Stochastic power allocation using causal channel information for delay-limited communications

Without delay constraints, ergodic capacity can be achieved through channel coding over time frames spanning the whole fading process of the channel without the need of channel state information (CSI) at the transmitter. If the channel capacity is delay-constrained, then causal CSI at the transmitter becomes important. In this letter, our aim is to resolve the optimal power-and-rate allocation in maximizing the expected capacity subject to total power constraint, given the causal CSI at the transmitter. The proposed solution is adaptive to the current and past CSI, and also the statistics of the future channels. Asymptotically in both the high and low signal-to-noise ratio (SNR) regimes, we show that at a particular constant in time, the optimal power policy has an interpretation of water-filling among the current channel and some estimates of the future channels     

Maximizing the data transmission rate of a cooperative relay system in an underwater acoustic channel

In this paper, we investigate the problem of maximizing the data transmission rate of a cooperative relay system in an underwater acoustic communication channel. With amplify‐and‐forward relaying and adaptive source transmission, we present optimal transmit signal power adaptation policies that maximize the data transmission rate, considering both frequency and time domains. The analysis takes into account a physical model of acoustic path loss and ambient noise power spectral density. Typical characteristics of underwater channel such as frequency‐dependent fading and time variations are also considered. Capacity bounds for channel state information (CSI) only at the receiver and CSI at both transmitter and receiver are presented. To maximize the data rate, we use the notion of an optimal bandwidth which corresponds to efficient allocation of signal power across the transmission bandwidth. Under the constraint of an average transmit power, the optimal transmit power adaptation policy is found to be ‘water‐pouring’ in frequency‐time domain, while the transmit power adaptation policy with a total power constraint is ‘water‐pouring’ in frequency domain. Results show that both frequency domain and frequency‐time domain power adaptation schemes provide much greater improvement in average data rate over that of the constant power case. Copyright © 2011 John Wiley & Sons, Ltd.     

Ergodic capacity and outage probability optimization for secondary user in cognitive radio networks under interference outage constraint

This paper considers a cognitive radio network where a secondary user (SU) coexists with a primary user (PU). The interference outage constraint is applied to protect the primary transmission. The power allocation problem to jointly maximize the ergodic capacity and minimize the outage probability of the SU, subject to the average transmit power constraint and the interference outage constraint, is studied. Suppose that the perfect knowledge of the instantaneous channel state information (CSI) of the interference link between the SU transmitter and the PU receiver is available at the SU, the optimal power allocation strategy is then proposed. Additionally, to manage more practical situations, we further assume only the interference link channel distribution is known and derive the corresponding optimal power allocation strategy. Extensive simulation results are given to verify the effectiveness of the proposed strategies. It is shown that the proposed strategies achieve high ergodic capacity and low outage probability simultaneously, whereas optimizing the ergodic capacity (or outage probability) only leads to much higher outage probability (or lower ergodic capacity). It is also shown that the SU performance is not degraded due to partial knowledge of the interference link CSI if tight transmit power constraint is applied.     

非理想信道状态信息下RIS辅助的安全通信

利用可重构智能表面(Reconfigurable Intelligent Surface, RIS)辅助无线发射机,可提高多用户无线网络的安全传输能力。在非理想信道状态信息(Channel State Information, CSI)下提出了鲁棒波束形成优化方法来提高系统对抗干扰和窃听攻击的能力。具体地,使用RIS辅助发射机,对RIS的相位波束形成和基站的传输功率进行联合优化,在分别满足有界CSI的最坏情况速率约束和统计CSI的速率中断概率约束来最小化系统的总传输功率。由于存在CSI误差,针对有界CSI和统计CSI误差约束,分别利用S-procedure来松弛保密速率约束和大偏差不等式(Large Deviation Inequality, LDI)来松弛保密速率中断概率约束。仿真结果表明,相比于无源反射法和传统波束形成方案,该方法可分别降低约88%和93%总传输功率,同时提高约15 dBm和12 dBm的干扰容限。     

Delay constrained throughput optimisation with imperfect CSI using discrete adaptive power

Link adaptation is an effective tool to overcome fading effects in wireless links. However, time-varying adaptive transmission rate leads to queueing delay, and moreover, in practise, imperfect channel state information (CSI) is available for the transmitter to adapt its transmission rate and power. This article aims to consider practical constraints to enhance the link adaptation scheme. We reformulate and optimise buffer delay constrained throughput of a wireless link based on outdated noisy CSI. Discrete power adaptation is proposed, in which a limited number of feedback bits (just the index of transmission power level) is required, while the performance is improved compared to the constant power and is close to continuous adaptive power. A unified scheme is set-up, where constant, discrete or continuous adaptive power transmission is utilised considering average or instantaneous bit error rate constraints based on imperfect CSI. The effectiveness of our designs is evaluated by numerical evaluations.     

