Channel Estimation and Hybrid Combining for mmWave: Phase Shifters or Switches? Roi M´ endez-Rial † , Cristian Rusu † , Ahmed Alkhateeb ‡ , Nuria Gonz´ alez-Prelcic † , and Robert W. Heath Jr. ‡ † Universidade de Vigo, Vigo, Spain, Email: {roimr,crusu,nuria}@gts.uvigo.es ‡ The University of Texas at Austin, Austin, TX 78712, Email: {aalkhateeb,rheath}@utexas.edu Abstract—Precoding/combining and large antenna arrays are essential in millimeter wave (mmWave) systems. In traditional MIMO systems, precoding/combining is usually done digitally at baseband with one radio frequency (RF) chain and one analog-to-digital converter (ADC) per antenna. The high cost and power consumption of RF chains and ADCs at mmWave frequencies make an all-digital processing approach prohibitive. When only a limited number of RF chains is available, hybrid architectures that split the precoding/combining processing into the analog and digital domains are attractive. A previously proposed hybrid solution employs phase shifters and mixers in the RF precoding/combining stage. It obtains near optimal spectral efficiencies with a reduced number of RF channels. In this paper we propose a different hybrid architecture, which simplifies the hardware at the receiver by replacing the phase shifters with switches. We present a new approach for compressed sensing based channel estimation for the hybrid architectures. Given the channel estimate, we propose a novel algorihtm that jointly designs the antenna subsets selected and the baseband combining. Using power consumption calculations and achievable rates, we compare the performance of hybrid combining with antenna switching and phase shifting, showing that antenna selection is preferred in a range of operating conditions. I. I NTRODUCTION Communication over millimeter wave (mmWave) frequen- cies [1] is the frontier for commercial wireless communication systems. Initial applications of mmWave to personal area networks (PAN) and local area networks (LAN) through the 60GHz unlicensed band are already standardized [2] and commercially available. The large bandwidths available at mmWave carrier frequencies also makes it interesting for 5G cellular systems [3], [4], [5], [6]. MmWave communication requires very large multiple-input multiple-output (MIMO) systems to provide sufficient antenna aperture. Unfortunately, at mmWave there are additional hard- ware constraints that have to imposed due to the practical limitations on the cost, complexity and power consumption with the current technology [7]. Due to mixed signal and baseband processing requirements, it may not be feasible to use one complete RF chain and one DAC or ADC per antenna, so precoding and combining can not be done entirely in the baseband. For this reason, systems like IEEE 802.11ad use analog beamforming / combining and only support single stream MIMO communication. Generalizing to larger numbers This work was supported by the Spanish Government and the European Regional Development Fund (ERDF) under project TACTICA; the National Science Foundation under Grant No. NSF-CCF-1319556; and by a gift from Huawei Technologies. of streams requires the use of precoding and combining, mak- ing functions like low complexity and low overhead channel estimation more essential. In previous work, a hybrid architecture that accounts for hardware constraints has been proposed [8], [9], resulting in precoder/combiner design algorithms that divide the op- timization process into the RF and the baseband stages, and channel estimation methods that exploit the sparse nature of the mmWave channel. This architecture is based on quantized phase shifters, as illustrated in Fig. 1. The digital combiner can correct for analog limitations and the joint system approaches the performance of unconstrained digital solutions [8], [9]. In this paper we propose a new hybrid architecture based on antenna switches. To reduce cost, complexity and power consumption, our design uses switches to multiple antennas as an alternative to phase shifters. In our case, the RF combiner design is performed by a subset antenna selection algorithm, instead of an optimization over all quantized phase values. We focus on switching at the mobile station (MS), where the complexity and power consumption limitations are especially important, and assume that phase shifters are used at the base station (BS). We introduce power consumption models for both architectures, and analyze the reduction that can be achieved by using switches instead of phase shifters. We also propose new channel estimation algorithms for this architecture that exploit the sparse nature of the mmWave channel. Once the channel is estimated, we develop two dif- ferent designs for the hybrid combiner. Numerical simulations compare the spectral efficiency that can be achieved between the hybrid architecture based on phase shifters and the one based on switches. The proposed switching solution provides a low cost and low power consumption alternative to the phase shifter architecture which performs equivalently when the number of bits used to quantize the phases is low. II. SYSTEM MODEL Consider the systems in Fig. 1 and Fig. 2, corresponding to a mmWave MIMO receiver based on phase shifters and switches respectively. The transmitting BS is equipped with N t antennas and L t RF chains while the receiving MS with N r antennas and L ps r (or L s r ) RF chains. N s data streams are transmitted from the BS to the MS assuming N s ≤ L t ≤ N t and N s ≤ L r ≤ N r . We will use the notation L r when referring to the number of RF chains in any of these architectures.