Max-min Power Control Research Articles

Cell-Free Massive MIMO: Joint Maximum-Ratio and Zero-Forcing Precoder With Power Control

Cell-free massive multiple-input multiple-output (MIMO) system is a promising architecture for next generation wireless systems by deploying a very large number of distributed access points (APs), which simultaneously serve a smaller number of user equipments (UEs) over the same time-frequency resources. It guarantees uniformly good service at high spectral efficiency with simple linear precoding techniques and max-min power control. In this article, we propose a new joint maximum-ratio and zero-forcing (JMRZF) precoding scheme, where part of APs are combined to perform centralized zero-forcing (ZF), while other APs apply simple maximum-ratio transmission (MRT). Our proposed precoder offers an adaptable trade-off between the spectral efficiency and front-haul signalling overhead. A corresponding AP subset selection scheme is also proposed which is based on large-scale fading coefficients. A closed-form expression for the achievable spectral efficiency of our proposed scheme is derived, which represents a generalized result including both fully distributed MRT and fully centralized ZF cases. Based on this closed-form expression, max-min power control is formulated and solved via the second order cone and first order methods. The former can obtain the global optimal solution, but its computational complexity is very high. On the other hand, the latter technique is sub-optimal, yet, it has very low computational complexity. Hence, it is suitable for large-scale cell-free massive MIMO systems with hundreds or thousands of APs and users. Numerical results show that our proposed JMRZF scheme can substantially outperform the local precoding schemes, even when a small part of APs are combined to deploy ZF and is implementable even when each AP has very few antennas. In addition, it is shown that our max-min power controls improves the spectral efficiency significantly, compared to the uniform power control scheme.

Efficient Max-Min Power Control for Cell-Free Massive MIMO Systems: An Alternating Projection-Based Approach

We consider the problem of max-min power control for downlink cell-free (CF) massive MIMO systems. Under the bisection framework, solving this problem amounts to solving a sequence of convex conic feasibility checking problems (CCFCP). Unfortunately, the problem size of the CCFCP of the CF massive MIMO system grows rapidly as the number of users and access points (AP) increases. Existing feasibility checking methods become computationally intractable even when the system consists of only a moderate number of users and APs. To address this limitation, we propose to reformulate the CCFCP as a two-set feasibility problem, which is then solved by the averaged alternating reflection (AAR) algorithm. The proposed method outperforms existing methods significantly in terms of computational efficiency.

Max-Min Power Control in Downlink Massive MIMO With Distributed Antenna Arrays

In this paper, we investigate optimal downlink power allocation in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays (DAAs) under correlated and uncorrelated channel fading. In DAA massive MIMO, the base station (BS) consists of multiple antenna sub-arrays. Notably, the antenna sub-arrays are deployed in arbitrary locations within a DAA massive MIMO cell. Consequently, the distance-dependent large-scale propagation coefficients are different from a user to these different antenna sub-arrays, which makes power control a challenging problem. We assume that the network operates in time-division duplex mode, where each BS obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum-ratio transmission in the downlink. We then derive a closed-form signal-to-interference-plus-noise ratio (SINR) expression, where the channels are subject to correlated fading. Based on the SINR expression, we propose a networkwide max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate the performance advantages offered by DAA massive MIMO. For some specific scenarios, DAA massive MIMO can improve the average per-user throughput up to 55%. Furthermore, we demonstrate that channel fading covariance is an important factor in determining the performance of DAA massive MIMO.

Scheduling and Power Allocation Dampens the Negative Effect of Channel Misreporting in Massive MIMO

We study the sensitivity of multi-user scheduling performance to channel magnitude misreporting in systems with massive antennas. We consider the round-robin scheduler combined with max-min and waterfilling power controls, respectively. We show that user scheduling combined with power allocation, in general, dampens the negative effect of channel misreporting compared to the purely physical layer analysis of channel misreporting without scheduling. We discover several interesting results. First, we observe a periodicity in rate-loss behavior as the number of misreporting users increases. Second, we find that the waterfilling power control is more robust to channel misreporting compared with max-min power control. Third, for homogeneous users with equal average signal-to-noise ratios (SNRs), channel underreporting is harmful but overreporting is beneficial for max-min power control; the opposite impact is found for waterfilling power control. For heterogeneous users with various average SNRs, however, both underreporting and overreporting harm the system for both power control policies, demonstrating the complex interactions across network layers due to channel misreporting.

