Optimal power control for underlay cognitive radio systems with arbitrary input distributions

In this paper, secure communication over a buffer-aided two-hop communication link, in which a source sends data to a destination with the aid of a trusted half-duplex relay node in the presence of a passive eavesdropper, is studied. It is assumed that there is no direct link between the source and the destination, and the buffer-aided relay forwards the information to the destination by employing the decode-and-forward (DF) scheme. Both the source and the relay transmissions are assumed to be vulnerable to the eavesdropper. The perfect channel side information (CSI) of the network is assumed to be available at the source and the relay. Initially, conventional relaying protocols where equal partition of the time for the reception and transmission of the relay is considered. Then, the optimal time fraction with the optimal power control policy that maximizes the secrecy throughput is identified. Subsequently, the optimal joint link selection and power control policy that maximizes the secrecy throughput is derived. Numerical results demonstrate that the joint link selection and power control scheme can significantly improve the achievable secrecy throughput of the buffer-aided two-hop communication system.

This paper studies energy-efficiency (EE) and throughput optimization in the presence of randomly arriving data and quality of service (QoS) constraints. For this purpose, maximum average arrival rates supported by transmitting signals with arbitrary input distributions are initially characterized in closed form by employing the effective bandwidth of time-varying sources (e.g., discrete-time Markov and Markov fluid sources, and discrete-time and continuous-time Markov modulated Poisson sources) and effective capacity of the time-varying wireless channel. Subsequently, EE is formulated as the ratio of the maximum average arrival rate to the total power consumption, in which circuit power is also taken into account. Following these characterizations, the optimal power control policies maximizing the EE or maximizing the throughput under a minimum EE constraint are obtained. Through numerical results, the performance of the optimal power control policies is evaluated for different signal constellations and is also compared with that of constant power transmission. The impact of QoS constraints, source characteristics, circuit power, input distributions on the EE, and the throughput is analyzed.

This paper studies optimal stochastic power control problem for a time-varying communication link, where the transmitter randomly harvests renewable energies from the environment. The harvested energies are stored in an energy buffer (or battery). Packets arrive at the transmitter data buffer with a constant rate μ. The objective is to maximize μ under the statistical delay and energy harvesting (EH) constraints. In order to study the optimal power control policy, we reformulate the problem as an infinite-horizon Markov decision process (MDP) using asymptotic delay analysis. The optimal policy and its structural properties are studied by employing the post-decision framework approach. We then propose an online power control algorithm, which converges to the optimal solution without requiring the statistical knowledge of the channel fading and EH processes. Numerical results demonstrate the effectiveness of the online algorithm for different delay constraints and EH settings.

It has been widely accepted that cognitive radio can substantially improve the spectrum utilization compared with traditional spectrum allocation strategies. Cognitive radio technology enables secondary users to coexist with primary users opportunistically or concurrently. In the latter scenario, the primary user allows the secondary user to access its licensed spectrum, as long as the quality of service (QoS) of the primary transmission is guaranteed. Beamforming is a practical way to achieve this goal by utilizing multiple antennas to limit the interference at the primary receiver (PR) to a tolerable level. With transmit beamforming and receive beamforming, a multi-antenna secondary transmitter (ST) with the knowledge of cross channel state information (CSI) can project signals to appropriate directions such that no harmful interference is received at PR, while the secondary receiver (SR) can separate and recover the intended signals reliably. Perfect or imperfect knowledge of cross CSI at ST results in different interference conditions as well as different transmit strategies. The interference received at PR in the perfect cross CSI case is controllable, and hence ST can precisely determine the transmit beamforming directions to gain the maximum benefit under the primary interference constraint. However, such a strategy is not always suitable in the imperfect cross CSI case, due to the uncertainty of CSI error directions and amplitudes. In this case, ST needs to ensure that the interference constraint would not be violated even with the worst CSI error. In this thesis, we first study cognitive beamforming subject to the secondary power constraint and the primary interference power constraint. With bounded error model for the cross CSI, we rewrite the error boundary expressions as a set of linear matrix equalities, and then convert the whole problem into a convex optimization problem to calculate the optimal solution. When no cross CSI is available at ST, we aim at maximizing the secondary sum throughput subject to the interference expectation constraint and interference outage probability constraint at PR, respectively. We prove that under the former constraint, the beamforming problem can be formulated as a conventional MIMO transmission problem, which can be easily solved via the water-filling method. Under the latter constraint, we find that the interference power is related to the eigenvalues of the covariance matrix of the secondary signals, and thus it can be expressed as a linear combination of multiple chi-square distributed variables. By exploiting the impact of the eigenvalues on the interference outage probability and establishing the relationship between the vibrations of secondary covariance matrix and its eigenvalues, we design an algorithm for this beamforming problem. In the second part of this thesis, we focus on beamforming in a multi-antenna cognitive radio system with transmission of multiple secondary data streams subject to the individual signal-to-noise ratio constraint per secondary data stream and the primary interference power constraint. The objective is to minimize the secondary transmit power consumption. Both perfect and imperfect cross CSI cases are considered and in both cases, the beamforming feasibility is tested. By exploiting the individual SNR constraints, we formulate the cognitive beamforming problem as an optimization problem on the Stiefel manifold. For zero forcing beamforming, we derive a closed form beamforming solution. For nonzero forcing beamforming, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. In the case of imperfect cross CSI, we apply the S-procedure method to reformulate the problem and provide an algorithm to obtain the beamforming solution. Finally, we raise some interesting open problems for the future work.

