Space-Constrained Massive MIMO: Hitting the Wall of Favorable Propagation

The recent development of the massive multiple-input multiple-output (MIMO) paradigm, has been extensively based on the pursuit of favorable propagation: in the asymptotic limit, the channel vectors become nearly orthogonal and interuser interference tends to zero [1]. In this context, previous studies
have considered fixed inter-antenna distance, which implies an increasing array aperture as the number of elements increases. Here, we focus on a practical, space-constrained topology, where an increase in the number of antenna elements in a fixed total space imposes an inversely proportional decrease in the inter-antenna distance. Our analysis shows that, contrary to existing studies, inter-user interference does not vanish in the massive MIMO regime, thereby creating a saturation effect on the achievable rate.

Sum-Rate and Power Scaling of Massive MIMO Systems with Channel Aging

This paper investigates the achievable sum-rate of massive multiple-input multiple-output (MIMO) systems in the presence of channel aging. For the uplink, by assuming that the base station (BS) deploys maximum ratio combining (MRC) or zero-forcing (ZF) receivers, we present tight closed-form lower bounds on the achievable sum-rate for both receivers with aged channel state information (CSI). In addition, the benefit of implementing channel prediction methods on the sum-rate is examined, and closed-form sum rate lower bounds are derived. Moreover, the impact of channel aging and channel prediction on the power scaling law is characterized. Extension to the downlink scenario and multi-cell scenario are also considered. It is found that, for a system with/without channel prediction, the transmit power of each user can be scaled down at most by 1= p M (where M is the number of BS antennas), which indicates that aged CSI does not degrade the power scaling law, and channel prediction does not enhance the power scaling law; instead, these phenomena affect the achievable sum-rate by degrading or enhancing the effective signal to interference and noise ratio, respectively.

A Tractable Approach to Uplink Spectral Efficiency of Two-Tier Massive MIMO Cellular HetNets

This letter investigates the uplink spectral efficiency (SE) of a two-tier cellular network, where massive multiple-input multiple-output macro base stations are overlaid with dense small cells. Macro user equipments (MUEs) and small cells with single user equipment uniformly scattered are modeled as two independent homogeneous Poisson point processes. By applying stochastic geometry, we analyze the SE of the multiuser uplink at a macro base station that employs a zero-forcing detector and we obtain a novel lower bound as well as its approximation. According to the simple and near-exact analytical expression, we observe that the ideal way to improve the SE is by increasing the MUE density and the base station antennas synchronously rather than increasing them individually. Furthermore, a large value of path loss exponent has a positive effect on the SE due to the reduced aggregated interference.

Beam division multiple access transmission for massive MIMO communications

We study multicarrier multiuser multiple-input multiple-output (MU-MIMO) systems, in which the base station employs an asymptotically large number of antennas. We analyze a fully correlated channel matrix and provide a beam domain channel model, where the channel gains are independent of sub-carriers. For this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate, based on which, we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter. Furthermore, we propose a beam division multiple access (BDMA) transmission scheme that simultaneously serves multiple users via different beams. By selecting users within non-overlapping beams, the MU-MIMO channels can be equivalently decomposed into multiple single-user MIMO channels; this scheme significantly reduces the overhead of channel estimation, as well as, the processing complexity at transceivers. For BDMA transmission, we work out an optimal pilot design criterion to minimize the mean square error (MSE) and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. Simulations demonstrate the near-optimal performance of BDMA transmission and the advantages of the proposed pilot sequences.

Effect of channel aging on the sum rate of uplink massive MIMO systems

This paper investigates the achievable sum-rate of uplink massive multiple-input multiple-output (MIMO) systems considering a practical channel impairment, namely, aged channel state information (CSI). Taking into account both maximum ratio combining (MRC) and zero-forcing (ZF) receivers at the base station, we present tight closed-form lower bounds on the sum-rate for both receivers, which provide efficient means to evaluate the sum-rate of the system. More importantly, we characterize the impact of channel aging on the power scaling law. Specifically, we show that the transmit power of each user can be scaled down by 1/√(M), which indicates that aged CSI does not affect the power scaling law; instead, it causes only a reduction on the sum rate by reducing the effective signal-to-interference-and-noise ratio (SINR).

