Beamformer designs for zero-forcing dirty paper coding

The power allocation that maximizes the sum rate of transceivers operating in the same frequency band is a difficult non-convex problem. In our earlier work, we proved that for transceivers operating under a total power constraint, the maximum sum rate occurs at the boundary of the feasible set formed by the hyper plane representing the power constraint. This finding is nontrivial considering that we are dealing with an interference limited system. In this paper, we study the convex structure of the sum rate on the boundary of the power constraint hyper plane. For two transceivers, we prove that the sum rate is always convex on the line created by the power constraint equality. In the case of three transceivers, we identify a region in the middle of the plane created by the power constraint equality, where the sum rate is concave. This is significant because it is in the middle of the boundary plane that the power allocation can be expected to be fair to all three users. We also provide a power allocation protocol and an algorithm that distribute the power among the transceivers with fairness. Simulation results are provided to support the theorems proven in the paper as well as to demonstrate the convergence of the algorithm to the global maximum sum rate. Results of the algorithm are compared with solutions based on Game theory.

Typical formulations of max-min weighted SIR problems involve either a total power constraint or individual power constraints. These formulations are unable to handle the complexities in multicell networks where each base station can be subject to its own sum power constraint. This paper considers the max-min weighted SIR problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we derive the uplink-downlink duality principle by applying Lagrange duality to the single-constraint problem. Next, we apply nonlinear Perron-Frobenius theory to derive a closed-form solution for the multiple-constraint problem. Then, by exploiting the structure of the closed-form solution, we relate the multiple-constraint problem with its single-constraint subproblems and establish the dual uplink problem. Finally, we further apply nonlinear Perron-Frobenius theory to derive an algorithm which converges geometrically fast to the optimal solution.

A novel unified approach to deal with arbitrary transmitted power constraints for designing jointly the MMSE precoders and decoders in downlink multiuser MIMO systems is developed. This work is an extension of the iterative approach developed in (Jinfan Zhang et al., 2005) for the total power constraint. An explicit expression relating Lagrange multipliers with the per-user constraint can be obtained using the proposed approach to mitigate the time consuming root searching for the Lagrange multipliers in (Jinfan Zhang et al., 2005). Moreover, the explicit expression allows the MMSE solution subject to arbitrary transmit power constraints. In this paper, total, per-user, per-antenna, and peak power constraints are formulated in under the same format and solved using the proposed approach. It is shown in some two-user numerical examples that the raw BER performance obtained from the practical per-antenna power constraint is similar to those of the per-user and total power constraints and is 1-1.5 dB better than that of the peak power constraint.

This paper presents a novel resource allocation framework for downlink transmissions in MIMO-OFDMA based cognitive radio (CR) networks. In this literature, due to the coexistence of primary and secondary users (SUs) in the same geographical area, the interference induced to the primary users’ (PUs) bands from SUs’ transmissions should be less than the tolerable interference threshold predefined by PU. Hence, the optimal resource allocation strategy is performed subject to the total power constraint in the cognitive base station and the interference power constraint for PUs so that the downlink sum throughput of the CR network can be maximize without causing unacceptable interference. To this aim, two sub-problems are presented and solved theoretically based on convex optimization framework that can be used in the main body of the proposed algorithm. Regarding to the first sub-problem, the resources are distributed among all SUs in a way that just the total power constraint is satisfied. Also, the sum throughput is maximized as the interference power onto the PUs’ bands keeps in a tolerable range in the second sub-problem. So, in order to find the optimum solution, our algorithm consists of three parts. The first two parts include these sub-problems while the last section includes a combination of them. For complexity reduction, two sub-optimal resource allocation algorithms are introduced based on the simplification of main problem constraints. The performance of different approaches is investigated via simulation. Conducted simulation results show that the optimal algorithm achieves better performance in comparison with benchmark algorithms and converges to sub-problem solutions in high and low regimes of interference thresholds.

In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR.

A two-way relay channel (TWRC) in which two terminals <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> exchange orthogonal frequency division multiplexing (OFDM) signals with the help of an amplify-and-forward (AF) relay <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> is considered here, and an efficient technique for allocating powers to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> parallel tones of OFDM is developed. A sum rate maximization problem is formulated by replacing the individual power constraints of the conventional sum rate maximization problem, which limit the power of each terminal, with the total power constraint limiting the sum of powers of all terminals. The maximization problem with the total power constraint yields a more efficient power allocation policy than the conventional problem with individual power constraints. It is shown that the closed-form solution of the maximization problem under the total power constraint can be obtained for a single-tone system ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> =1). Based on this result, a two-step suboptimal approach is proposed in which the power is optimally assigned to each tone first, and then at each tone the assigned power is distributed to the three terminals. The proposed method is shown to assign 50% of the total power to relay <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> irrespective of the channels. It is demonstrated that the proposed method is considerably simpler to implement than the conventional dual-decomposition method (DDM), yet the performance of the former is almost identical to that of the latter.

In this paper, we study the channel estimation and the optimal training design for relay networks that operate under the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decode-and-forward</i> (DF) strategy with the knowledge of the interference covariance. In addition to the total power constraint on all the relays, we introduce individual power constraint for each relay, which reflects the practical scenario where all relays are separated from one another. Considering the individual power constraint for the relay networks is the major difference from that in the traditional point-to-point communication systems where only a total power constraint exists for all colocated antennas. Two types of channel estimation are involved: maximum likelihood (ML) and minimum mean square error (MMSE). For ML channel estimation, the channels are assumed as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deterministic</i> and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory. For MMSE channel estimation, however, the second-order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex. We instead consider three special yet reasonable scenarios. The problem in the first scenario is convex and could be efficiently solved by state-of-the-art optimization tools. Closed-form waterfilling type solutions are found in the remaining two scenarios, of which the first one has an interesting physical interpretation as pouring water into caves.

