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© 2018 IEEE. We consider a multi-link interference network that is tapped by an external eavesdropper. To conceal information from the eavesdropper, legitimate links are equipped with transmitter-based friendly jamming (TxFJ) and receiver-based friendly jamming (RxFJ). Each link seeks to maximize its secrecy rate by determining the best power assignment (PA) for the information, TxFJ, and RxFJ signals. Joint optimization of these parameters is a non-convex problem. Hence, we seek sub-optimal solutions. Specifically, we find a lower bound on the allocated power to TxFJ above which positive secrecy is achievable for a given link. Once positive secrecy is achieved, the secrecy rate becomes monotonically increasing in the power at the transmitter (Alice). Therefore, the rest of Alice's power is allocated to the information signal. Despite its sub-optimality, such an approach precludes the possibility of employing successive interference cancellation by the eavesdropper. The RxFJ PA of a link is adjusted using an on-off PA that depends only on the link's local channel state information (CSI). With every link following such a strategy, we model this interaction as a non-cooperative game. We derive sufficient conditions for the uniqueness of the resulting Nash equilibrium. We then propose an algorithm to implement the PA game. Lastly, we relax knowledge of eavesdropper's CSI (E-CSI) and propose a framework that is robust to unknown E-CSI. Our results indicate that this robust framework performs close to when E-CSI is fully known to legitimate links. Moreover, empirically it is shown that the secrecy sum-rate scales with the power budget of transmitters.

In this paper, we investigate the energy-efficient user scheduling and power control problem in downlink multicell multiuser orthogonal frequency division multiple access networks, where only the channel distribution information is available. The resulting optimization problem is a combinatorial problem, which belongs to the class of cardinality constrained fractional programming problems subject to a maximum outage probability constraint. To solve the original problem, we derive a centralized joint user scheduling and power control solution satisfying the generalized Karush–Kuhn–Tucker conditions by resorting to the successive convex approximation (SCA). In particular, the proposed scheme can be used to solve the resource allocation problem subject to each user's minimum throughput constraint even if all the subcarriers have the same channel gain. A decentralized power control scheme is proposed to maximize the energy efficiency through combining SCA and alternating direction method of multipliers. Simulation results demonstrate the effectiveness of the proposed schemes.

We consider a two-hop amplify-and-forward relay network with energy harvesting nodes, and design online joint power control at the source and the relay to maximize the long-term time-averaged rate over fading channels. We formulate the problem as a joint stochastic optimization problem under battery operational constraints and finite storage capacity constraints. In seeking an online solution, we transform the problem into one that enables us to leverage Lyapunov optimization to develop an online algorithm to provide the joint power control solution for the source and the relay in a fading environment. The joint power control solution is derived in closed-form and only depends on the current energy arrival at each node and fading condition over each hop, without requiring any statistical knowledge of them. Our proposed algorithm not only adapts the power based on the battery energy levels to conserves energy, but also exploits opportunistic transmission based on fading condition. Through analysis, we show that the performance gap of our proposed algorithm to the optimal power control policy is bounded. Simulation results demonstrate a significant gain of our proposed online joint power control algorithm over other alternative methods, including pernode separate power control and heuristic joint power control methods.

In this paper, we study the tone reservation method for reducing the peak-to-average power ratio (PAPR) in general orthonormal transmission systems. We prove that strong solvability, where the peak value of the transmit signal has to be bounded by a constant times the energy of the information symbols, is equivalent to weak solvability, where the peak value of the transmit signal has to be only bounded. Further, we show that in the case where the PAPR problem is not weakly solvable, almost all information sequences lead to an unbounded transmit signal.

In this paper, we consider delay-optimal power control for an energy harvesting wireless system with finite energy storage. The wireless system is powered solely by a renewable energy source with bursty data arrivals, and is characterized by a data queue and an energy queue. We consider a delay-optimal power control problem and formulate an infinite horizon average cost Markov Decision Process (MDP). To deal with the curse of dimensionality, we introduce a virtual continuous time system and derive closed-form approximate priority functions for the discrete time MDP at various operating regimes. Based on the approximation, we obtain an online power control solution which is adaptive to the channel state information as well as the data and energy queue state information. The derived power control solution has a multi-level water-filling structure, where the water level is determined jointly by the data and energy queue lengths. We show through simulations that the proposed scheme has significant performance gain compared with various baselines., Comment: 17 pages, 9 figures, 1 table. Accepted for publication in IEEE Transactions on Signal Processing