Power control for delay constrained multi‐channel communications using outdated CSI

In this paper, we study the power allocation scheme for a single user, multi‐channel system, e.g., orthogonal frequency‐division multiplexing (OFDM) systems, under time‐variant wireless fading channels. We assume the receiver feeds back perfectly estimated channel state information (CSI) to the transmitter after a processing delay. The objective of the power allocation is to maximize throughput subject to quality‐of‐service (QoS) constraint. The QoS measure of our consideration is a triplet of data rate, delay, and delay bound violation probability. A two‐step sub‐optimal power allocation scheme is proposed to address the impact of outdated CSI. In the first step, the total transmission power that can be used within one block is determined according to the summation of the channel gains of all the channels. In the second step, the total transmission power is allocated among all the channels. The proposed power control scheme is less sensitive to the feedback delay. Compared to the optimal power allocation scheme designed for the perfect CSI scenario, it has lower computational complexity while achieving comparable capacity. Copyright © 2010 John Wiley & Sons, Ltd.     

Limiting performance of block-fading channels with multipleantennas

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the “delay-limited” (or “nonergodic”) capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

Capacity of multiple-antenna systems with both receiver and transmitter channel state information

The capacity of multiple-antenna systems operating in Rayleigh flat fading is considered under the assumptions that channel state information (CSI) is available at both transmitter and receiver, and that the transmitter is subjected to an average power constraint. First, the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna. The optimal power-allocation scheme for such a system is shown to be a water-filling algorithm, and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas (with a single transmitter antenna) whose outputs are combined via maximal ratio combining. A suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case. It is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas (with a single transmitter antenna) combined via selection combining. Next, the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system. The optimal power allocation scheme for such a multiple-antenna system is given by a matrix water-filling algorithm. In order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation, approximate expressions for the cutoff transmission value are also provided. It is shown that, compared to the case in which there is only receiver CSI, large capacity gains are available with optimal power and rate adaptation schemes. The increased capacity is shown to come at the price of channel outage, and bounds are derived for this outage probability.     

Uplink throughput maximization with combined sum and individual power constraints

Optimal power allocation in cellular uplink systems is used to maximize the average throughput under individual and sum power constraints. In the uplink, the transmit power of the mobiles is limited leading to individual power constraints. Additionally, in order to reduce the inter-cell interference, the sum power is constraint. First, we approximate the individual and sum power constraints by a combined constraint on a suitable l-norm of the power allocation vector. Then, we derive the optimal power allocation for individual and sum power constraints as well as for the combined constraint for the three CSI scenarios with uninformed transmitter, long-term feedback, and perfect CSI. The results and illustrations show that under combined sum and individual power constraints completely different power allocation strategies are optimal than with pure sum or pure individual power constraints     

Robust Cognitive Beamforming With Bounded Channel Uncertainties

This paper studies the robust beamforming design for a multi-antenna cognitive radio (CR) network, which transmits to multiple secondary users (SUs) and coexists with a primary network of multiple users. We aim to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINRs) of the SUs, subject to the constraints of the total SU transmit power and the received interference power at the primary users (PUs) by optimizing the beamforming vectors at the SU transmitter based on imperfect channel state information (CSI). To model the uncertainty in CSI, we consider a bounded region for both cases of channel matrices and channel covariance matrices. As such, the optimization is done while satisfying the interference constraints for all possible CSI error realizations. We shall first derive equivalent conditions for the interference constraints and then convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation, which leads to iterative algorithms for obtaining the robust optimal beamforming solution. Results demonstrate the achieved robustness and the performance gain over conventional approaches and that the proposed algorithms can obtain the exact robust optimal solution with high probability.      

Optimum power control over fading channels

We study optimal constant-rate coding schemes for a block-fading channel with strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We show that the information outage probability is minimized by concatenating a standard “Gaussian” code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the transmitted power and we derive the corresponding power-allocation strategies. In addition, we propose an algorithm that approaches the optimal power allocation when the fading statistics are not known. Numerical examples for different fading channels are provided, and some applications discussed. In particular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for the delay-limited capacity of the Rayleigh block-fading channel with transmission over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmission. The optimal power-allocation strategy in this case corresponds to selection diversity at the transmitter. From the single-user point of view considered in this paper, there exists an optimal repetition diversity order (or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

On the Impacts of Channel Estimation Errors and Feedback Delay on the Ergodic Capacity for Spectrum Sharing Cognitive Radio

Spectrum sharing cognitive radio aims to improve the spectrum efficiency via sharing the spectrum band licensed to the primary user (PU) with the secondary user (SU) concurrently provided that the interference caused by the SU to the PU is limited. The channel state information (CSI) between the secondary transmitter (STx) and the primary receiver (PRx) is used by the STx to calculate the appropriate transmit power to limit the interference. We assume that this CSI is not only having channel estimation errors but also outdated due to feedback delay, which is different from existing studies. We derive closed-form expressions for the ergodic capacities of the SU with this imperfect CSI under the average interference power (AIP) constraint and the peak interference power (PIP) constraint. Illustrative results are presented to show the effects of the imperfect CSI. It is shown that the ergodic capacity of the SU is robust to the channel estimation errors and feedback delay under high feedback delay. It is also shown that decreasing the distance between STx and secondary receiver (SRx) or increasing the distance between STx and PRx can mitigate the impact of the imperfect CSI and significantly increase the ergodic capacity of the SU.     

