Aggregate Power Constraint Research Articles

Secure transmission for wireless collaborative systems based on second‐order channel statistics

AbstractIn this article, we investigate the maximum secrecy rates (SRs) and the optimal beamforming schemes for a collaborative wireless network under uncertain channel levels of available second‐order statistics. Both decode‐and‐forward (DF) and amplify‐and‐forward (AF) strategies under the aggregate and individual power constraints are considered. We have derived the maximum SRs and the optimal beamforming vectors under aforementioned conditions and an efficient cooperation paradigm to provide secrecy in a multirelay environment. A closed‐form maximum SR in the DF scheme under aggregate power constraint is presented. Next, the upper and lower bounds for the maximum SR under aggregate power constraint in the AF scheme is derived. The optimization problem in the AF scheme can be converted into a convex semidefinite programming problem, which is efficiently solved by the bisection method. Moreover, the optimal beamforming weights are also obtained to maximize the SRs under both aggregate and individual relay power constraints. Numerical results are provided to demonstrate the effectiveness of proposed algorithms.

Multi-antenna Decode and Forward Relay Selection over Nakagami-m Fading Channels

This paper analyzes the performance of opportunistic relay under aggregate power constraint in Decode-and-Forward (DF) relay networks over independent, non-identical, Nakagami-m fading channels, assuming multiple antennas are available at the relay node. According to whether instantaneous Signal-to-Noise Ratio (SNR) or average SNR can be exploited for relay selection, two opportunistic relay schemes, opportunistic multi-antenna relay selection (OMRS) and average best relay selection (ABRS) are proposed. The closed form expressions of outage probability and error performance for binary phase shift keying (BPSK) modulation of OMRS and ABRS are determined using the moment generating function (MGF) of the total signal-to-noise ratio (SNR) at the destination. Simulations are provided to verify the correctness of theoretical analysis. It is observed that OMRS is outage-optimal among multi-antenna relay selection schemes and approaches the Beamforming (BF) scheme known as theoretical outage-optimal very closely. Compared with previous single-antenna Opportunistic Relaying (OR) scheme, OMRS brings remarkable performance improvement obtained from maximum ratio combining (MRC) and beamforming, which proves that multiple antennas at the relays could provide more array gain and diversity order. It also shows that the performance of ABRS in asymmetric channels is close to OMRS in the low and median SNR range.

Two-Tier Cellular Networks for Throughput Maximization of Static and Mobile Users

In small cell networks, high mobility of users results in frequent handoff and thus severely restricts the data rate for mobile users. To alleviate this problem, we propose to use heterogeneous, two-tier network structure where static users are served by both macro and micro base stations, whereas the mobile (i.e., moving) users are served only by macro base stations having larger cells; the idea is to prevent frequent data outage for mobile users due to handoff. We use the classical two-tier Poisson network model with different transmit powers (cf [1]), assume independent Poisson process of static users and doubly stochastic Poisson process of mobile users moving at a constant speed along infinite straight lines generated by a Poisson line process. Using stochastic geometry, we calculate the average downlink data rate of the typical static and mobile (i.e., moving) users, the latter accounted for handoff outage periods. We consider also the average throughput of these two types of users defined as their average data rates divided by the mean total number of users co-served by the same base station. We find that if the density of a homogeneous network and/or the speed of mobile users is high, it is advantageous to let the mobile users connect only to some optimal fraction of BSs to reduce the frequency of handoffs during which the connection is not assured. If a heterogeneous structure of the network is allowed, one can further jointly optimize the mean throughput of mobile and static users by appropriately tuning the powers of micro and macro base stations subject to some aggregate power constraint ensuring unchanged mean data rates of static users via the network equivalence property (see [2]).