Efficient optimization techniques are important to manage interference in emerging dense wireless networks. Here, we address interference management through power control as a general utility maximization problem. For the class of utility functions that are concave in the logarithm of the optimization variables, we propose a power control algorithm based on fixed-point iterations. The iterations converge to the globally optimal power vector. One key benefit is that, for a network with N transmitters and a centralized implementation of the power control algorithm, the computational complexity per iteration of the algorithm is O(N2). When implemented in a distributed fashion and allowing for a signaling complexity of N messages per iteration, the computation complexity is reduced to O(N). We show that the proposed centralized and distributed versions of the algorithm converge to the optimal power vector at a linear rate. Our numerical results suggest that in most instances, the algorithm takes fewer than ten iterations to converge, even fewer if the initialization is close to the optimal power vector. The proposed algorithm is, therefore, very efficient for power control in slowly fading channels. Furthermore, unlike previous works in the literature, the proposed algorithm does not require the objective function to be separable into a sum of individual utilities. As an example, we present results for power control in a two-hop decode-and-forward cooperative relay network and illustrate the performance gains due to interference management.

In this paper, we study the joint relay selection and discrete power control problem for cognitive relay networks via a game-theoretic approach subject to the interference power constraint at the primary receivers and the total available power constraint for the secondary relays. The problem is formulated as a noncooperative game where the achievable rate of the cognitive relay network is used to design a common utility. This game is shown to be a potential game which possesses at least one pure strategy Nash equilibrium (NE) and an optimal strategy profile that maximizes the rate of cognitive relay network constitutes a pure strategy NE of our proposed game. We prove that under some mild conditions, our proposed game can guarantee the feasibility of a pure strategy NE without advance knowledge of infeasible strategy profiles. Moreover, we find that the price of anarchy (PoA) of our proposed game is equal to 1 under some conditions. In order to achieve the pure strategy NE, we design a centralized iterative algorithm and a decentralized stochastic learning algorithm based on learning automata. The convergence and the complexity of our designed algorithms are discussed. It is shown that our designed algorithms can achieve optimal or near-optimal rate performance with low complexity.

We study distributed algorithms for adapting transmit beamformers and linear receiver filters in a Time-Division Duplex Multiple-Input Multiple-Output (MIMO) interference network. Each transmitter transmits a single beam, and neither the transmitters nor receivers have a priori Channel State Information (CSI). Given a fixed set of powers, we present an adaptive version of the Max-SINR algorithm: pilot symbols are alternately transmitted in the forward direction (transmitters to receivers) and in the reverse direction (receivers to transmitters). Unlike previous channel estimation schemes, transmissions in each direction are synchronized across the source or destination nodes, and the pilots are used to update the filters/beams directly using a least squares criterion. To improve the performance with limited training, we include exponential weighting of the least squares objective across data frames. In addition, bi-directional training can be used to implement analog interference pricing for power control: training in the forward direction is used to measure received signal-to-interference plus noise ratios (SINRs) and interference prices, and those estimates combined with synchronous backward training are used to update the powers. Given sufficient training this method achieves the same performance as interference pricing updates with perfect CSI. Numerical results are presented that illustrate the performance of these methods in different settings.

This paper deals with optimal joint user power control and relay distributed beamforming for two-way relay networks, where two end-users exchange information through multiple relays, each of which is assumed to have its own power constraint. The problem includes the design of the distributed beamformer at the relays and the power control scheme for the two end-users to optimize the network performance. Considering the overall two-way network performance, we maximize the lower signal-to-noise ratio (SNR) of the two communication links. For single-relay networks, this maximization problem is solved analytically. For multi-relay networks, we propose an iterative numerical algorithm to find the optimal solution. While the complexity of the optimal algorithm is too high for large networks, two sub-optimal algorithms with low complexity are also proposed, which are numerically shown to perform close to the optimal technique. It is also shown via simulation that for two-way networks with both single relay and multiple relays, proper user power control and relay distributed beamforming can significantly improve the network performance, especially when the power constraints of the two end-users in the networks are unbalanced. Our approach also improves the power efficiency of the network largely.

In this paper, we consider an interference multiple-input multiple-output (MIMO) relay system where multiple source nodes communicate with their desired destination nodes concurrently with the aid of distributed relay nodes all equipped with multiple antennas. We aim at minimizing the total source and relay transmit power such that a minimum signal-to-interference-plus-noise ratio (SINR) threshold is maintained at each receiver. An iterative joint power control and beamforming algorithm is developed to achieve this goal. The proposed algorithm exploits transmit-relay-receive beamforming technique to mitigate the interferences from the unintended sources in conjunction with transmit power control. In particular, we apply the semidefinite relaxation technique to transform the relay transmission power minimization problem into a semidefinite programming (SDP) problem which can be efficiently solved by interior point-based methods. Numerical simulations are performed to demonstrate the effectiveness of the proposed iterative algorithm.

