Sundeep Rangan

Millimeter-Wave Cellular Wireless Networks: Potentials and Challenges

Millimeter-wave (mmW) frequencies between 30 and 300 GHz are a new frontier for cellular communication that offers the promise of orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from multielement antenna arrays. This paper surveys measurements and capacity studies to assess this technology with a focus on small cell deployments in urban environments. The conclusions are extremely encouraging; measurements in New York City at 28 and 73 GHz demonstrate that, even in an urban canyon environment, significant non-line-of-sight (NLOS) outdoor, street-level coverage is possible up to approximately 200 m from a potential low-power microcell or picocell base station. In addition, based on statistical channel models from these measurements, it is shown that mmW systems can offer more than an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks at current cell densities. Cellular systems, however, will need to be significantly redesigned to fully achieve these gains. Specifically, the requirement of highly directional and adaptive transmissions, directional isolation between links, and significant possibilities of outage have strong implications on multiple access, channel structure, synchronization, and receiver design. To address these challenges, the paper discusses how various technologies including adaptive beamforming, multihop relaying, heterogeneous network architectures, and carrier aggregation can be leveraged in the mmW context.

Millimeter Wave Channel Modeling and Cellular Capacity Evaluation

With the severe spectrum shortage in conventional cellular bands, millimeter wave (mmW) frequencies between 30 and 300 GHz have been attracting growing attention as a possible candidate for next-generation micro- and picocellular wireless networks. The mmW bands offer orders of magnitude greater spectrum than current cellular allocations and enable very high-dimensional antenna arrays for further gains via beamforming and spatial multiplexing. This paper uses recent real-world measurements at 28 and 73 GHz in New York, NY, USA, to derive detailed spatial statistical models of the channels and uses these models to provide a realistic assessment of mmW micro- and picocellular networks in a dense urban deployment. Statistical models are derived for key channel parameters, including the path loss, number of spatial clusters, angular dispersion, and outage. It is found that, even in highly non-line-of-sight environments, strong signals can be detected 100-200 m from potential cell sites, potentially with multiple clusters to support spatial multiplexing. Moreover, a system simulation based on the models predicts that mmW systems can offer an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks with no increase in cell density from current urban deployments.

Generalized approximate message passing for estimation with random linear mixing

We consider the estimation of a random vector observed through a linear transform followed by a componentwise probabilistic measurement channel. Although such linear mixing estimation problems are generally highly non-convex, Gaussian approximations of belief propagation (BP) have proven to be computationally attractive and highly effective in a range of applications. Recently, Bayati and Montanari have provided a rigorous and extremely general analysis of a large class of approximate message passing (AMP) algorithms that includes many Gaussian approximate BP methods. This paper extends their analysis to a larger class of algorithms to include what we call generalized AMP (G-AMP). G-AMP incorporates general (possibly non-AWGN) measurement channels. Similar to the AWGN output channel case, we show that the asymptotic behavior of the G-AMP algorithm under large i.i.d. Gaussian transform matrices is described by a simple set of state evolution (SE) equations. The general SE equations recover and extend several earlier results, including SE equations for approximate BP on general output channels by Guo and Wang.

An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.

Mimo for millimeter-wave wireless communications: beamforming, spatial multiplexing, or both?

The use of mmWave frequencies for wireless communications offers channel bandwidths far greater than previously available, while enabling dozens or even hundreds of antenna elements to be used at the user equipment, base stations, and access points. To date, MIMO techniques, such as spatial multiplexing, beamforming, and diversity, have been widely deployed in lower-frequency systems such as IEEE 802.11n/ac (wireless local area networks) and 3GPP LTE 4G cellphone standards. Given the tiny wavelengths associated with mmWave, coupled with differences in the propagation and antennas used, it is unclear how well spatial multiplexing with multiple streams will be suited to future mmWave mobile communications. This tutorial explores the fundamental issues involved in selecting the best communications approaches for mmWave frequencies, and provides insights, challenges, and appropriate uses of each MIMO technique based on early knowledge of the mmWave propagation environment.