Performance of Distributed Massive MIMO and Small-Cell Systems Under Hardware and Channel Impairments

Deploying a large number of distributed access points (AP)s to serve a smaller number of users is one of the promising network architectures for future wireless communication systems. Such network architecture can be operated as a distributed massive multiple-input multiple-output (MIMO) system or as a small-cell (SC) system to satisfy the anticipated high rate requirements for beyond-5G networks. However, in a practical scenario with non-ideal hardware components and high-velocity users, the network experiences an inevitable performance degradation. This paper aims at analyzing the network performance under the operation of distributed massive MIMO and SC systems, taking into account the impairments of real and dynamic systems. Considering multiple-antennas APs, we derive novel closed-form expressions for the downlink (DL) spectral efficiency of both systems. We reveal that limiting the number of served users per AP in distributed massive MIMO systems leads to a corresponding loss in the performance, especially under max-min power control. Besides, despite the SC system provides the largest per-user average DL rate under the deployment of ideal APs, distributed massive MIMO systems become superior in the presence of non-ideal APs. Notably, while increasing the number of deployed non-ideal APs can reduce the introduced loss in distributed massive MIMO systems, this leads to an extra performance loss in SC systems. Finally, we show that the presence of high-velocity users is more harsh in SC systems. In addition, our results show that the SC system operation is more suitable for low-velocity users, however, it is better to operate networks with high velocities users under the distributed massive MIMO systems operation.

An Improved Dropping Algorithm for Line-of-Sight Massive MIMO With Tomlinson–Harashima Precoding

One of the problems in line-of-sight massive MIMO is that a few users can have correlated channel vectors. To alleviate this problem, a dropping algorithm has been proposed in the literature, which drops some of the correlated users to make the spatial correlation among the remaining users be less than a certain threshold. Thresholds were found by running a large number of simulations. In this letter, the same dropping algorithm is analyzed for a known nonlinear precoder: Tomlinson-Harashima precoder. Instead of simulation-based thresholds, closed-form analytical expressions are derived in this letter for two power allocation schemes: max-min and equal received power control schemes. It is shown that the derived thresholds are optimal in terms of achievable sum-rate when there is only one correlated pair of users. For channels with multiple pairs of correlated users, simulation results show that using the derived thresholds improves the 5th percentile sum-rate. Due to the fairness criterion of max-min, the improvement for max-min power control is much higher than equal received power control.

Cell-Free Massive MIMO Systems With Low Resolution ADCs

This paper investigates the achievable performance of cell-free massive multiple-input multiple-output (MIMO) systems with low resolution analog-to-digital converters (ADCs) at both the access points (APs) and users. A closed-form expression for the achievable rate is derived, which enables the study of the effects of AP number, antenna number per AP, user number, and ADC resolution on the achievable rate. In addition, a simple asymptotic approximation for the individual user rate is presented, which shows that the user rate is mainly constrained by the ADC resolution at the user. Moreover, we propose an ADC resolution bits allocation scheme aiming at maximizing the sum rate subject to the total ADC resolution bits constraint, which substantially outperforms the equal ADC resolution bits allocation scheme. Furthermore, a max–min power control scheme is proposed, which not only ensures user fairness, but also improves the achievable rate. Finally, simulation results are provided to corroborate the analytical results.

Cluster Grouping and Power Control For Angle-Domain MmWave MIMO NOMA Systems

This paper investigates the performance of angle-domain millimeter-wave (mmWave) multi-input multi-output nonorthogonal multiple access systems in the presence of angular estimation error. A closed-form expression for the achievable rate is presented, based on which an asymptotic approximation is derived. The analytical findings indicate that, as the number of BS antennas goes to infinity, the achievable rate is mainly determined by the antenna number to beam number ratio (ANTBNR) as well as the spatial direction distance. In particular, a large ANTBNR would cause a severe rate loss, and the achievable rate is an increasing function with respect to the spatial direction distance. Capitalizing on this key observation, a novel cluster grouping scheme is designed to mitigate the intercluster interference, which shows a great advantage over a random cluster grouping scheme. Furthermore, a max-min power control scheme is proposed, aiming at enhancing user fairness. Finally, simulation results are provided to corroborate the analytical results.

An Improved Dropping Algorithm for Line-of-Sight Massive MIMO With Max-Min Power Control

In line-of-sight massive MIMO, there is a nonnegligible probability that two users become highly correlated, which leads to a reduction in the achievable sum-rates of linear precoders. In this letter, threshold values of a previously proposed dropping algorithm are found analytically to avoid repeating a large number of simulations to find the optimal threshold. These thresholds allow us to improve conjugate beamforming (CB) and zero-forcing (ZF) sum-rates with max–min power control. By using the proposed threshold values, the CB and ZF sum-rates are maximized, when there are only two correlated users. In addition, by using the derived thresholds, a modified dropping algorithm is proposed for channels with any number of correlated users. The results of the simulation scenarios show that at signal to noise ratio of 20 dB and 120 antennas at the base station, the modified algorithm improves the average CB and ZF sum-rates up to 36% and 5%, respectively.

