Omar El Ayach

Spatially Sparse Precoding in Millimeter Wave MIMO Systems

Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications and all cellular systems. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.

Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems

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 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.

Interference Alignment with Analog Channel State Feedback

Interference alignment (IA) is a multiplexing gain optimal transmission strategy for the interference channel. While the achieved sum rate with IA is much higher than previously thought possible, the improvement comes at the cost of requiring network channel state information at the transmitters. This can be achieved by explicit feedback, a flexible yet potentially costly approach that incurs large overhead. In this paper we propose analog feedback as an alternative to limited feedback or reciprocity based alignment. We show that the full multiplexing gain observed with perfect channel knowledge is preserved by analog feedback and that the mean loss in sum rate is bounded by a constant when signal-to-noise ratio is comparable in both forward and feedback channels. When signal-to-noise ratios are not quite symmetric, a fraction of the multiplexing gain is achieved. We consider the overhead of training and feedback and use this framework to numerically optimize the systems effective throughput. We present simulation results to demonstrate the performance of IA with analog feedback, verify our theoretical analysis, and extend our conclusions on optimal training and feedback length.

Low complexity precoding for large millimeter wave MIMO systems

Millimeter wave (mmWave) systems must overcome heavy signal attenuation to support high-throughput wireless communication links. The small wavelength in mmWave systems enables beamforming using large antenna arrays to combat path loss with directional transmission. Beamforming with multiple data streams, known as precoding, can be used to achieve even higher performance. Both beamforming and precoding are done at baseband in traditional microwave systems. In mmWave systems, however, the high cost of mixed-signal and radio frequency chains (RF) makes operating in the passband and analog domains attractive. This hardware limitation places additional constraints on precoder design. In this paper, we consider single user beamforming and precoding in mmWave systems with large arrays. We exploit the structure of mmWave channels to formulate the precoder design problem as a sparsity constrained least squares problem. Using the principle of basis pursuit, we develop a precoding algorithm that approximates the optimal unconstrained precoder using a low dimensional basis representation that can be efficiently implemented in RF hardware. We present numerical results on the performance of the proposed algorithm and show that it allows mmWave systems to approach waterfilling capacity.

The capacity optimality of beam steering in large millimeter wave MIMO systems

Millimeter wave (mmWave) systems must overcome the heavy attenuation at high frequency to support high-throughput wireless communication. The small wavelength in mmWave systems enables beamforming using large antenna arrays to combat path loss with large array gain. Beamforming in traditional microwave systems is often done at baseband for maximum flexibility. Such baseband processing requires a dedicated transceiver chain per antenna element. The high cost of radio frequency (RF) chains in mmWave systems, however, makes supporting each antenna with a dedicated RF chain expensive. This mismatch between the number of antennas and transceiver chains makes baseband processing infeasible; thus mmWave systems typically rely on a traditional approach known as beam steering which can be done at RF using inexpensive phase shifters. Unlike baseband precoding, however, traditional beam steering is not explicitly designed to achieve the capacity of the mmWave channel. In this paper, we consider both beamforming and multi-stream precoding in single user systems with large mmWave antenna arrays at both transmitter and receiver. Using a realistic channel model, we show that the unconstrained capacity-achieving precoding solutions converge to simple beam steering solutions. Therefore, in large mmWave systems, no rate loss is incurred by adopting the traditional lower-complexity solution.

Coverage and capacity in mmWave cellular systems

Millimeter wave (mmWave) communication has recently been proposed for use in commercial cellular systems as a solution to the microwave spectrum gridlock. MmWave spectrum is (potentially) available around the globe and recent hardware advances make mass market deployments feasible. In this paper, we study the coverage and capacity of mmWave cellular systems with a special focus on their key differentiating factors such as the limited scattering nature of mmWave channels, and the use of RF beamforming strategies such as beam steering to provide highly directional transmission with limited hardware complexity.We show that, in general, coverage in mmWave systems can rival or even exceed coverage in microwave systems assuming that the link budgets promised by existing mmWave system designs are in fact achieved. This comparable coverage translates into a superior average rate performance for mmWave systems as a result of the larger bandwidth available for transmission.

Multimode precoding in millimeter wave MIMO transmitters with multiple antenna sub-arrays

Millimeter wave (mmWave) systems must use beamforming to overcome the heavy attenuation at mmWave frequencies and establish high-quality communication links with reasonably high spectral efficiency. When received signal power is sufficiently large and the propagation channel is sufficiently rich, beamforming with multiple data streams, known as precoding, could further increase data rates in mmWave systems. The high cost of digital devices in mmWave systems, however, implies that precoding is predominantly done in the analog domain, making mmWave precoding significantly more constrained than traditional multiple-input multiple-output (MIMO) solutions. In this paper, we propose an iterative precoding algorithm for a practical mmWave transmitter architecture in which all precoding is done in the analog domain. In addition to precoding, the proposed algorithm allows the mmWave system to adapt the rank of its transmission in response to varying propagation conditions. We present numerical results showing that the proposed multimode precoding algorithm allows systems to achieve large data rates, in some cases approaching channel capacity.

Single-sided adaptive estimation of multi-path millimeter wave channels

Millimeter wave (mmWave) cellular systems will enable ultra high data rates by communicating over the large bandwidth available in mmWave frequencies. To overcome the channel propagation characteristics in this frequency band, large antenna arrays need to be deployed at both the base station and mobile users. While these large arrays provide sufficient beamforming gains to meet the required link margins, they make it challenging to estimate the mmWave channel. In this paper, we propose a mmWave channel estimation algorithm that exploits the sparse nature of the channel and leverages tools from adaptive compressed sensing to efficiently estimate the channel with a small training overhead. The proposed algorithm considers practical hardware constraints on the training beamforming design, and does not require the availability of a feedback channel between the base station and the mobile user. Simulation results indicate that comparable precoding gains can be achieved by the proposed channel estimation algorithm relative to the case when perfect channel knowledge exists.

Real world feasibility of interference alignment using MIMO-OFDM channel measurements

Interference alignment (IA) has been shown to achieve linear sum capacity growth, at high SNR, with the number of users in the interference channel by cooperatively precoding transmitted signals to align interference subspaces at the receivers. The theory of IA was derived under assumptions about the richness of the propagation channel; practical channels do not guarantee such ideal decorrelation. This paper presents the first experimental study of IA in measured interference channel and shows that IA achieves the claimed scaling factors in a variety of measured channel settings for a 3 user, 2 antennas per node setup.

Interference alignment with analog CSI feedback

Interference alignment has been used to derive and realize the maximum multiplexing gain of the MIMO interference channel. Interference alignment requires some form of channel state information at the transmitter. This paper proposes analog CSI feedback as an alternative to limited feedback or reciprocity based alignment. We show that the maximum degrees of freedom of the K-user interference channel are preserved with the suggested feedback strategy, and that the mean loss in sum rate incurred by imperfect CSI is bounded by a constant provided that the signal-to-noise ratio is comparable in both forward and reverse channels. Finally, demonstrate the performance of the proposed strategy through simulation.