Compressive Sampling and Lossy Compression

Recent results in compressive sampling have shown that sparse signals can be recovered from a small number of random measurements. This property raises the question of whether random measurements can provide an efficient representation of sparse signals in an information-theoretic sense. Through both theoretical and experimental results, we show that encoding a sparse signal through simple scalar quantization of random measurements incurs a significant penalty relative to direct or adaptive encoding of the sparse signal. Information theory provides alternative quantization strategies, but they come at the cost of much greater estimation complexity.

Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing

The replica method is a nonrigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to study estimators that are maximum a posteriori (MAP) under a postulated prior distribution. It is shown that with random linear measurements and Gaussian noise, the replica-symmetric prediction of the asymptotic behavior of the postulated MAP estimate of an -dimensional vector “decouples” as scalar postulated MAP estimators. The result is based on applying a hardening argument to the replica analysis of postulated posterior mean estimators of Tanaka and of Guo and Verdú. The replica-symmetric postulated MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, least absolute shrinkage and selection operator (LASSO), linear estimation with thresholding, and zero norm-regularized estimation. In the case of LASSO estimation, the scalar estimator reduces to a soft-thresholding operator, and for zero norm-regularized estimation, it reduces to a hard threshold. Among other benefits, the replica method provides a computationally tractable method for precisely predicting various performance metrics including mean-squared error and sparsity pattern recovery probability.

Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of sparse common support (SCS) channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.

Message-Passing De-Quantization With Applications to Compressed Sensing

Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal-sometimes greatly so. This paper develops message-passing de-quantization (MPDQ) algorithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowing the linear expansion to be overcomplete or undercomplete and the scalar quantization to be regular or non-regular. The algorithm is based on generalized approximate message passing (GAMP), a recently-developed Gaussian approximation of loopy belief propagation for estimation with linear transforms and nonlinear componentwise-separable output channels. For MPDQ, scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization. The algorithm is computationally simple and can incorporate arbitrary separable priors on the input vector including sparsity-inducing priors that arise in the context of compressed sensing. Moreover, under the assumption of a Gaussian measurement matrix with i.i.d. entries, the asymptotic error performance of MPDQ can be accurately predicted and tracked through a simple set of scalar state evolution equations. We additionally use state evolution to design MSE-optimal scalar quantizers for MPDQ signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers. In particular, our results show that non-regular quantization can greatly improve rate-distortion performance in some problems with oversampling or with undersampling combined with a sparsity-inducing prior.Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal—sometimes greatly so. This paper develops generalized approximate message passing (GAMP) alg orithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowi ng the linear expansion to be overcomplete or undercomplete and th e scalar quantization to be regular or non-regular. GAMP is a recently-developed class of algorithms that uses Gaussianpproximations in belief propagation and allows arbitrary separable input and output channels. Scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization. Non-regular quantization is empirically demonstrated to greatly improve rate–distortion performance in some problems with oversampling or with undersampling combined with a sparsit yinducing prior. Under the assumption of a Gaussian measurement matrix with i.i.d. entries, the asymptotic error performan ce of GAMP can be accurately predicted and tracked through the state evolution formalism. We additionally use state evolution t o design MSE-optimal scalar quantizers for GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.

Directional Cell Discovery in Millimeter Wave Cellular Networks

The acute disparity between increasing bandwidth demand and available spectrum has brought millimeter wave (mmWave) bands to the forefront of candidate solutions for the next-generation cellular networks. Highly directional transmissions are essential for cellular communication in these frequencies to compensate for higher isotropic path loss. This reliance on directional beamforming, however, complicates initial cell search since mobiles and base stations must jointly search over a potentially large angular directional space to locate a suitable path to initiate communication. To address this problem, this paper proposes a directional cell discovery procedure where base stations periodically transmit synchronization signals, potentially in time-varying random directions, to scan the angular space. Detectors for these signals are derived based on a Generalized Likelihood Ratio Test (GLRT) under various signal and receiver assumptions. The detectors are then simulated under realistic design parameters and channels based on actual experimental measurements at 28 GHz in New York City. The study reveals two key findings: 1) digital beamforming can significantly outperform analog beamforming even when digital beamforming uses very low quantization to compensate for the additional power requirements and 2) omnidirectional transmissions of the synchronization signals from the base station generally outperform random directional scanning.