On the MIMO Capacity With Joint Sum and Per-Antenna Power Constraints: A New Efficient Numerical Method

We determine the capacity-optimal transmission strategy for a multiple-input-multiple-output (MIMO) Gaussian channel under multiple power constraints, namely joint sum power constraint (SPC), per group power constraints (PGPC), and per antenna power constraints (PAPC). First, we focus on cases where we can analytically determine the optimal transmit strategy under joint SPC-PGPC-PAPC. We obtain results for the following cases: 1) $n_{t} \times 1$ multiple-input-single-output (MISO); 2) MIMO channel with full column rank and full rank optimal covariance matrix; and 3) $2 \times n_{r}$ MIMO channel. These results generalize some recent results for the special cases of PAPC only and joint SPC-PAPC. Then, we propose a projected factored gradient descent (PFGD) algorithm for the general MIMO Gaussian channel under joint SPC-PGPC-PAPC including the possibility of additional rank constraints. This algorithm matches the solution of standard convex optimization tools with lower complexity. The algorithm also overcomes the limitations of existing algorithms, in terms of accuracy and applicability to low rank channels.

Joint Beamforming and power allocation schemes are considered for cognitive radio (CR) multiple input single output (MISO) system in this paper. We considered the robust downlink beamforming and power allocation problem with per-antenna power constraints which is more realistic in practice, instead of sum-power constraint, under the imperfect channel state information (CSI). Since the given optimization problem is a non-convex problem which is difficult to handle, we transformed it into second order cone program (SOCP) problem, which can be solved efficiently. Simulation shows that the proposed scheme indeed has a better performance in CR system.

We consider the downlink transmission of a wireless communication system where M antennas transmit independent information to a subset of K users, each equipped with a single antenna. The Shannon capacity of this MIMO broadcast channel (MIMO-BC) can be achieved using a non-linear preceding technique known as dirty paper coding (DPC) which is difficult to implement in practice. Motivated to study simpler transmission techniques, we focus on a linear precoding technique based on the zero-forcing (ZF) algorithm. In contrast to the typical sum power constraint (SPC), we consider a per-antenna power constraint (PAPC) motivated both by current antenna array designs where each antenna is powered by a separate amplifier and by future wireless networks where spatially separated antennas transmit cooperatively to users. We show that the problem of power allocation for maximizing the weighted sum rate under ZF with PAPC is a constrained convex optimization problem that can be solved using conventional numerical optimization techniques. For the special case of two users, we find an analytic solution based on waterfilling techniques. For the case where the number of users increases without bound, we show that ZF with PAPC is asymptotically optimal in the sense that the ratio of the expected sum-rate capacities between ZF with PAPC and DPC with SPC approaches one. We also show how the results can be generalized for multiple frequency bands and for a hybrid power constraint. Finally, we provide numerical results that show ZF with PAPC achieves a significant fraction of the optimum DPC sum-rate capacity in practical cases where K is bounded

MISO NOMA downlink beamforming optimization with per-antenna power constraints

We consider the MIMO broadcast channel (MIMO-BC) where an array equipped with M antennas transmits distinct information to K users, each equipped with N antennas. We propose a linear precoding technique, called multiuser eigenmode transmission (MET), based on the block diagonalization precoding technique. MET addresses the shortcomings of previous ZF-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm. We consider both the typical sum-power constraint (SPC), and a per-antenna power constraint (PAPC) motivated by array architectures where antennas are powered by separate amplifiers and are either co-located or spatially separated. Numerical results show that the proposed MET technique outperforms previous linear techniques with both SPC and PAPC. Asymptotically as the number of user K increases without bound, we show that block diagonalization with receive antenna selection under PAPC and SPC are asymptotically optimal.

Massive multiple input multiple output (MIMO) is the key technology in the 5G communication network. Blind source separation (BSS) plays an important role in MIMO communication when information about the transmitted signals or channel is not available. Independent component analysis (ICA) is one of the well-known BSS technique applied in MIMO wireless communication. Existing BSS techniques like ICA assumes number of receiving antennas to be greater than or equal to the number of transmit antennas and hence cannot be applied to multiple input single output (MISO) communication scenario, that happens during downlink massive MIMO communication. In single channel blind source separation (SCBSS) the source signals are retrieved from a single observed mixture (single channel or single receiving antenna) of the source signals. In this paper, we investigate the application of SCBSS to MISO communication system. Using ensemble empirical mode decomposition (EEMD), the MISO communication system is converted to a pseudo MIMO system followed by the application of principal component analysis (PCA) and ICA algorithms to separate the transmitted signals. The algorithm is successfully applied to 2 X 1 MISO system and with a slight modification to n X 1 MISO system. Simulation results are provided to validate the performance of the algorithm.

