Achievable Ergodic Sum-rate Research Articles

Power Allocation for an Energy-Efficient Massive MIMO System With Imperfect CSI

Massive multiple-input and multiple-output (MIMO) has been recognized as a core technology for the fifth generation networks due to its huge spectral utilization brought by multiplexing gain and array gain. Most previous works on Massive MIMO systems have focused on the power optimization to maximize the system energy efficiency, in which the ergodic achievable sum-rate is replaced with a lower bound closed-form expression, which can result in suboptimal performance. In this paper, we aim to optimize the power assignment to achieve the maximum energy efficiency for a downlink system of single-cell Massive MIMO based on a tight approximate expression for the achievable sum-rate. Considering two linear precoding strategies at base station, i.e., maximum ratio transmission and zero-forcing, we first derive the corresponding approximate closed-form of the achievable sum-rate under imperfect channel state information. Furthermore, an energy-efficient power allocation scheme is formulated as a non-convex optimization problem. An iterative power allocation algorithm that maximizes the system energy efficiency is developed based on the Lagrangian dual approach. Simulation results demonstrate the tightness of the proposed approximate closed-form expressions, and show that our designed algorithm yields much better energy efficiency performance over the existing algorithms.

On the Feasibility of Full-Duplex Large-Scale MIMO Cellular Systems

This paper concerns the feasibility of full-duplex large-scale multiple-input-multiple-output cellular systems. We first derive the analytic model of the ergodic achievable sum-rate for cell-boundary users. The model is derived by applying a simple linear filter, i.e., matched filter or zero-forcing filter, to the base-station (BS). In the analytic model, we consider large-scale fading, pilot contamination, transmitter noise, and receiver distortion. In addition, to solve the critical pilot overhead problem induced by self-interference channel estimation, we propose a pilot transmission scheme—the simultaneous pilot transmission (SPT)—and assess its performance, in terms of the ergodic sum-rate. In considering two multicell scenarios, cooperative and non-cooperative multicell systems, we obtain the ergodic achievable sum-rate by reflecting the characteristic of each scenarios, such as limited front-haul capacity and procedures of channel estimation. With all derived results, to investigate the feasibility, we observe the tradeoffs between the full- and half-duplex systems, between the SPT and conventional scheme, and between the two multicell scenarios with respect to various system parameters and environment. In the end, we confirm the tightness of our analytic model and advantages of full-duplex, SPT, and cooperation of BSs in our system model.

BDMA in Multicell Massive MIMO Communications: Power Allocation Algorithms

We investigate power allocation strategies for beam division multiple access transmission in multicell massive multiple-input-multiple-output (MIMO) communications. Focusing on massive MIMO downlink with only statistical channel state information at serving base stations and multiantenna terminals, the eigenmatrices of channel transmit covariance matrices become identical and independent of terminals. Utilizing these eigenmatrices as precoding matrices, we consider power allocation of beam domain transmission. By treating cochannel user interferences as noises, the objective function of achievable ergodic sum-rate of the multicell massive MIMO downlink reduces to a difference of concave functions. We identify the orthogonality conditions for optimal power allocation. The results show that the transmit power allocated to the users should be nonoverlapping across beams defined by the channel transmit covariance matrices. We present two algorithms to optimize power allocation in the beam space. We also prove the convergence of the algorithms and show that the solution obtained by the algorithms satisfies the orthogonality conditions. Numerical results confirm the efficiency and the improved performance of the proposed algorithms.

