Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver.Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel.Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results also illustrate that the proposed channel estimation and precoding algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.

Antenna arrays will be an important ingredient in millimeter wave (mmWave) cellular systems. A natural application of antenna arrays is simultaneous transmission to multiple users. Unfortunately, the hardware constraints in mmWave systems make it difficult to apply conventional lower frequency multiuser MIMO precoding techniques at mmWave. This paper develops low complexity hybrid analog/digital precoding for downlink multiuser mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is inspired by the power consumption of complete radio frequency and mixed signal hardware. The proposed algorithm configures hybrid precoders at the transmitter and analog combiners at multiple receivers with a small training and feedback overhead. The performance of the proposed algorithm is analyzed in the large dimensional regime and in single path channels. When the analog and digital precoding vectors are selected from quantized codebooks, the rate loss due to the joint quantization is characterized and insights are given into the performance of hybrid beamforming compared with analog-only beamforming solutions. Analytical and simulation results show that the proposed techniques offer higher sum rates compared with analog-only beamforming solutions, and approach the performance of the unconstrained digital beamforming with relatively small codebooks.Comment: 30 pages, 6 figures, submitted to IEEE Transactions on Wireless Communication

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Abstract-This paper describes a least squares (LS) channel estimation scheme for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on pilot tones. We first compute the mean square error (MSE) of the LS channel estimate. We then derive optimal pilot sequences and optimal placement of the pilot tones with respect to this MSE. It is shown that the optimal pilot sequences are equipowered, equispaced, and phase shift orthogonal. To reduce the training overhead, an LS channel estimation scheme over multiple OFDM symbols is also discussed. Moreover, to enhance channel estimation, a recursive LS (RLS) algorithm is proposed, for which we derive the optimal forgetting or tracking factor. This factor is found to be a function of both the noise variance and the channel Doppler spread. Through simulations, it is shown that the optimal pilot sequences derived in this paper outperform both the orthogonal and random pilot sequences. It is also shown that a considerable gain in signal-to-noise ratio (SNR) can be obtained by using the RLS algorithm, especially in slowly time-varying channels.

Abstract-Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving (regularized) TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined "errors-in-variables" models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.

Abstract-In this paper, we deal with channel estimation for orthogonal frequency-division multiplexing (OFDM) systems. The channels are assumed to be time-varying (TV) and approximated by a basis expansion model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but approximately banded. Based on this observation, we propose novel channel estimators to combat both the noise and the out-of-band interference. In addition, the effect of a receiver window on channel estimation is also studied. Our claims are supported by simulation results, which are obtained considering Jakes' channels with fairly high Doppler spreads.Index Terms-Basis expansion model (BEM), orthogonal frequency-division multiplexing (OFDM), pilot-assisted modulation, time-varying (TV) channels.

Abstract-Next-generation cellular standards may leverage the large bandwidth available at millimeter wave (mmWave) frequencies to provide gigabit-per-second data rates in outdoor wireless systems. A main challenge in realizing mmWave cellular is achieving sufficient operating link margin, which is enabled via directional beamforming with large antenna arrays. Due to the high cost and power consumption of high-bandwidth mixed-signal devices, mmWave beamforming will likely include a combination of analog and digital processing. In this paper, we develop an iterative hybrid beamforming algorithm for the single user mmWave channel. The proposed algorithm accounts for the limitations of analog beamforming circuitry and assumes only partial channel knowledge at both the base and mobile stations. The precoding strategy exploits the sparse nature of the mmWave channel and uses a variant of matching pursuit to provide simple solutions to the hybrid beamforming problem. Simulation results show that the proposed algorithm can approach the rates achieved by unconstrained digital beamforming solutions.

Abstract-A new scheme to sample signals defined in the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so-called graph-shift operator. Most of the works that have looked at this problem have focused on using the value of the signal observed at a subset of nodes to recover the signal in the entire graph. Differently, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-shift operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle (which is the support of time-varying signals), our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, which is critical to guarantee recovery when sampling time-varying signals, is preserved. Sampling and interpolation are analyzed first in the absence of noise and then noise is considered. We then study the recovery of the sampled signal when the specific set of frequencies that is active is not known. Moreover, we present a more general sampling scheme, under which, either our aggregation approach or the alternative approach of sampling a graph signal by observing the value of the signal at a subset of nodes can be both viewed as particular cases. The last part of the paper presents numerical experiments that illustrate the results developed through both synthetic graph signals and a real-world graph of the economy of the United States.