In transmit beamforming (BF) systems, one of key issues is how to design an appropriate BF vector to optimize the performance of the whole system. This paper addresses the transmit BF design problem for cyclic prefixed (CP) transmissions over Multiple Input Single Output (MISO) frequency-selective channels under per-antenna power constraints (PPC).In previous studies, several methods have been used to solve this problem, however, all lead to suboptimal solutions. In an attempt to get the optimal solution, we propose an efficient algorithm based on barrier method, which performs closely to the optimal total power constraint (TPC) solution and significantly outperforms the existing PPC solutions. Moreover, the simulation results also show that the proposed algorithm is robust on the different antenna power allocation and antenna number.

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.

This paper considers a two user Gaussian multiple-input single-output (MISO) broadcast channel with a per-antenna peak power constraint (or simply peak power constraint). It is more realistic to consider the peak power constraint on each transmit antenna because each antenna is equipped with its own power amplifier in many practical implementations. Assuming the perfect channel state information (CSI) at the transmitter, we propose an achievable scheme using a dirty-tape coding (DTC). The uniform input in a fixed range of the DTC scheme helps to control the peak power of the transmit signal easily. We also present an optimization algorithm that finds the capacity achieving beamforming vectors and power allocations under a per-antenna average power constraint used in our achievable scheme. Simulation results show that as the transmit power increases, the achievable rate region under the peak power constraint is getting close to the capacity region under the reduced per-antenna average power constraint by 1/3. Compared to a non-DTC scheme based on minimum mean square error (MMSE) beamforming, the proposed scheme performs better.

Many MIMO capacity analyses and precoding algorithms are obtained based on the assumption of total power constraint while assuming power can be allocated freely across antennas. In practical MIMO systems, however, per-antenna power constraints are often more predominant design consideration than the total power constraints. In this paper, we study the transmission schemes for MIMO systems with per-antenna power constraints. We derive the necessary and sufficient conditions for the optimal transmission scheme. We also develop an iterative algorithm and prove its convergence to the optimal solution.

This paper considers transmit covariance optimization for a multi-input multi-output (MIMO) Gaussian wiretap channel. Specifically, we aim to maximize the MIMO secrecy capacity by judiciously designing the transmit covariance under the sum power and per-antenna power constraints. The MIMO secrecy capacity maximization (SCM) problem is nonconvex, and so far there is no tractable solution available. We propose an alternating optimization (AO) approach to handle the SCM problem. In particular, our development consists of two steps: First, we show that the SCM problem can be reexpressed to a form that can be conveniently processed by AO. Second, we develop a custom-designed fast algorithm for each AO iteration. Interestingly, with this fast implementation, the overall AO algorithm can be viewed as performing iterative reweighting and water-filling. Finally, the convergence of the proposed algorithm to a stationary solution of SCM is shown, and numerical results are provided to demonstrate its efficacy.

In this paper, we consider the single-user MIMO channel with per-antenna power constraint. We formulate the capacity optimization problem with per-antenna constraint in the SDP framework and analyze its optimality conditions. We establish in closed-form the optimal input covariance matrix as a function of the dual variable. We then propose a simple algorithm to find this optimal input covariance and the capacity. Results show that the capacity with per-antenna power can be significantly different from those with sum power or with independent multiple access constraint.

Block diagonalization (BD) is a practically favorable precoding technique that eliminates the interuser interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in a cooperative multi-cell system, where the signals from different base stations (BSs) to all the mobile stations (MSs) are jointly designed with the perfect knowledge of the downlink channels and transmit messages. Specifically, this paper studies the BD precoder design to maximize the weighted sum-rate achievable for all the MSs. The associated optimization problem can be formulated in an auxiliary MIMO broadcast channel (BC) with a set of transmit power constraints equivalent to those for different BSs in the multi-cell system. Based on convex optimization techniques, this paper designs an efficient algorithm to solve this problem, and derives the structure of the corresponding optimal BD precoding matrix. Moreover, for the special case of single-antenna BSs and MSs, it is shown that the proposed solution leads to the optimal zero-forcing beamforming (ZF-BF) precoder design for the multiple-input single-output (MISO) BC with the per-antenna power constraints.

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

We propose an iterative mode-dropping algorithm that optimizes input signals to achieve the sum capacity of the MIMO-MAC with per-antenna power constraint. The algorithm successively optimizes each user's input covariance matrix by applying mode-dropping to the equivalent single-user MIMO rate maximization problem. Both analysis and simulation show fast convergence. We then use the algorithm to briefly highlight the difference in MIMO-MAC capacities under sum and per-antenna power constraints.