Performance Analysis and Power Control of Cell-Free Massive MIMO Systems With Hardware Impairments

As an interesting network architecture for future wireless communication systems, cell-free (CF) massive multiple-input multiple-output (MIMO) distributes an excess number of access points (APs) with single or multiple antennas to cooperatively communicate with several user equipments (UEs). To realize CF massive MIMO in production, hardware impairments become a crucial problem since cheaper and low-quality antennas are needed to ensure economic and energy feasibility. In this paper, we propose a framework for performance analysis in the CF massive MIMO with classical hardware distortion models. For both uplink and downlink, closed-form spectral and energy efficiency expressions are derived, respectively. Based on these results, we provide significant insights into the practical impact of hardware impairments on CF massive MIMO. For example, the impact of hardware distortion at the APs asymptotically vanishes. Furthermore, in order to ensure uniformly good service to the users, we propose a max–min power control algorithm to maximize the minimum UE rate. Via analytical and numerical results, we prove that CF massive MIMO can tolerate hardware impairments without performance reduction.

Massive MIMO With Max-Min Power Control in Line-of-Sight Propagation Environment

Massive MIMO relies on the asymptotic orthogonality of channel vectors to different users. For $M$ service antennas, the expected correlation between a pair of channel vectors under line-of-sight (LoS) conditions decreases at least as fast as $\log (M)/M$ , while in independent and identically distributed (iid) Rayleigh fading, it decreases much slower at $1/\sqrt {M}$ , but the variance is higher under LoS. This signifies that typically channel vectors are more nearly orthogonal under LoS, but with a non-negligible probability, they can have an anomalously large correlation. A single-cell analysis discloses that Massive MIMO with max-min power control performs comparably under LoS and iid Rayleigh, when a simple algorithm is applied under LoS to drop a small number of high-correlation users from service.

Precoding and Power Optimization in Cell-Free Massive MIMO Systems

Cell-free Massive multiple-input multiple-output (MIMO) comprises a large number of distributed low-cost low-power single antenna access points (APs) connected to a network controller. The number of AP antennas is significantly larger than the number of users. The system is not partitioned into cells and each user is served by all APs simultaneously. The simplest linear precoding schemes are conjugate beamforming and zero-forcing. Max-min power control provides equal throughput to all users and is considered in this paper. Surprisingly, under max-min power control, most APs are found to transmit at less than full power. The zero-forcing precoder significantly outperforms conjugate beamforming. For zero-forcing, a near-optimal power control algorithm is developed that is considerably simpler than exact max-min power control. An alternative to cell-free systems is small-cell operation in which each user is served by only one AP for which power optimization algorithms are also developed. Cell-free Massive MIMO is shown to provide five- to ten-fold improvement in 95%-likely per-user throughput over small-cell operation.

Cell-Free Massive MIMO Versus Small Cells

A Cell-Free Massive MIMO (multiple-input multiple-output) system comprises a very large number of distributed access points (APs), which simultaneously serve a much smaller number of users over the same time/frequency resources based on directly measured channel characteristics. The APs and users have only one antenna each. The APs acquire channel state information through time-division duplex operation and the reception of uplink pilot signals transmitted by the users. The APs perform multiplexing/de-multiplexing through conjugate beamforming on the downlink and matched filtering on the uplink. Closed-form expressions for individual user uplink and downlink throughputs lead to max–min power control algorithms. Max–min power control ensures uniformly good service throughout the area of coverage. A pilot assignment algorithm helps to mitigate the effects of pilot contamination, but power control is far more important in that regard. Cell-Free Massive MIMO has considerably improved performance with respect to a conventional small-cell scheme, whereby each user is served by a dedicated AP, in terms of both 95%-likely per-user throughput and immunity to shadow fading spatial correlation. Under uncorrelated shadow fading conditions, the cell-free scheme provides nearly fivefold improvement in 95%-likely per-user throughput over the small-cell scheme, and tenfold improvement when shadow fading is correlated.

Max–Min Power Control in Wireless Networks With Successive Interference Cancelation

We consider a wireless network comprising a number of cochannel (hence mutually interfering) links. We study the power control problem of maximizing the rate that all links can simultaneously support under a novel setup, where receivers have interference cancelation (IC) capabilities. The problem of allocating the transmitting power is intertwined with determining the links on which receivers can perform IC and the order of cancelations. We provide and prove the theoretical results of the problem complexity and structural properties. For the problem solution, we propose a mixed-integer linear programming framework that enables jointly determining the optimal power and the IC patterns using off-the-shelf algorithms. This allows for the accurate assessment of the potential of IC for power control. Extensive numerical results are presented for performance evaluation, demonstrating the benefit of deploying IC in power control.