JOINT POWER ALLOCATION FOR DF CONCATENATED MIMO SUCCESSIVE RELAYING SCHEME UNDER NETWORK POWER CONSTRAINTS

Power efficiency is a vital consideration in wireless system. In this paper, we propose a framework for efficient power allocation in decode and forward multiple input multiple output successive relaying systems under network power constraints. Our aim is to maximize the information rate at each link by an optimal power allocation scheme via the primal dual algorithm. Then, we jointly allocate power to the source and transmitting relay under network power constraints. The simulated results show that the proposed joint power allocation scheme under network power constraint can outperform the uniform power allocation under an aggregate power constraints.

Power Allocation for Full-Duplex Relaying-Based D2D Communication Underlaying Cellular Networks

Device-to-device (D2D) communications allow direct transmissions between two proximate user equipments (UEs), which can improve local services in cellular networks. Considering full-duplex (FD) relaying can achieve higher spectrum and energy efficiency than half-duplex (HD) relaying, we propose a new D2D communication scheme that allows D2D links to underlay cellular downlink by assigning D2D transmitters as FD relays to assist cellular downlink transmissions. The system objective is to optimize the achievable rates for the D2D users while fulfilling the minimum rate requirements of the cellular users. To this end, we first derive the achievable rates for both the D2D users and the cellular users. Then we accomplish the system target by optimizing the transmission powers at the base station (BS) and at the D2D transmitter. Under the aggregate power constraint, we can solve the optimal power-allocation problem in closed form. The simulation results show that the proposed FD relaying-based D2D communication scheme outperforms the traditional cellular communication mode and the existing HD relaying-based D2D communication scheme in the maximal achievable rate.

Robust Transceiver Design for Broadband Multiuser Multi-Relay Networks

In this paper, we study the robust design of the relay beamforming (rBF) and destination equalization (dEQ) filters for broadband multiuser multi-relay networks employing single-carrier frequency-division multiple access (SC-FDMA) and orthogonal frequency-division multiple access (OFDMA). Thereby, we consider the realistic case where only imperfect channel state information is available for rBF and dEQ filter optimization. Our goal is to maximize a lower bound for the weighted achievable bit rate (ABR) of the network, subject to either individual relay power constraints (Ind-PCs) or an aggregate relay power constraint (Agg-PC). We first derive the optimal dEQ filters and the phases of the optimal rBF filter coefficients, which are independent of the power constraints. For the Agg-PC, the amplitude optimization of the rBF filter coefficients is decomposed into two subproblems, which correspond to the optimization of the power allocation across the relays and the power allocation across the users and subcarriers, respectively. We obtain a closed-form structural solution for the first subproblem by fixing the powers across users and subcarriers, and the global optimal solution for the second subproblem. For the Ind-PCs, the corresponding optimization problem is formulated as a reverse-convex problem with convex constraints. Subsequently, the constrained convex concave procedure is applied to approximate the original non-convex problem with a sequence of convex problems, which can be efficiently solved using convex optimization techniques. Simulation results validate the excellent performance of the proposed robust rBF and dEQ filter designs and show their superiority compared to conventional non-robust and naive relaying schemes.

A Relay Selection and Power Allocation Scheme for Cooperative Wireless Sensor Networks

This paper investigates optimal relay selection and power allocation under an aggregate power constraint for cooperative wireless sensor networks assisted by amplify-and-forward relay nodes. By considering both transmission power and circuit power consumptions, the received signal-to-noise ratio (SNR) at the destination node is calculated, based on which, a relay selection and power allocation scheme is developed. The core idea is to adaptively adjust the selected relays and their transmission power to maximize the received SNR according to the channel state information. The proposed scheme is derived by recasting the optimization problem into a three-layered problem?determining the number of relays to be activated, selecting the active relays, and performing power allocation among the selected relays. Monte Carlo simulation results demonstrate that the proposed scheme provides a higher received SNR and a lower bit error rate as compared to the average power allocation scheme.