Statistical Eigenmode Transmission for the MU-MIMO Downlink in Rician Fading

In this paper, we study the achievable ergodic sum-rate of multiuser multiple-input multiple-output downlink systems in Rician fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by using the Mullen's inequality, and then use it to analyze the effect of channel mean information on the achievable ergodic sum-rate. A novel statistical-eigenmode space-division multiple-access (SE-SDMA) downlink transmission scheme is then proposed. For this scheme, we derive an exact analytical closed-form expression for the achievable ergodic rate and present tractable tight upper and lower bounds. Based on our analysis, we gain valuable insights into the impact of the system parameters, such as the number of transmit antennas, the signal-to-noise ratio (SNR) and Rician $K$-factor, on the system sum-rate. Results show that the sum-rate converges to a saturation value in the high SNR regime and tends to a lower limit for the low Rician $K$-factor case. In addition, we compare the achievable ergodic sum-rate between SE-SDMA and zero-forcing beamforming with perfect channel state information at the base station. Our results reveal that the rate gap tends to zero in the high Rician $K$-factor regime.

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.

On the Asymptotic Sum Rate of Downlink Cellular Systems With Random User Locations

We consider a downlink cellular communication system with a multi-antenna base station (BS). A regularized zero forcing precoder is employed at the BS to manage the inter-user interference within the cell. Using methods from random matrix theory, we derive a deterministic approximation for the achievable ergodic sum rate, taking into account the randomness from both fading and random user locations. The obtained approximation describes well the behavior of finite-sized systems and enables efficient optimization of the precoder matrix.

Transmission mode switching for device-to-device communication aided by relay node

Abstract In this paper, we investigate the strategy of transmission mode switching for device-to-device (D2D) communication in both single-cell scenario and multi-cell scenarios, which selects the transmission mode to guarantee the maximum ergodic achievable sum-rate among three transmission modes. We first introduce the basic operation principles of three communication transmission modes which are named as traditional cellular communication mode, direct D2D communication mode and two-way decode-and-forward (DF)-relayed D2D communication mode. Then we derive the corresponding expressions for the ergodic achievable sum-rates of each transmission mode, and get the crossing points of different transmission modes to attain maximum ergodic achievable sum-rate of the system. From the analytical results, we can see that the proper operating region of each transmission mode is related to different interference level and distance of the D2D users. Based on the analytical results, we obtain a reliable communication transmission mode switching strategy which guarantees the system to choose the mode with the maximum ergodic achievable sum-rate so as to improve the performance of D2D communication. Numerical results demonstrate that by applying mode switching, the ergodic achievable sum-rate of the system achieves a remarkable enhancement.

Virtual MIMO in Multi-Cell Distributed Antenna Systems: Coordinated Transmissions with Large-Scale CSIT

The virtual multiple input multiple output (MIMO) technique can dramatically improve the performance of a multi-cell distributed antenna system (DAS), thanks to its great potentials for inter-cell interference mitigation. One of the most challenging issues for virtual MIMO is the acquisition of channel state information at the transmitter (CSIT), which usually leads to an overwhelming amount of system overhead. In this work, we focus on the case that only the slowly-varying large-scale channel state is required at the transmitter, and explore the performance gain that can be achieved by coordinated transmissions for virtual MIMO with large-scale CSIT. Aiming at maximizing the achievable ergodic sum rate, the input covariances for all the mobile terminals (MTs) are jointly optimized, which turns out to be a complicated non-convex problem with a non-closed-form objective function. Further analysis reveals that the coordinated transmission problem can be recast as a Max-Min problem with a closed-form objective function and linear constraints. Then, by appealing to the successive approximation method and the saddle-point theory of concave-convex functions, we propose an iterative algorithm for coordinated transmissions with large-scale CSIT and establish its convergence. Simulation results corroborate that the proposed scheme converges quickly, and it yields significant performance gains compared to the existing schemes. Moreover, it is observed that the proposed scheme can achieve a nearly globally-optimal point under the diagonal input covariance constraint. Since the acquisition of large-scale CSIT is far less demanding than that of full CSIT, we believe that the proposed coordinated transmissions with large-scale CSIT in DASs shed some light on virtual MIMO in the making.

