Subcarrier-pair based resource allocation for cooperative multi-relay OFDM systems

We study the joint allocation of three types of resources, namely, power, subcarriers and relay nodes, in cooperative two-hop multi-relay OFDM systems. Each relay adopts the amplify-and-forward (AF) protocol. The objective is to maximize the system transmission rate subject to individual power constraints on each node. 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 decomposition method, we solve this problem efficiently in an asymptotically optimal manner. We further propose two suboptimal algorithms to trade off performance for complexity. Simulation results demonstrate that the proposed subcarrier-pair based resource allocation schemes significantly outperform the symbol based benchmark scheme. Moreover, it is shown that subcarrier pairing plays an important role in improving the system performance.

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.

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.

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.

This paper presents a simple synchronous distributed power allocation algorithm that maximizes the total transmission rate of a number of radios operating in an unlicensed band, with either a total power constraint or individual power constraints. The redistribution of power by the algorithm also results in a fairer rate distribution. The algorithm is not based on Game theory or Lagrangian dual. Rather it uses the sensitivity of each user's rate to changes in the power levels of all users in the system, to steer the power distribution towards the global maximum sum rate. The algorithm's complexity scales with the number of users in the system. Simulation results demonstrate that the algorithm does converge to the global maximum sum rate and, at the same time, redistributes the power among the users to achieve a more equitable rate distribution. Results of the algorithm are also compared with solutions based on Game theory.

A new approach to distributed cooperative beamforming in relay networks with frequency selective fading is proposed. It is assumed that all the relay nodes are equipped with finite impulse response (FIR) filters and use a filter-and-forward (FF) strategy to compensate for the transmitter-to-relay and relay-to-destination channels. Three relevant half-duplex distributed beamforming problems are considered. The first problem amounts to minimizing the total relay transmitted power subject to the destination quality-of-service (QoS) constraint. In the second and third problems, the destination QoS is maximized subject to the total and individual relay transmitted power constraints, respectively. For the first and second problems, closed-form solutions are obtained, whereas the third problem is solved using convex optimization. The latter convex optimization technique can be also directly extended to the case when the individual and total power constraints should be jointly taken into account. Simulation results demonstrate that in the frequency selective fading case, the proposed FF approach provides substantial performance improvements as compared to the commonly used amplify-and-forward (AF) relay beamforming strategy.

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.

The design of wireless sensor networks for signal processing applications has to consider the limited battery power of the sensor nodes. In this paper, a combined routing path selection and power allocation strategy is presented that is especially designed for distributed detection in sensor networks with a serial topology. The objective is to minimize the global probability of detection error of the serial network under a total network power constraint. The cross-layer approach for the selection of a routing path through the network is based on the local observation SNR of the sensors as well as fading conditions and is efficiently implemented by a backward greedy algorithm. After the routing path is established, a subsequently performed power allocation algorithm aims to optimally distribute a total power budget with respect to the detection performance of the sensor network.

In this paper, we investigate distributed beamforming design for non-regenerative MIMO relay networks, in which all nodes are equipped with multiple antennas. We first give an unified formulation for SNR maximizing beamforming algorithm, which is suitable for both MIMO relay and SISO relay networks, and for both instantaneous channel state information and stochastic channel state information. Based on the general formulation, we design two distributed SNR maximizing beamforming algorithms. First, we design a beamforming algorithm for MIMO relay based on instantaneous channel state information with individual power constraints, using positive semidefinite programming (SDP). In order to reduce network cost for channel estimation, second, we also deign a beamforming algorithm for MIMO relay networks based on stochastic channel state information. We prove that in a symmetric network for the beamforming algorithm based on stochastic channel state information with individual power constraints, there exists a closed-form solution that has almost the same performance as that of the numerical methods. This result can be easily extended to a general beamforming algorithm based on stochastic channel state information, but with total power constraint.

We consider distributed estimation in wireless sensor networks (WSNs). Using linear minimum mean squared error (LMMSE) estimator, we derive mean squared error (MSE) to measure the quality of estimation. We introduce a global signal to noise ratio (SNR), where we can derive capacity of data collection in terms of mutual information as reciprocity of MSE. Based on the global SNR, we derive equal power allocation and optimal power allocation in orthogonal multiple access channel (MAC) models. We also derive asymptotic behavior of the global SNR when the power and the number of sensors become unlimited. We minimize MSE as well as maximize mutual information by considering total and individual power constraints. We show that MSE and mutual information of equal power allocation outperforms optimal power allocation. Moreover, system with individual power constraint is worse than the system without that because the suggested power to be allocated is constrained by maximum transmit power of the sensors.

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation in a single-relay multiple-access system. The optimization objective is to maximize the weighted sum-rate under total and individual power constraints on the transmitters. By observing the special structure of a three-dimensional assignment problem derived from the original problem, we propose a polynomial-time algorithm based on continuity relaxation and dual minimization. The proposed method is shown to be optimal for all relaying strategies that give a concave rate function in terms of power constraints.

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.

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.

The problem of resource allocation for OFDMA downlink is investigated in this paper. The problem is formulated as a rate adaptive problem, which is to maximize the system throughput while subject to total transmission power constraints. A distributed resource allocation scheme to solve this combinatorial optimization problem is presented. The problem is decomposed into a principal problem with regard to the base station and several subproblems with regard to the users. In particular, we consider regarding users as relay nodes that could send feedback information back to the base station. By solving the subproblems, each user obtains its own subcarriers and power allocation scheme. The base station could make sure all the constraints are met and the system throughput is maximized by solving the principal problem. Simulation results show that the proposed algorithm converges quickly to an approximated optimal solution in a small number of iterations.

Power allocation in multi-hop OFDM transmission systems with amplify-and-forward relaying: A unified approach