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About: Precoding is a(n) research topic. Over the lifetime, 18750 publication(s) have been published within this topic receiving 305327 citation(s). more


Open accessJournal ArticleDOI: 10.1109/TWC.2014.011714.130846
Omar El Ayach1, Sridhar Rajagopal2, Shadi Abu-Surra2, Zhouyue Pi2  +1 moreInstitutions (3)
Abstract: 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. more

Topics: Precoding (60%), MIMO (54%), Beamforming (54%)

2,426 Citations

Journal ArticleDOI: 10.1109/JSAC.2003.810294
Abstract: We provide an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper. more

Topics: 3G MIMO (71%), Multi-user MIMO (68%), MIMO (68%) more

2,360 Citations

Open accessJournal ArticleDOI: 10.1109/JSAC.2013.130205
Abstract: We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively. more

  • Fig. 1. In each of the L cells is one BS, equipped with N antennas, and K single-antenna UTs. We assume channel reciprocity, i.e., the downlink channel hHjlk is the Hermitian transpose of the uplink channel hjlk .
    Fig. 1. In each of the L cells is one BS, equipped with N antennas, and K single-antenna UTs. We assume channel reciprocity, i.e., the downlink channel hHjlk is the Hermitian transpose of the uplink channel hjlk .
  • Fig. 2. Ergodic achievable rate with MF and MMSE detection versus number of antennas N for P ∈ {N,N/3}, ρtr = 6 dB and ρ = 10 dB.
    Fig. 2. Ergodic achievable rate with MF and MMSE detection versus number of antennas N for P ∈ {N,N/3}, ρtr = 6 dB and ρ = 10 dB.
  • Fig. 5. 7–cell hexagonal system layout. The distance between two adjacent cells is normalized to 2. There are K = 10 UTs uniformly distributed on a circle of radius 2/3 around each BS.
    Fig. 5. 7–cell hexagonal system layout. The distance between two adjacent cells is normalized to 2. There are K = 10 UTs uniformly distributed on a circle of radius 2/3 around each BS.
Topics: Many antennas (60%), Precoding (54%), MIMO (52%) more

2,268 Citations

Journal ArticleDOI: 10.1109/18.641562
Andrea Goldsmith1, Pravin Varaiya2Institutions (2)
Abstract: We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading. more

Topics: Channel state information (70%), Fading (69%), Fading distribution (69%) more

2,107 Citations

Open accessJournal ArticleDOI: 10.1109/JSTSP.2014.2334278
Abstract: 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. more

Topics: Precoding (71%), Zero-forcing precoding (67%), Communication channel (56%) more

1,916 Citations

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