Throughput-optimal multihop wireless network operation entails a key physical-layer optimization problem: maximizing a weighted sum of link rates, with weights given by the differential queue backlogs. This emerges in joint back-pressure routing and power control, which is central in cross-layer wireless networking. We begin by showing that the core problem is not only nonconvex, but also NP-hard. This is a negative result, which however comes with a positive flip side: drawing from related developments in the digital subscriber line (DSL) literature, we propose effective ways to approximate it. Exploiting quasi-periodicity of the power allocation in stable setups due to the push-pull nature of the solution, we derive two custom algorithms that offer excellent throughput performance at reasonable, worst-case polynomial complexity. Judicious simulations illustrate the merits of the proposed algorithms.

This paper studies the two-hop relay broadcast channel (BC) for a relay-assisted wireless cellular network where the multiuser independent downlink signals from the base station (BS) are first transmitted to a fixed relay station (RS), and then forwarded by the RS to multiple mobile users. Assuming both the BS and RS are equipped with multiantennas, we study the joint optimization of linear beamforming and power control at the BS and RS so as to minimize their weighted sum-power consumption under the user minimum signal-to-interference-noise-ratio (SINR) - quality-of-service (QoS) - constraints. We apply two well-known criteria in the literature, namely, the ldquoSINR balancingrdquo and the ldquochannel-inversion,rdquo for the design of linear precoding in the traditional nonrelay-assisted multiantenna BC to the relay-assisted multiantenna BC. First, a convergence-ensured iterative SINR-balancing algorithm is proposed to successively in turn optimize the transmit parameters at one station (BS or RS) with those at the other station being fixed. Second, a joint BS and RS channel-inversion algorithm is proposed together with a novel technique, termed ldquoeigenmode switching,rdquo at the RS to reduce the power penalty of the channel inversion. Simulation results show that the proposed joint beamforming and power control schemes provide substantial power savings to achieve the assigned user QoS constraints.

In various applications, the effect of errors in gradient-based iterations is of particular importance when seeking saddle points of the Lagrangian function associated with constrained convex optimization problems. Of particular interest here are problems arising in power control applications, where network utility is maximized subject to minimum signal-to-interference-plus-noise ratio (SINR) constraints, maximum interference constraints, maximum received power constraints, or simultaneous minimum and maximum SINR constraints. Especially when the gradient iterations are executed in a disributed fashion, imperfect exchanges among the link nodes may result in erroneous gradient vectors. In order to assess and cope with such errors, two running averages (ergodic sequences) are formed from the iterates generated by the perturbed saddle point method, each with complementary strengths. Under the assumptions of problem convexity and error boundedness, bounds on the constraint violation and the suboptimality per iteration index are derived. The two types of running averages are tested on a spectrum sharing problem with minimum and maximum SINR constraints, as well as maximum interference constraints., Submitted to IEEE Transactions on Signal Processing

This paper addresses the problem of power control in wireless networks with elastic traffic and no central network controller, such as ad hoc networks or hybrid mesh networks. We propose a novel power allocation iteration, prove its local quadratic convergence, and design a feedback/handshake scheme for a distributed implementation of the iteration. The combined feature of quadratic convergence and amenability to decentralized realization makes the algorithm suitable for efficient online application and incorporation in multihop policies. To the best of our knowledge, a similarly fast convergence and decentralization are not offered by any known power control algorithm. The proposed power control concept is designed and analyzed using the powerful framework of convex-concave functions and min-max functions.

A cooperative communication network is considered wherein L sources aim to transmit to their designated destinations through the use of a multiple-antenna relay. All sources transmit to the relay in a shared channel in the first transmission phase. Then, the relay linearly processes its received signal vector using L relaying matrices and retransmits the resultant signals towards the destinations in dedicated channels in the second transmission phase. The goal is to jointly optimize the sources' transmit powers and the relaying matrices such that the worst normalized signal-to-interference-plus-noise ratio (SINR) among all L destinations is maximized while the relays' transmit powers in the dedicated channels as well as the sources' individual and total transmit powers do not exceed predetermined thresholds. It is shown that the jointly optimal sources' transmit powers and the relaying matrices are the solutions to an optimization problem with a nonconvex objective function and multiple nonconvex constraints. To solve this problem, it is first proved that all normalized SINRs are equal at the optimal point of the objective function. Then, the optimization problem is transformed through multiple stages into an equivalent problem that is amenable to an iterative solution. Finally, an efficient iterative algorithm is developed that offers the jointly optimal sources' transmit powers and the relaying matrices. An extension to the above problem is then studied in the case when the cooperative communication network acts as a cognitive system that is expected to operate such that its interfering effect on the primary users is below some admissibility thresholds. In such a case, the sources' and relay's transmit powers should further satisfy some additional constraints that compel a new technique to tackle the problem of the joint optimization of the sources' transmit powers and the relaying matrices. An iterative solution to the latter problem is also proposed and the efficiency and the high rate of convergence of the proposed iterative algorithms in both the original and the cognitive cases are verified by simulation examples.