Robust Power Allocation for Multicarrier Amplify-and-Forward Relaying Systems

It has been shown that adaptive power allocation can provide a substantial performance gain in wireless communication systems when perfect channel state information (CSI) is available at the transmitter. In the case when only imperfect CSI is available, the performance may significantly degrade, and robust power-allocation schemes are developed to save this kind of degradation. In this paper, we investigate power-allocation strategies for multicarrier systems, in which each subcarrier employs single amplify-and-forward (AF) relaying scheme. Optimal power-allocation schemes are proposed by maximizing the approximated channel capacity under an aggregate power constraint (APC) and a separate power constraint (SPC). By comparison with the uniform power-allocation (UPA) scheme and the best channel power-allocation (BCPA) scheme, we confirm that both the APC and SPC schemes achieve a performance gain over benchmark schemes. In addition, the impact of channel uncertainty is also considered in this paper by modeling the uncertainty regions as bounded sets, and results show that the uncertainty can degrade the worst case performance significantly.

Impact of Channel Estimation Error on Bidirectional MABC-AF Relaying With Asymmetric Traffic Requirements

Channel estimation error results in severe performance deterioration in wireless networks. In this paper, we study the impact of imperfect channel estimation (ICE) on the outage performance of bidirectional relaying where the two sources have asymmetric traffic requirements (ATRs). In particular, we focus on the amplify-and-forward (AF) relay-assisted multiple-access broadcast (MABC) protocol, i.e., MABC-AF, which has received much attention due to its high spectrum efficiency and low complexity. In the single-relay scenario, we derive exact and generalized closed-form expressions for system outage probability, which indicate that the system outage is determined by the unidirectional outage in the case of highly asymmetric traffic patterns. For more insights into our approach, the closed-form asymptotic expressions are also evaluated, manifesting the interesting error floor (EF) phenomenon due to ICE. Using these analytical results, we further develop a robust and practical optimum power-allocation (OPA) algorithm that minimizes the system outage probability under aggregate and individual node power constraints. In the multirelay scenario, by taking into account the traffic knowledge, a novel relay selection criterion is proposed for asymmetric MABC-AF, followed by its impact on the system outage probability in the presence of ICE. Numerical results validate the accuracy of our analytical results and highlight the effect of the proposed OPA algorithm under various traffic requirements and channel estimation errors. Furthermore, the results also show that the proposed relay selection criterion is superior to the classical max-min criterion with ATRs, and the performance improvement becomes remarkable as channel estimation error increases.

Optimal power control of parallel orthogonal-frequency-division-multiplexing relaying networks

This article studies the power allocation (PA) problem for dual-hop orthogonal-frequency-division-multiplexing (OFDM) relaying networks, in which a source communicates with a destination with the help of multiple amplify-and-forward relays that employ parallel transmission protocol. The objective is to maximise the system achievable rate, under which an aggregate power constraint is imposed on all relays, and an individual link rate constraint is imposed on each OFDM subchannel. Based on Zhao et al's prior work, the simpler PA problem without considering those rate constraints is firstly solved by optimally allocating the total power across all OFDM subchannels. Then, for the original problem with both power and rate constraints, an order structure is proposed such that in the optimal PA scheme, those subchannels that attain respective maximum link rates are determined one by one, that is the complexity to determine those subchannels is considerably reduced from exponential to linear order.

Asymptotic Performances of Near-Optimal Selective Distributed Beamforming for Two-Way Relaying with Partial Channel State Information

In this letter, we consider distributed beamforming (DBF) techniques for a two-way relaying network in which two sources exchange information through K intermediate relays under an aggregate power constraint. Especially, we construct a simple selective DBF that can be obtained at each relay with partial channel state information (CSI). By asymptotic analysis, the proposed selective DBF is shown to achieve full diversity gain K for each source and that the sum of capacities at the two sources increases as log K. Numerical investigation also shows that the selective DBF provides near optimum performance.