Energy efficient transmission scheduling for delay constrained wireless networks

In this paper, we address the problem of energy efficient packet scheduling in a wireless environment. We consider a wireless transmitter which is limited by its finite battery resource. Our objective is to design a transmission schedule that maximizes battery lifetime subject to some delay constraints. To achieve this, we exploit two previously unconnected ideas: (i) channel coding can be used to conserve energy by transmitting at reduced power levels over longer durations; (ii) electro-chemical mechanisms in batteries allow them to recover energy during idle periods. While the first idea favors extending transmission durations, the second idea requires the transmitter to be idle to allow for recovery. In other words, bursty packet transmissions interspersed with idle periods extend battery life. Therefore, a strategy which is based entirely on either one or the other idea is not optimal. We provide a framework to merge the two ideas. We consider two kinds of delay constraints, one a deadline constraint and the other an average delay constraint and show that energy aware scheduling strategies for both these scenarios can result in significant energy savings.     

Communication with causal CSI and controlled information outage

In this letter, a Rayleigh block-fading (BF) channel, subject to an information outage probability constraint, is considered. The transmitter is assumed to have causal knowledge of the channel state information (CSI), which is exploited to intelligently allocate the power over the blocks (and hence vary the channel mutual information) to minimize the average transmitted power per block for satisfying the outage probability constraint for a given target code-rate. We first show that the optimal solution to this problem can be obtained by solving the reverse problem of minimizing the outage probability for a range of long-term power constraints through repeated uses of dynamic programming (DP), which is nevertheless prohibitively complex. Then, we develop a suboptimal allocation algorithm which still uses DP to exploit the CSI causality but at a much reduced complexity. A performance lower-bound is further derived, which permits us to see that the proposed algorithm is near-optimal, especially in the small outage probability regime. A scheme called equal-outage-probability per block (EOPPB) which compromises the performance further for reducing the complexity is also devised. To compare the methods, we evaluate both analytically and numerically their complexities and performance. The results are finally generalized to multipleinput multiple-output (MIMO) BF channels.     

Design of Optimal Linear Precoder and Decoder for MIMO Channels with Per Antenna Power Constraint and Imperfect CSI

This paper addresses the problem of designing joint optimum precoder and decoder for multiple-input multiple-output communication system. Conventionally, most of the joint precoder and decoder designs are based on the sum power constraint (SPC) at the transmitter and perfect channel state information (CSI). However, in practice, per-antenna power constraint is more realistic as the power at each transmit antenna is limited individually by the linearity of the power amplifier. Further, the estimate of CSI cannot be obtained perfectly by any methods. Under imperfect CSI, the aim is to design jointly optimum precoder and decoder subject to a power constraint that jointly meets both per-antenna and SPCs. The objective function is formulated into an optimization problem that minimizes the mean square error in estimating the transmitted signal. The simulation results show that the proposed scheme has a near-optimum performance under practical constraints.     

Optimal precoder design for non‐regenerative multiple‐input multiple‐output cognitive relay systems with perfect and imperfect channel state information

This paper studies optimal precoder design for non‐regenerative multiple‐input multiple‐output (MIMO) cognitive relay systems, where the secondary user (SU) and relay station (RS) share the same spectrum with the primary user (PU). We aim to maximize the system capacity subject to the transmit power constraints at the SU transmitter (SU‐Tx) and RS, and the interference power constraint at the PU. We jointly optimize precoders for the SU‐Tx and RS with perfect and imperfect channel state information (CSI) between the SU‐Tx/RS and PU, where our design approach is based on the alternate optimization method. With perfect CSI, we derive the optimal structures of the RS and SU‐Tx precoding matrices and develop the gradient projection algorithm to find numerical solution of the RS precoder. Under imperfect CSI, we derive equivalent conditions for the interference power constraints and convert the robust SU‐Tx precoder optimization into the form of semi‐definite programming. For the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex by using an upper bound and apply the gradient projection algorithm to deal with it. Simulation results demonstrate the effectiveness of the proposed schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

Energy Efficiency-Delay Tradeoffs in CDMA Networks: A Game-Theoretic Approach

A game-theoretic approach for studying energy efficiency-delay tradeoffs in multiple-access networks is proposed. Focusing on the uplink of a code-division multiple-access (CDMA) network, a noncooperative game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying its (transmission) delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user's delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a large-system analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and (linear) minimum-mean-square-error (MMSE) multiuser detectors. The effects of delay quality-of-service (QoS) constraints on the users' utilities (in bits per joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified. Using the proposed framework, the tradeoffs between energy efficiency and delay are quantified in a competitive multiuser setting.     

认知无线传感器网络中基于GSC的协作传输机制

针对无线传感器网络中单个节点能量和发射功率均受限的特点,在发送端已知信道状态信息(CSI)的条件下提出了一种基于广义选择合并算法(GSC)的协作传输机制。根据GSC算法和节点的功率受限条件来决定具体参与协作传输的节点个数,并结合信道状态和节点的剩余能量来对节点进行调度。理论分析和仿真结果表明该机制能够有效地延长网络寿命。