In this paper, we consider a wireless amplify-and-forward relay network with one relay node and multiple source-destination pairs/users and propose a pricing framework that enables the relay to set prices to maximize either its revenue or any desirable system utility. Specifically, depending on the quality of the received signals, the relay sets prices and correspondingly charges the users utilizing its resources for their transmissions. The price is determined in such a way that the relay's revenue or system utility is maximized. Given the specified price, the users competitively employ the relay node to forward their signals. We model each user as a rational player, which aims at maximizing its own net utility through power allocation, and analyze the competition among the users within the framework of noncooperative game theory. It is shown that, in the game played by the users, there always exists a unique pure Nash equilibrium point that can be achieved through distributed iterations. Next, subject to the availability of complete information about the users at the relay, we propose a low-complexity uniform pricing algorithm and an optimal differentiated pricing algorithm, in which the relay either charges the users at a suboptimal uniform price or charges different users at different prices. We also show that, by applying the differentiated pricing algorithm that enforces the users to transmit at certain power levels, any system utility can be maximized. Extensive simulations are conducted to quantify the performance of the proposed methods.

Consider a scenario in which K users and a jammer share a common spectrum of N orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise. The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network. For this noncooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game. The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori. Simulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterative water-filling algorithm to oscillate.

Power control is an important factor for direct-sequence code division multiple access (DS-CDMA) cellular radio systems to achieve higher communication link quality and better system capacity. In order to track the desired signal-to-interference-plus-noise ratio (SINR) under round-trip delay, multiple access interference (MAI), channel fading, and noise, a time delay-based state-space model is developed for representing the tracking error dynamics and a state feedback controller is introduced for SINR tracking control. Then the power tracking problem can be regarded as a control problem. In this paper, a robust Hinfin power tracking control design is proposed to achieve a robust optimal SINR tracking from the minimization of the worst-case effect point of view. This robust optimal power tracking design problem can be transformed to solving the eigenvalue problem (EVP) under some linear matrix inequality (LMI) constraints. The LMI Matlab toolbox can be used to efficiently solve the EVP via convex optimization to achieve a robust optimal SINR tracking design. Under the proposed distributed framework, the information of channel gain is not needed

We consider amplify-and-forward multi-antenna relaying between a single pair of source and destination under relay per-antenna power constraints. We design the optimal relay processing matrix to minimize the maximum per-antenna power budget for a received SNR target. With given transmit and receive beamformers at the source and destination, respectively, we first focus on the equivalent system with single-antenna source and destination. Although non-convex, we show that the optimization satisfies strong Lagrange duality and can be solved in the Lagrangian dual domain. We reveal a prominent structure of this problem, by establishing its duality with direct SIMO beamforming system with an uncertain noise. This enables us to derive a semi-closed form expression for the optimal relay processing matrix that depends on a set of dual variables, which can be determined through numerical optimization with a significantly reduced problem space. We further show that the dual problem has a semi-definite programming form, which enables efficient numerical optimization methods to determine the dual variables with polynomial complexity. Using this result, the reverse problem of SNR maximization under a set of relay per-antenna power constraints is then addressed. We then consider the maximum relay beamforming achievable rate under different combinations of antenna setups at source and destination. In particular, we generalize the duality to MIMO relay beamforming vs. direct MIMO beamforming, and establish the dual relation of the two systems for different multi-antenna setups at source and destination.

This paper considers a noncooperative game in which competing users sharing a frequency-selective interference channel selfishly optimize their power allocation in order to improve their achievable rates. Previously, it was shown that a user having the knowledge of its opponents' channel state information can make foresighted decisions and substantially improve its performance compared with the case in which it deploys the conventional iterative water-filling algorithm, which does not exploit such knowledge. This paper discusses how a foresighted user can acquire this knowledge by modeling its experienced interference as a function of its own power allocation. To characterize the outcome of the multiuser interaction, the conjectural equilibrium is introduced, and the existence of this equilibrium for the investigated water-filling game is proven. Importantly, we show that both the Nash equilibrium and the Stackelberg equilibrium are special cases of the conjectural equilibrium. We also develop practical algorithms to form accurate beliefs and select desirable power allocation strategies. Numerical simulations indicate that a foresighted user without any a priori knowledge of its competitors' private information can effectively learn how the other users will respond to its actions, and induce the entire system to an operating point that improves both its own achievable rate as well as the rates of the other participants in the water-filling game.