Cooperative Space–Time Coding with Amplify-and- Forward Relaying

Cooperative diversity using distributed space-time codes has been recently proposed to form virtual antennas in order to achieve diversity gain. In this paper, we consider a multi-relay network operating in amplify-and-forward (AAF) mode. Motivated by protocol III presented in (Nabar et al. 2004), we propose a cooperative diversity protocol implementing space---time coding for an arbitrary number of relay nodes when the source-destination link contributes in the second phase. We consider the use of real-orthogonal and quasi-orthogonal designs of space---time codes as they give better performance than random linear-dispersion codes. The pairwise error probability (PEP) has been derived and the theoretical analysis demonstrates that the proposed protocol achieves a diversity of order N?+?1, where N is the number of relay nodes. No instantaneous channel state information is required at the relay nodes. The optimum power allocation that minimizes the PEP is obtained with numerical and theoretical analysis. The aggregate system power constraint is considered in the optimization. Simulation results demonstrate an improvement over the existing orthogonal protocols for different source-destination channel conditions. The results also show that the proposed scheme is robust to the channel estimation errors

Outage analysis of opportunistic multi-antenna relay selection in decode-and-forward relay networks

This article studies the closed-form expressions of outage performance for opportunistic relay under aggregate power constraint in decode-and-forward (DF) relay networks over Rayleigh fading channels, assuming that multiple antennas are available at the relay node. According to whether instantaneous signal-to-noise ratio (SNR) or average SNR can be utilized for relay selection, two opportunistic relay schemes, opportunistic multi-antenna relay selection (OMRS) and average best relay selection (ABRS) are proposed. The performances of both two schemes are evaluated by means of theoretical analysis and simulation. It is observed that OMRS is outage-optimal among multi-antenna relay selection schemes and closely approaches the beamforming (BF) scheme known as theoretical outage-optimal. Compared with previous single-antenna opportunistic relaying (OR) scheme, OMRS brings remarkable performance improvement, which is obtained from maximum ratio combining (MRC) and beamforming techniques. It is also shown that the performance of ABRS in asymmetric channels is close to OMRS in the low and median SNR range.

Robust Power Allocation Algorithms for Wireless Relay Networks

Resource allocation promises significant benefits in wireless networks. In order to fully reap these benefits, it is important to design efficient resource allocation algorithms. Here, we develop relay power allocation (RPA) algorithms for coherent and noncoherent amplify-and-forward (AF) relay networks. The goal is to maximize the output signal-to-noise ratio under individual as well as aggregate relay power constraints. We show that these RPA problems, in the presence of perfect global channel state information (CSI), can be formulated as quasiconvex optimization problems. In such settings, the optimal solutions can be efficiently obtained via a sequence of convex feasibility problems, in the form of second-order cone programs. The benefits of our RPA algorithms, however, depend on the quality of the global CSI, which is rarely perfect in practice. To address this issue, we introduce the robust optimization methodology that accounts for uncertainties in the global CSI. We show that the robust counterparts of our convex feasibility problems with ellipsoidal uncertainty sets are semi-definite programs. Our results reveal that ignoring uncertainties associated with global CSI often leads to poor performance, highlighting the importance of robust algorithm designs in practical wireless networks.

Cooperative Communications with Outage-Optimal Opportunistic Relaying

In this paper, we present simple opportunistic relaying with decode-and-forward (DaF) and amplify-and-forward (AaF) strategies under an aggregate power constraint. In particular, we consider distributed relay-selection algorithms requiring only local channel knowledge. We show that opportunistic DaF relaying is outage-optimal, that is, it is equivalent in outage behavior to the optimal DaF strategy that employs all potential relays. We further show that opportunistic AaF relaying is outage-optimal among single-relay selection methods and significantly outperforms an AaF strategy based on equal-power multiple-relay transmissions with local channel knowledge. These findings reveal that cooperation offers diversity benefits even when cooperative relays choose not to transmit but rather choose to cooperatively listen; they act as passive relays and give priority to the transmission of a single opportunistic relay. Numerical and simulation results are presented to verify our analysis.

Outage optimality of opportunistic amplify-and-forward relaying

In this paper, we show that optimal selection and transmission of a single relay among a set of multiple amplify-and-forward (AF) candidates minimize the outage probability (i.e., outage-optimal) and outperform any other strategy that involves simultaneous transmissions from more than one AF relay under an aggregate power constraint. This outage optimality demonstrates that cooperation benefits are maximized with intelligent scheduling among AF relays.