Exponential Diversity Achieving Spatio–Temporal Power Allocation Scheme for Fading Channels

In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.     

Outage analysis of the hybrid free-space optical and radio-frequency channel

We study the hybrid free-space optical (FSO) and radio-frequency (RF) channel from an information theoretic perspective. Since both links operate at vastly different carrier frequencies, we model the hybrid channel as a pair of parallel channels. Moreover, since the FSO channel signals at a higher rate than the RF channel, we incorporate this key feature in the parallel channel model. Both channels experience fading due to scintillation, which is slow compared to typical signalling rates. Under this framework, we study the fundamental limits of the hybrid channel. In particular, we analyse the outage probability in the large signal-to-noise ratio (SNR) regime, and obtain the outage diversity or SNR exponent of the hybrid system. First we consider the case when only the receiver has perfect channel state information (CSIR case), and obtain the exponents for general scintillation distributions. These exponents relate key system design parameters to the asymptotic outage performance and illustrate the benefits of using hybrid systems with respect to independent FSO or RF links. We next consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves significant power savings (on the order of tens of dBs) over uniform power allocation. We show that the suboptimal algorithm has the same diversity as the optimal power allocation strategy.     

On the capacity of some channels with channel state information

We study the capacity of some channels whose conditional output probability distribution depends on a state process independent of the channel input and where channel state information (CSI) signals are available both at the transmitter (CSIT) and at the receiver (CSIR). When the channel state and the CSI signals are jointly independent and identically distributed (i.i.d.), the channel reduces to a case studied by Shannon (1958). In this case, we show that when the CSIT is a deterministic function of the CSIR, optimal coding is particularly simple. When the state process has memory, we provide a general capacity formula and we give some more restrictive conditions under which the capacity has still a simple single-letter characterization, allowing simple optimal coding. Finally, we turn to the additive white Gaussian noise (AWGN) channel with fading and we provide a generalization of some results about capacity with CSI for this channel. In particular, we show that variable-rate coding (or multiplexing of several codebooks) is not needed to achieve capacity and, even when the CSIT is not perfect, the capacity achieving power allocation is of the waferfilling type     

Optimizing the Power Allocation for Rayleigh Block-Fading Channels with Outage Capacity Constraints

This letter studies the power distribution over K blocks of coded information to support a certain rate in Rayleigh- fading channels given the causal channel state information at the transmitter (CSIT). For K = 2, we shall show that since the channel in the future is random, the optimal power policy tends to pour all the power for the first block, which disables the time diversity. By introducing outage capacity as a constraint, time-diversity can be unleashed by stochastically distributing the power among the blocks. For K = 2, we derive the stochastic- optimal power allocation in closed-form for the transmit power minimization problem subject to an outage capacity constraint. For K > 2, we propose to minimize the power by constraining the upper bound of the outage probability, and in so doing, the problem is convex which permits to derive the optimal power policy. Numerical results demonstrate that the proposed power policy exploiting CSIT gives significant power reduction when compared to an equal-power policy.     

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.     

基于中断概率的协作通信中继选择与功率分配算法

研究了功率受限情况下多中继协作通信网络的中继选择和功率优化问题。在AF网络中,提出了一种低复杂度中继选择与功率分配算法,其目标是在总功率一定的条件下使系统的中断概率最小。本算法对源节点和所有潜在中继节点进行功率分配,结合当前信噪比选择最优的中继集合,通过最速下降法求出使系统中断概率最低的功率分配因子。该算法不需要知道大量瞬时信道信息、不需要系统在等功率条件下进行中继选择,只需求得中继节点排列矩阵便可根据当前信噪比自适应获得最优中继节点集合。仿真结果表明,在相同条件下,该算法明显优于不同中继节点集合下几种算法的中断性能,并且与传统的SAF及AAF算法相比,有效降低了中断概率,提升了系统性能和功率效率。     

Performance Analysis of Generic Amplify-and-Forward Cooperative Networks over Asymmetric Fading Channels

In this paper, we analyze the performance of multi-hop multi-branch amplify-and-forward (AF) networks over generalized fading channels. Using the moment generating function (MGF)-based approach, we develop general expressions for the outage probability and symbol-error rate (SER) performance of the system with maximal ratio combining (MRC) receiver. The MGF-based approach relies on numerical integration. To gain insights into system performance, we therefore investigate the asymptotic outage and SER performance of the system with MRC and selection combining (SC) receiver at the destination. In particular, we develop the asymptotic statistics of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop link. We further derive the cumulative density function of the sum of the individual end-to-end SNRs, received from different diversity paths for MRC receiver. We also study the power allocation problem in a multi-hop multi-branch system with MRC receiver. In generalized Gamma fading environments, we seek to find the power allocation strategy that maximizes the SNR at the destination subject to a total power constraint. By means of simulations, we validate our theoretical developments and verify the efficiency of our proposed power allocation in improving the received SNR compared to a generic cooperative system with no power allocation. We also conclude that our asymptotic expressions for the outage probability and SER match the simulations very well in medium-to-high-SNR regime.     