This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per co- herence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.

In this paper, we consider a cooperative cognitive radio relay network (CCRRN), in which there is a pair of primary transmitter (PT) and primary receiver (PR) with each having a single antenna, a secondary transmitter (ST) equipped with two antennas and a secondary receiver (SR) having a single antenna. We assume that ST operates in a half-duplex mode with an amplify-and-forward (AF) cooperative transmission scheme adopted. For such a system, a novel transmission scheme for CCRRN based on uniquely-factorable constellation pair (UFCP) is proposed, which enables ST to transmit its own information to SR without knowing its channel links to PR and SR while assisting PT transmission. It is shown that one of significant advantages of our proposed new scheme is that in a noise-free case, PR and SR are able to decode their own signals uniquely and that in a Gaussian noise case, they are still able to reliably decode their own signals with full diversity. In addition, a tight upper bound of average pairwise error probability (PEP) for the maximum likelihood (ML) detector is derived, showing that full diversity is achieved. With this, an optimal power allocation strategy is proposed that minimizes the worst-case upper bound.

This paper illustrates the performance of bit error rate based selection combining (BER-SC) protocol for adaptive cooperative cognitive radios. In the proposed framework, the unlicensed (i.e. secondary) system utilizes an adaptive mode of transmission to help the licensed (i.e. primary) system to achieve the desired quality of service in exchange for opportunistic spectrum access. The total transmission is divided in two phases. In Phase I, the primary transmitter (PT) broadcasts the data to the primary receiver (PR), which is overheard by the secondary transmitter (ST) and secondary receiver (SR). In Phase II, ST decodes the primary data and linearly combines its own data with the primary data. Using M-QAM the combined data is adaptively modulated, where M = 4, 16 or 64 depending on the received channel feedback, and relayed to PR and SR. At PR, BER-SC is employed to retrieve the primary data, and at SR interference cancellation is used to retrieve the secondary data. The analytical expressions are derived for the BER and the outage probability. The obtained results demonstrate the higher performance gains for both primary and secondary system by using adaptive mode of transmission at ST and BER-SC at PR.

Non-orthogonal multiple access protocol for overlay cognitive radio networks using spatial modulation and antenna selection

The optimal transmitter power control policy in an interleave division multiple access (IDMA) spread spectrum uplink channel is derived. The policy is applied to an IDMA channel with repetition code and a chip-by-chip maximum-likelihood decoder whose sum-rate is compared to the capacity of a linear minimum mean square error multiuser detector and to the Cover-Wyner capacity

We consider in this paper, a spectrum sharing cognitive radio system with a ratio selection scheme; where one out of N independent-and-identically-distributed transmit antennas is selected such that the ratio of the secondary transmitter (ST) to the secondary receiver (SR) channel gain to the interference from the ST to the primary receiver (PR) channel gain is maximized. Although previous works considered perfect, outdated, or partial channel state information at the transmitter, we stress that using such assumptions may lead to a feedback overhead for updating the SR with the ST-PR interference channel estimation. Considering only statistical knowledge of the ST-PR channel gain, we investigate a ratio selection scheme using a mean value (MV)-based power allocation strategy referred to as MV-based scheme. We first provide the exact statistics in terms of probability density function and cumulative distribution function of the secondary channel gain as well as of the interference channel gain. Furthermore, we derive exact cumulative density function of the received signal-to-noise ratio at the SR where the ST uses a power allocation based on instantaneous perfect channel state information (CSI) referred to as CSI-based scheme. These statistics are then used to derive exact closed form expressions of the outage probability, symbol error rate, and ergodic capacity of the secondary system when the interference channel from the primary transmitter (PT) to the SR is ignored. Furthermore, an asymptotical analysis is also carried out for the MV-based scheme as well as for the CSI-based scheme to derive the generalized diversity gain for each. Subsequently, we address the performance analysis based on exact statistics of the combined signal-to-interference-plus-noise ratio at the SR of the more challenging case; when the PT-SR interference channel is considered. Numerical results in a Rayleigh fading environment manifest that the MV-based scheme outperforms the CSI-based scheme provided that a low interference power constraint is deployed, implying that the MV-based scheme is more suitable for practical systems.