Beam division multiple access for massive MIMO downlink transmission

We study a multiuser multicarrier downlink communication system in which the base station (BS) employs a large number of antennas. By assuming frequency-division duplex operation, we provide a beam domain channel model as the number of BS antennas grows asymptotically large. With this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate before developing necessary conditions to asymptotically maximize the upper bound, with only statistical channel state information at the BS. Inspired by these conditions, we propose a beam division multiple access (BDMA) transmission scheme, where the BS communicates with users via different beams. For BDMA transmission, we design user scheduling to select users within non-overlapping beams, work out an optimal pilot design under a minimum mean square error criterion, and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. The proposed BDMA scheme reduces significantly the pilot overhead, as well as, the processing complexity at transceivers. Simulations demonstrate the high spectral efficiency of BDMA transmission and the advantages in the bit error rate performance of the proposed pilot sequences.

Performance of downlink massive MIMO in Ricean fading channels with ZF precoder

We investigate the achievable sum rate and energy efficiency of zero-forcing precoded downlink massive multiple-input multiple-output systems in Ricean fading channels. A simple and accurate approximation of the average sum rate is presented, which is valid for a system with arbitrary rank channel means. Based on this expression, the optimal power allocation strategy maximizing the average sum rate is derived. Moreover, considering a general power consumption model, the energy efficiency of the system with rank-1 channel means is characterized. Specifically, the impact of key system parameters, such as the number of users N, the number of BS antennas M, Ricean factor K and the signal-to-noise ratio (SNR) ρ are studied, and closed-form expressions for the optimal ρ and M maximizing the energy efficiency are derived. Our findings show that the optimal power allocation scheme follows the water filling principle, and it can substantially enhance the average sum rate in the presence of strong line-of-sight effect in the low SNR regime. In addition, we demonstrate that the Ricean factor K has significant impact on the optimal values of M, N and ρ.

Massive MIMO in sparse channels

Massive multi-user multiple-input multiple-output (MU-MIMO) systems are cellular networks where the base stations (BSs) are equipped with hundreds of antennas, N, and communicate with tens of mobile stations (MSs), K, such that, N ≫ K ≫ 1. Contrary to most prior works, in this paper, we consider the uplink of a single-cell massive MIMO system operating in sparse channels with limited scattering. This case is of particular importance in most propagation scenarios, where the prevalent Rayleigh fading assumption becomes idealistic. We derive analytical approximations for the achievable rates of maximum-ratio combining (MRC) and zero-forcing (ZF) receivers. Furthermore, we study the asymptotic behavior of the achievable rates for both MRC and ZF receivers, when N and K go to infinity under the condition that N/K → c ≥ 1. Our results indicate that the achievable rate of MRC receivers reaches an asymptotic saturation limit, whereas the achievable rate of ZF receivers grows logarithmically with the number of MSs.

Massive MIMO with Optimal Power and Training Duration Allocation

We consider the uplink of massive multicell multiple-input multiple-output systems, where the base stations (BSs), equipped with massive arrays, serve simultaneously several terminals in the same frequency band. We assume that the BS estimates the channel from uplink training, and then uses the maximum ratio combining technique to detect the signals transmitted from all terminals in its own cell. We propose an optimal resource allocation scheme which jointly selects the training duration, training signal power, and data signal power in order to maximize the sum spectral efficiency, for a given total energy budget spent in a coherence interval. Numerical results verify the benefits of the optimal resource allocation scheme. Furthermore, we show that more training signal power should be used at low signal-to-noise ratio (SNRs), and vice versa at high SNRs. Interestingly, for the entire SNR regime, the optimal training duration is equal to the number of terminals.

Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean K-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, M, grows large, while the transmit power of each user can be scaled down proportionally to 1/M. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean K-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to 1/√M. In addition, we show that with an increasing Ricean K-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers.

Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on colocated or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today’s conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phasedrifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as p N, instead of linearly, by careful circuit-aware system design.