空时协作系统的中断概率分析和功率分配研究

提出了选择中继协议下最小化系统中断概率的最优功率分配方案,并给出了最佳功率分配的闭式解。根据协作节点间是否存在交互信息,分别通过对系统中断概率的分析,推出了高信噪比下中断概率的理论界。基于理论界,在功率受限情况下,通过拉格朗日乘数法,得到最优功率分配的闭合解。仿真结果表明,所推理论界在高信噪比下与仿真值近似相等,最优功率分配点的系统性能也要优于其它功率分配点。     

Power Allocation for Amplify-and-Forward Relaying with Correlated Shadowing

Power allocation is a key technique to exploit the benefits of cooperative relaying. In this paper, we investigate the effect of shadowing on the power allocation of amplify-and-forward cooperative relaying systems. Considering the joint effects of path loss, correlated shadowing and flat Rayleigh fading, the approximate outage probability at high signal-to-noise ratio (SNR) is first derived. Then we solve the power allocation problem by minimizing the approximate outage probability subject to a total power constraint. It is shown by the analytical results that the correlation coefficients and the standard deviations of shadowing have significant impacts on the power allocation. The simulation results show that the proposed power allocation scheme yields about 2 dB SNR gain compared to the equal power allocation in the high SNR regime.     

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     

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation     

Optimal power allocation for cognitive radio under interference outage constraint

Cognitive radio is able to share the spectrum with primary licensed user, which greatly improves the spectrum efficiency. We study the optimal power allocation for cognitive radio to maximize its ergodic capacity under interference outage constraint. An optimal power allocation scheme for the secondary user with complete channel state information is proposed and its approximation is presented in closed form in Rayleigh fading channels. When the complete channel state information is not available, a more practical transmitter-side joint access ratio and transmit power constraint is proposed. The new constraint guarantees the same impact on interference outage probability at primary user receiver. Both the optimal power allocation and transmit rate under the new constraint are presented in closed form. Simulation results evaluate the performance of proposed power allocation schemes and verify our analysis.     

Outage capacities and optimal power allocation for fading multiple-access channels

We derive the outage capacity region of an M-user fading multiple-access channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given a required rate and average power constraint for each user, we find a successive decoding strategy and a power allocation policy that achieves points on the boundary of the outage probability region. We discuss the scenario where an outage must be declared simultaneously for all users (common outage) and when outages can be declared individually (individual outage) for each user.     

Opportunistic power allocation strategies and fair subcarrier allocation in OFDM-based cognitive radio networks

In this paper we have studied the subcarrier and optimal power allocation strategy for OFDM-based cognitive radio (CR) networks. Firstly, in order to protect the primary user communication from the interference of the cognitive user transmissions in fading wireless channels, we design an opportunistic power control scheme to maximize the cognitive user capacity without degrading primary user’s QoS. The mathematical optimization problem is formulated as maximizing the capacity of the secondary users under the interference constraint at the primary receiver and the Lagrange method is applied to obtain the optimal solution. Secondly, in order to limit the outage probability within primary user’s tolerable range we analyze the outage probability of the primary user with respect to the interference power of the secondary user for imperfect CSI. Finally, in order to get the better tradeoff between fairness and system capacity in cognitive radio networks, we proposed an optimal algorithm of jointing subcarrier and power allocation scheme among multiple secondary users in OFDM-based cognitive radio networks. Simulation results demonstrate that our scheme can improve the capacity performance and efficiently guarantee the fairness of secondary users.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

Power allocation for multi-antenna systems with space-time block coding in the presence of estimation error and delayed feedback

Based on imperfect channel state information with channel estimation error at the receiver and delayed feedback at the transmitter, a suboptimal power allocation (PA) scheme to minimize bit error rate (BER) under a power constraint is developed for beamforming multi-antenna systems with space-time block coding. The proposed scheme is based on a so-called compressed signal-to-noise ratio criterion, where a single compressed factor is utilized, and it can be used to generalize some existing schemes by setting the compressed factor to different forms. A closed-form compressed factor is derived to minimize the BER, and the resultant close-form expression of power allocation is attained. This closed-form expression is computational efficient and can obtain the BER performance close to the existing optimal approach which requires numerical search. Simulation results show that the proposed scheme can provide BER lower than the equal power allocation scheme. However, due to the impact of both estimation error and delayed feedback, it has performance degradation when compared to the PA scheme with estimation error or delayed feedback only.     