This correspondence considers a hybrid cognitive radio (H-CR) where the primary transmitter (PT) transmits message to the primary receiver (PR) whenever traffic occurs by allowing interference level <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> from the secondary transmitter (ST) to the PR, and the ST transmits messages to the secondary receiver (SR) by controlling the transmitting power based on spectrum sensing and interference level <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> . The ST opportunistically adopts maximum power when it detects that the PT is not transmitting and controls the transmitting power to restrict the interference level from the ST to the PR below <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> when alerted that the PT is transmitting. The closed-form expressions of the average rates for the H-CR are derived. Based on the analytical results, the detection probability α and interference level <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> are optimized to maximize the average rate of the ST by guaranteeing the average rate of the PT. Analysis and simulation results demonstrate that the former matches well to the latter and the average rate for the ST of the H-CR is better than that of two existing CRs where the ST transmits messages to the SR with maximum power only when the ST recognizes that the PT is not transmitting or with controlled power to limit an interference level from the ST to the PR below a constant irrespective of the PT's activity.

We study power control for an energy harvesting communication system with independent and identically distributed Bernoulli energy arrivals. It is assumed that the transmitter is equipped with a finite-sized rechargeable battery and is able to look ahead to observe a fixed number of future arrivals. A complete characterization is provided for the optimal power control policy that achieves the maximum long-term average throughput over an additive white Gaussian noise channel.

In this paper, we first study the Decode-and-Forward strategy for secrecy in a single-relay network. We propose a suboptimal Decode-and-Forward with Zero Forcing (DF/ZF) strategy for which we obtain the optimal power control policy. Next, we consider the multiple relay problem. We propose three different strategies based on DF/ZF. The first strategy is a single-hop strategy in which all the relays decode the source message at the same time, then perform beamforming such that all the relays' signals are eliminated from the eavesdropper's observation (full zero-forcing). We give the achievable rate by this strategy and derive the optimal power control policy. We show that, in this strategy, the relays which are far from the source create a bottleneck and limit the achievable rate. The second strategy is a multiple hop strategy that overcomes the drawback of the first strategy, however, with the disadvantage of enabling partial zero-forcing only, assuming that all the relays are required to transmit fresh information in every transmission block. The third strategy is also a multiple hop strategy in which full zero-forcing is possible and the rate achieved does not suffer from the drawback of the first strategy.

A general theory of online power control for discrete-time battery limited energy harvesting communications is developed, which leads to, among other things, an explicit characterization of a maximin optimal policy. This policy only requires the knowledge of the (effective) mean of the energy arrival process and maximizes the minimum asymptotic expected average reward (with the minimization taken over all energy arrival distributions of a given (effective) mean). Moreover, it is universally near optimal and has a strictly better worst-case performance as well as a strictly improved lower multiplicative factor in comparison with the fixed fraction policy proposed by Shaviv and \"{O}zg\"{u}r when the objective is to maximize the throughput over an additive white Gaussian noise channel. The competitiveness of this maximin optimal policy is also demonstrated via numerical examples.

We study the stochastic user scheduling and power control problem for an uplink multi-user network over time-varying channels, where the users randomly harvest renewable energies from the environment. For each user, the renewable energies and arriving data packets with a constant rate are stored in energy (battery) and data buffers, respectively. Users have statistical packet delay constraints in terms of maximum acceptable delay-outage probabilities. We classify the users as prioritized and non-prioritized users. Our goal is to maximize the arrival rate of the non-prioritized user while supporting the minimum data rate requirements for the prioritized users. We reformulate the problem as an infinite-horizon Markov decision process (MDP) using asymptotic delay analysis and study the optimal scheduling and power control policy. Since the optimal policy requires centralized processing with high computational complexity, we develop a reduced-complexity distributed algorithm, which can be implemented at each individual user. Online algorithm is devised, which does not require the statistical knowledge of the channel fading and energy harvesting (EH) processes. Numerical results demonstrate the effectiveness of the centralized and distributed schemes for different delay constraints and EH settings.