On the Number of RF Chains and Phase Shifters, and Scheduling Design with Hybrid Analog-Digital Beamforming

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple input multiple output (MIMO) systems with frequency selective channels. For this system, first we determine the required number of radio frequency (RF) chains and phase shifters (PSs) such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + 1)$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all sub-carriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only $20-40$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a)$ is less than $r_t$, we propose a simple user scheduling algorithm to select the best set of users in each sub-carrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.Comment: IEEE Transactions on Wireless Communications (Minor Revision

Multiuser Millimeter Wave Beamforming Strategies with Quantized and Statistical CSIT

To alleviate the high cost of hardware in mmWave systems, hybrid analog/digital precoding is typically employed. In the conventional two-stage feedback scheme, the analog beamformer is determined by beam search and feedback to maximize the desired signal power of each user. The digital precoder is designed based on quantization and feedback of effective channel to mitigate multiuser interference. Alternatively, we propose a one-stage feedback scheme which effectively reduces the complexity of the signalling and feedback procedure. Specifically, the second-order channel statistics are leveraged to design digital precoder for interference mitigation while all feedback overhead is reserved for precise analog beamforming. Under a fixed total feedback constraint, we investigate the conditions under which the one-stage feedback scheme outperforms the conventional two-stage counterpart. Moreover, a rate splitting (RS) transmission strategy is introduced to further tackle the multiuser interference and enhance the rate performance. Consider (1) RS precoded by the one-stage feedback scheme and (2) conventional transmission strategy precoded by the two-stage scheme with the same first-stage feedback as (1) and also certain amount of extra second-stage feedback. We show that (1) can achieve a sum rate comparable to that of (2). Hence, RS enables remarkable saving in the second-stage training and feedback overhead.Comment: submitted to TW

Codebook Based Hybrid Precoding for Millimeter Wave Multiuser Systems

In millimeter wave (mmWave) systems, antenna architecture limitations make it difficult to apply conventional fully digital precoding techniques but call for low cost analog radio-frequency (RF) and digital baseband hybrid precoding methods. This paper investigates joint RF-baseband hybrid precoding for the downlink of multiuser multi-antenna mmWave systems with a limited number of RF chains. Two performance measures, maximizing the spectral efficiency and the energy efficiency of the system, are considered. We propose a codebook based RF precoding design and obtain the channel state information via a beam sweep procedure. Via the codebook based design, the original system is transformed into a virtual multiuser downlink system with the RF chain constraint. Consequently, we are able to simplify the complicated hybrid precoding optimization problems to joint codeword selection and precoder design (JWSPD) problems. Then, we propose efficient methods to address the JWSPD problems and jointly optimize the RF and baseband precoders under the two performance measures. Finally, extensive numerical results are provided to validate the effectiveness of the proposed hybrid precoders.Comment: 35 pages, 9 figures, to appear in Trans. on Signal Process, 201

Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems

Despite its promising performance gain, the realization of mmWave massive MIMO still faces several practical challenges. In particular, implementing massive MIMO in the digital domain requires hundreds of RF chains matching the number of antennas. Furthermore, designing these components to operate at the mmWave frequencies is challenging and costly. These motivated the recent development of hybrid-beamforming where MIMO processing is divided for separate implementation in the analog and digital domains, called the analog and digital beamforming, respectively. Analog beamforming using a phase array introduces uni-modulus constraints on the beamforming coefficients, rendering the conventional MIMO techniques unsuitable and call for new designs. In this paper, we present a systematic design framework for hybrid beamforming for multi-cell multiuser massive MIMO systems over mmWave channels characterized by sparse propagation paths. The framework relies on the decomposition of analog beamforming vectors and path observation vectors into Kronecker products of factors being uni-modulus vectors. Exploiting properties of Kronecker mixed products, different factors of the analog beamformer are designed for either nulling interference paths or coherently combining data paths. Furthermore, a channel estimation scheme is designed for enabling the proposed hybrid beamforming. The scheme estimates the AoA of data and interference paths by analog beam scanning and data-path gains by analog beam steering. The performance of the channel estimation scheme is analyzed. In particular, the AoA spectrum resulting from beam scanning, which displays the magnitude distribution of paths over the AoA range, is derived in closed-form. It is shown that the inter-cell interference level diminishes inversely with the array size, the square root of pilot sequence length and the spatial separation between paths.Comment: Submitted to IEEE JSAC Special Issue on Millimeter Wave Communications for Future Mobile Networks, minor revisio

Multiuser Precoding and Channel Estimation for Hybrid Millimeter Wave MIMO Systems

In this paper, we develop a low-complexity channel estimation for hybrid millimeter wave (mmWave) systems, where the number of radio frequency (RF) chains is much less than the number of antennas equipped at each transceiver. The proposed channel estimation algorithm aims to estimate the strongest angle-of-arrivals (AoAs) at both the base station (BS) and the users. Then all the users transmit orthogonal pilot symbols to the BS via these estimated strongest AoAs to facilitate the channel estimation. The algorithm does not require any explicit channel state information (CSI) feedback from the users and the associated signalling overhead of the algorithm is only proportional to the number of users, which is significantly less compared to various existing schemes. Besides, the proposed algorithm is applicable to both non-sparse and sparse mmWave channel environments. Based on the estimated CSI, zero-forcing (ZF) precoding is adopted for multiuser downlink transmission. In addition, we derive a tight achievable rate upper bound of the system. Our analytical and simulation results show that the proposed scheme offer a considerable achievable rate gain compared to fully digital systems, where the number of RF chains equipped at each transceiver is equal to the number of antennas. Furthermore, the achievable rate performance gap between the considered hybrid mmWave systems and the fully digital system is characterized, which provides useful system design insights.Comment: 6 pages, accepted for presentation, ICC 201