In this paper, we study the joint allocation of three types of resources, namely, power, subcarriers and relay nodes, in multi-relay assisted dual-hop cooperative OFDM systems. All the relays adopt the amplify-and-forward protocol and assist the transmission from the source to destination simultaneously but on orthogonal subcarriers. The objective is to maximize the system transmission rate subject to individual power constraints on each node or a total network power constraint. We formulate such a problem as a subcarrier-pair based resource allocation that seeks the joint optimization of subcarrier pairing, subcarrier-pair-to-relay assignment, and power allocation. Using a dual approach, we solve this problem efficiently in an asymptotically optimal manner. Specifically, for the optimization problem with individual power constraints, the computational complexity is polynomial in the number of subcarriers and relay nodes, whereas the complexity of the problem with a total power constraint is polynomial in the number of subcarriers.We further propose two suboptimal algorithms for the former to trade off performance for complexity. Simulation studies are conducted to evaluate the average transmission rate and outage probability of the proposed algorithms. The impact of relay location is also discussed.

The power allocation that maximizes the sum rate of transceivers operating in the same frequency band is a difficult non-convex problem. Lack of a convex structure excludes the direct application of Lagrangian dual techniques as the duality gap might not be zero. This paper advances current knowledge by introducing three significant steps in finding a solution. First, we show that for transceivers operating under a total power constraint, the maximum sum rate occurs at the boundary of the feasible set formed by the hyper plane representing the power constraint. This conclusion is nontrivial considering that we are dealing with an interference limited system. Second, we prove that the duality gap is zero for this problem, despite the lack of concavity of the objective. We do this by showing that the maximum sum rate is concave in the power constraint. Third, we propose an iterative algorithm that finds the optimal power allocation by solving the dual problem. Simulation results are provided to support the theorems proven in the paper as well as to demonstrate the convergence of the algorithm to the global maximum sum rate. Results of the algorithm are also compared with solutions based on Game theory.

Consider a Rayleigh flat fading relay channel under two different power constraints: sum power constraint and individual power constraints. In this paper a simple method for resource allocation based on partial channel state information at transmitter and full channel state information at receiver is introduced. It is shown that by using different time portions for the source and the relay in relaying, when the distance from relay to the source is very different from its distance to the destination, achievable rate can be enhanced and outage probability can be reduced under sum power constraint. Also in the case of individual power constraints, time allocation scheme can improve the achievable rate and outage probability.

In this paper, we propose a secure unmanned aerial vehicle (UAV) mobile edge computing (MEC) system where multiple ground users offload large computing tasks to a nearby legitimate UAV in the presence of multiple eavesdropping UAVs with imperfect locations. To enhance security, jamming signals are transmitted from both the full-duplex legitimate UAV and non-offloading ground users. For this system, we design a low-complexity iterative algorithm to maximize the minimum secrecy capacity subject to latency, minimum offloading and total power constraints. Specifically, we jointly optimize the UAV location, users' transmit power, UAV jamming power, offloading ratio, UAV computing capacity, and offloading user association. Numerical results show that our proposed algorithm significantly outperforms baseline strategies over a wide range of UAV self-interference (SI) efficiencies, locations and packet sizes of ground users. Furthermore, we show that there exists a fundamental tradeoff between the security and latency of UAV-enabled MEC systems which depends on the UAV SI efficiency and total UAV power constraints.

Multiple-input multiple-output (MIMO) systems have been widely studied for improving throughput and robustness of optical wireless communication (OWC) systems. Indeed, with MIMO, the likelihood of simultaneous interruption of all optical beams is greatly reduced. For throughput improvement, many power loading strategies are obtained for a total power constraint while allowing power to be freely exchanged among light-emitting diodes (LEDs). In scenarios with unequal distances between LEDs and the user terminal, more power is allocated to the LED that has a better channel than to others. In practice, every optical front-end has its own power limitation and a per-LED power constraint is more meaningful than a total power constraint. This paper studies to what extent this has an impact on the performance of LED-based distributed MIMO (D-MIMO) OWC links. We formulate the achievable rate optimization problem for both cases, when the total power is constrained or when under a per-LED power constraint. Results show that, the achievable rate under a per-LED power constraint is lower than under a total power constraint, but it is higher than if the power is uniformly spread over the entire bandwidth. It also allows for transmit power saving, at a cost of higher computational complexity. In addition, under a per-LED power constraint, LEDs with better channel condition tends to use a modulation bandwidth far above the 3-dB bandwidth.

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

Multi-user multiple input multiple output (MU-MIMO) system is an excellent choice for the next generation broadband communications because of its great potential in enhancing MIMO system capacity. One major challenge of such system is the jointly optimal transceiver beamforming design that maximizes the sum capacity under a total power constraint. Existing approaches have provided convex optimization solution by exploiting the duality between transmitter and receiver. However, with high computation complexity, these approaches are ineligible of practical implementation. In this paper, we aim to provide complexity efficient transceiver beamformer and power allocation design in MU-MIMO downlink (broadcast) channels. We first develop an iterative sub-optimal algorithm based on cyclic self-SINR-maximization (CSSM) beamforming design and water-filling power allocation. Comparing to convex-optimization-based (COB) approaches, the proposed solution (i.e. CSSM-WF algorithm) have insignificant sum-rate degradation but very low computational complexity and extremely fast converging speed. Trying to improve the performance of CSSM-WF algorithm, we then introduce another algorithm denoted as efficient COB (ECOB) algorithm in which CSSM-WF algorithm is used to generate a good start point for optimal COB approaches. Simulation results prove the efficiency of both proposed algorithms.

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.