Worst-Case Robust MIMO Transmission With Imperfect Channel Knowledge

In this paper, we consider robust transmit strategies, against the imperfectness of the channel state information at the transmitter (CSIT), for multi-input multi-output (MIMO) communication systems. Following a worst-case deterministic model, the actual channel is assumed to be inside an ellipsoid centered at a nominal channel. The objective is to maximize the worst-case received signal-to-noise ratio (SNR), or to minimize the worst-case Chernoff bound of the error probability, thus leading to a maximin problem. Moreover, we also consider the QoS problem, as a complement of the maximin design, which minimizes the transmit power consumption and meanwhile keeps the received SNR above a given threshold for any channel realization in the ellipsoid. It is shown that, for a general class of power constraints, both the maximin and QoS problems can be equivalently transformed into convex problems, or even further into semidefinite programs (SDPs), thus efficiently solvable by the numerical methods. The most interesting result is that the optimal transmit directions, i.e., the eigenvectors of the transmit covariance, are just the right singular vectors of the nominal channel under some mild conditions. This result leads to a channel-diagonalizing structure, as in the cases of perfect CSIT and statistical CSIT with mean or covariance feedback, and reduces the complicated matrix-valued problem to a scalar power allocation problem. Then we provide the closed-form solution to the resulting power allocation problem.     

Energy‐efficient outage‐constrained power allocation based on statistical channel knowledge for dual‐hop cognitive relay networks

This paper investigates the power allocation problem in decode‐and‐forward cognitive dual‐hop systems over Rayleigh fading channels. In order to optimize the performance of the secondary network in terms of power consumption, an outage‐constrained power allocation scheme is proposed. The secondary nodes adjust their transmit power subject to an average interference constraint at the primary receiver and an outage probability constraint for the secondary receivers while having only statistical channel knowledge with respect to the primary nodes. We compare this approach with a power allocation scheme based on instantaneous channel state information under a peak interference constraint. Analytical and numerical results show that the proposed approach, without requiring the constant interchange of channel state information, can achieve a similar performance in terms of outage probability as that of power allocation based on instantaneous channel knowledge. Moreover, the transmit power allocated by the proposed approach is considerably smaller than the power allocated by the method based on instantaneous channel knowledge in more than 50% of the time. Copyright © 2015 John Wiley & Sons, Ltd.     

基于信道统计特性的中继选择算法

该文提出了一种在非再生协作网络中,基于信道统计特性的最优中继选择方法。首先在等功率条件下,根据信道统计特性,定义一个等效信道增益的参数,该参数反映了中继节点在协作过程中两个阶段的信道特性。然后提出一种基于该参数的降序排列的中继选择方法。该方法在不同的信噪比范围内,选择不同的节点集合,使得系统的吞吐率中断概率最小。分析表明该选择方法的分集增益阶数能达到N+1,N为中继节点数目。仿真结果表明这种中继选择算法的中断概率性能优于其他算法。该方法进一步与功率分配相结合,构成了一种低复杂度的次优的中继选择方法。仿真结果表明这种次优算法能够取得和穷举算法相似的性能。     

Performance analysis of maximum ratio transmission with imperfect channel estimation

Maximal ratio transmission (MRT) is designed assuming the availability of perfect channel state information (CSI) at both the transmitter and the receiver. However, perfect CSI is not available in practice. This paper investigates the impact of Gaussian estimation errors on the MRT performance in independently and identically distributed (i.i.d.) Rayleigh fading channels. We derive the cumulative distribution function (cdf), the probability density function (pdf) and the moment generating function (mgf) of the MRT output signal-to-noise ratio (SNR) with imperfect CSI, enabling the evaluation of some useful performance metrics such as the average error rate and the outage performance. Numerical and simulation results are provided to show the impact of imperfect CSI on the MRT performance.