spread CDMA: Asymptotics via Statistical Physics

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear MMSE detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio suffers a degradation due to the multiple-access interference. The uncoded error performance (e.g., symbol-error-rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems.Comment: To be published in IEEE Transactions on Information Theor

Many-Access Channels: The Gaussian Case with Random User Activities

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. This work proposes a new paradigm, referred to as many-user information theory, where the number of users is allowed to grow with the blocklength. This paradigm is motivated by emerging systems with a massive number of users in an area, such as machine-to-machine communication systems and sensor networks. The focus of the current paper is the many-access channel model, which consists of a single receiver and many transmitters, whose number increases unboundedly with the blocklength. Moreover, an unknown subset of transmitters may transmit in a given block and need to be identified. A new notion of capacity is introduced and characterized for the Gaussian many-access channel with random user activities. The capacity can be achieved by first detecting the set of active users and then decoding their messages.Comment: 5 pages, 2 figures, to appear in Proceedings of ISIT 201

Tracking Angles of Departure and Arrival in a Mobile Millimeter Wave Channel

Millimeter wave provides a very promising approach for meeting the ever-growing traffic demand in next generation wireless networks. To utilize this band, it is crucial to obtain the channel state information in order to perform beamforming and combining to compensate for severe path loss. In contrast to lower frequencies, a typical millimeter wave channel consists of a few dominant paths. Thus it is generally sufficient to estimate the path gains, angles of departure (AoDs), and angles of arrival (AoAs) of those paths. Proposed in this paper is a dual timescale model to characterize abrupt channel changes (e.g., blockage) and slow variations of AoDs and AoAs. This work focuses on tracking the slow variations and detecting abrupt changes. A Kalman filter based tracking algorithm and an abrupt change detection method are proposed. The tracking algorithm is compared with the adaptive algorithm due to Alkhateeb, Ayach, Leus and Heath (2014) in the case with single radio frequency chain. Simulation results show that to achieve the same tracking performance, the proposed algorithm requires much lower signal-to-noise-ratio (SNR) and much fewer pilots than the other algorithm. Moreover, the change detection method can always detect abrupt changes with moderate number of pilots and SNR.Comment: 6 pages, 7 figures, submitted to ICC 201

Statistical Physics of Signal Estimation in Gaussian Noise: Theory and Examples of Phase Transitions

We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal and its noisy version. The paper consists of essentially two parts. In the first, we derive several statistical-mechanical relationships between a few important quantities in this problem area, such as the MMSE, the differential entropy, the Fisher information, the free energy, and a generalized notion of temperature. We also draw analogies and differences between certain relations pertaining to the estimation problem and the parallel relations in thermodynamics and statistical physics. In the second part of the paper, we provide several application examples, where we demonstrate how certain analysis tools that are customary in statistical physics, prove useful in the analysis of the MMSE. In most of these examples, the corresponding statistical-mechanical systems turn out to consist of strong interactions that cause phase transitions, which in turn are reflected as irregularities and discontinuities (similar to threshold effects) in the behavior of the MMSE.Comment: Submitted to the IEEE Transactions on Information Theor