Alternative Awaiting and Broadcast for Two-Way Relay Fading Channels

We investigate a two-way relay (TWR) fading channel where two source nodes wish to exchange information with the help of a relay node. Given traditional TWR protocols, transmission rates in both directions are known to be limited by the hop with lower capacity, i.e., the min operations between uplink and downlink. In this paper, we propose a new transmission protocol, called alternative awaiting and broadcast (AAB), to cancel the min operations in the TWR fading channels. The operational principles, a new upper bound on ergodic sum capacity (ESC), and a convergence behavior of the average delay of signal transmission (ST) (in the relay buffer) for the proposed AAB protocol are analyzed. Moreover, we propose a suboptimal encoding/decoding solution for the AAB protocol and derive an achievable ergodic sum rate (ESR) with a corresponding average delay of ST. Numerical results show that 1) the proposed AAB protocol significantly improves the achievable ESR compared with the traditional TWR protocols, and 2) considering the average delay of system service (SS) (in the source buffer), the average delay of ST induced by the proposed AAB protocol is very small and negligible.

Jamming Energy Allocation in Training-Based Multiple Access Systems

We consider the problem of jamming attack in a multiple access channel with training-based transmission. First, we derive upper and lower bounds on the maximum achievable ergodic sum-rate which explicitly shows the impact of jamming during both the training phase and the data transmission phase. Then, from the jammer's design perspective, we analytically find the optimal jamming energy allocation between the two phases that minimizes the derived bounds on the ergodic sum-rate. Numerical results demonstrate that the obtained optimal jamming design reduces the ergodic sum-rate of the legitimate users considerably in comparison to fixed power jamming.

Ergodic and Outage Performance of Fading Broadcast Channels With 1-Bit Feedback

In this paper, the ergodic sum rate and the outage probability of a downlink single-antenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1-bit feedback per fading block per user is available at the base station. We first study the ergodic sum rate of the 1-bit feedback scheme and consider the impact of feedback delay on the system. A closed-form expression for the achievable ergodic sum rate is presented as a function of the fading temporal correlation coefficient. It is proved that the sum rate scales as log log K, which is the same scaling law achieved by the optimal nondelayed full CSI feedback scheme. The sum-rate degradation due to outdated CSI is also evaluated in the asymptotic regimes of either large K or low SNR. The outage performance of the 1-bit feedback scheme for both instantaneous and outdated feedback is then investigated. Expressions for the outage probabilities are derived, along with the corresponding diversity-multiplexing tradeoffs (DMTs). It is shown that, with instantaneous feedback, a power allocation based on the feedback bits enables doubling of the DMT compared with the case with short-term power constraint in which a dynamic power allocation is not allowed. However, with outdated feedback, the advantage of power allocation is lost, and the DMT reverts to that achievable with no CSI feedback. Nevertheless, for finite SNR, improvement in terms of outage probability can still be obtained.

Practical Power Allocation for Cooperative Distributed Antenna Systems

In this letter, we address the problem of downlink power allocation for the generalized distributed antenna system (DAS) with cooperative clusters. Considering practical applications, we assume that only the large-scale channel state information is available at the transmitter. The power allocation scheme is investigated with the target of ergodic achievable sum rate maximization. Based on some approximations and the Rayleigh Quotient Theory, the simple selective power allocation scheme is derived for the low SNR scenario and the high SNR scenario, respectively. The methods are applicable in practice due to their low complexity.

Sum-Rate Analysis of Downlink Channels with 1-Bit Feedback

The sum-rate capacity of a single-input single-output (SISO) downlink with Rayleigh flat fading channels and K users, grows as log log K when optimal scheduling is employed. However, the optimal scheduling requires that the full channel state information (CSI) for all users be available to the transmitter. In this work it is shown that the same rate growth holds even if the feedback rate from the users to the transmitter is reduced to 1-bit per fading block. A simple analysis for this setup is presented, resulting in a closed form expression for the achievable ergodic sum-rate. The mechanism of setting a sub-optimal threshold is elucidated by simple lower and upper bounds to the sum-rate. Among the insights afforded by the sum-rate expression and the bounds, is that application of the sub-optimal threshold demonstrates the same scaling law as the optimal full CSI scheme, asymptotically with the number of users K