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     

Power adaptation for BPSK signaling with average and peak power constraints in Rayleigh fading channels

We consider power adaptation strategies for binary phase-shift keying signals in Rayleigh fading channels under the assumption that channel state information is provided at both the transmitter and the receiver. We first derive a closed-form expression for the optimal power adaptation that minimizes average bit-error rate (BER) subject to average and peak transmission power constraints. Then, we analyze the average BER for channel inversion power adaptation with the same constraints. Our results show that the performance difference between the optimal power adaptation and the channel inversion becomes negligibly small as available average transmission power increases and/or peak-to-average power ratio decreases. We also find that an optimal peak-to-average power ratio exists that minimizes the average BER in the channel inversion scheme.     

Optimal power control in interference-limited fading wirelesschannels with outage-probability specifications

We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored. This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods. We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability     

Power allocation in a transmit diversity system with mean channel gain information

We study the power allocation problem in a transmit diversity wireless system with mean channel gain information. In Rayleigh fading for a given set of mean channel gains and nodes, we seek to find the power allocation that minimizes the outage probability subject to a total power constraint. The optimal solution is shown to be computationally intensive when the number of channels is large. Instead, we derive a simple solution based on the upper bound to the outage probability which can be summarized as equal power allocation with channel selection. Numerical results show that the proposed solution is near-optimal over a wide range of parameter values. The problem addressed and the solution are relevant to a decode-and-forward cooperative relaying system with only partial channel information available to the relays.     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

Cross-layer Adaptive Transmission: Optimal Strategies in Fading Channels

We consider cross-layer adaptive transmission for a single-user system with stochastic data traffic and a time- varying wireless channel. The objective is to vary the transmit power and rate according to the buffer and channel conditions so that the system throughput, defined as the long-term average rate of successful data transmission, is maximized, subject to an average transmit power constraint. When adaptation is subject to a fixed bit error rate (BER) requirement, maximizing the system throughput is equivalent to minimizing packet loss due to buffer overflow. When the BER requirement is relaxed, maximizing the system throughput is equivalent to minimizing total packet loss due to buffer overflow and transmission errors. In both cases, we obtain optimal transmission policies through dynamic programming. We identify an interesting structural property of these optimal policies, i.e., for certain correlated fading channel models, the optimal transmit power and rate can increase when the channel gain decreases toward outage. This is in sharp contrast to the water-filling structure of policies that maximize the rate of transmission over fading channels. Numerical results are provided to support the theoretical development.     

Service outage based power and rate allocation for parallel fading channels

The service outage based allocation problem explores variable-rate transmission schemes and combines the concepts of ergodic capacity and outage capacity for fading channels. A service outage occurs when the transmission rate is below a given basic rate r/sub o/. The allocation problem is to maximize the expected rate subject to the average power constraint and the constraint that the outage probability is less than /spl epsi/. A general class of probabilistic power allocation schemes is considered for an M-parallel fading channel model. The optimum power allocation scheme is derived and shown to be deterministic except at channel states of a boundary set. The resulting service outage achievable rate ranges from 1-/spl epsi/ of the outage capacity up to the ergodic capacity with increasing average power. Two near-optimum schemes are also derived by exploiting the fact that the outage probability is usually small. The second near-optimum scheme significantly reduces the computational complexity of the optimum solution; moreover, it has a simple structure for the implementation of transmission of mixed real-time and non-real-time services.     

Optimal power control for Rayleigh-faded multiuser systems with outage constraints

How can we achieve the conflicting goals of reduced transmission power and increased capacity in a wireless network, without attempting to follow the instantaneous state of a fading channel? In this paper, we address this problem by jointly considering power control and multiuser detection (MUD) with outage-probability constraints in a Rayleigh fast-fading environment. The resulting power-control algorithms (PCAs) utilize the statistics of the channel and operate on a much slower timescale than traditional schemes. We propose an optimal iterative solution that is conceptually simple and finds the minimum sum power of all users while meeting their outage targets. Using a derived bound on outage probability, we introduce a mapping from outage to average signal-to-interference ratio (SIR) constraints. This allows us to propose a suboptimal iterative scheme that is a variation of an existing solution to a joint power control and MUD problem involving SIR constraints. We further use a recent result that transforms complex SIR expressions into a compact and decoupled form, to develop a noniterative and computationally inexpensive PCA for large systems of users. Simulation results are presented showing the closeness of the optimal and mapped schemes, speed of convergence, and performance comparisons.     

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.     

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     

Queue length aware power control for delay‐ constrained communication over fading channels

In this paper, we study efficient power control schemes for delay sensitive communication over fading channels. Our objective is to find a power control law that optimizes the link layer performance, specifically, minimizes the packet drop probability, subject to a long‐term average power constraint. We assume the buffer at the transmitter is finite; hence packet drop happens when the buffer is full. The fading channel under our study has a continuous state, e.g., Rayleigh fading. Since the channel state space is continuous, dynamic programming is not applicable for power control. In this paper, we propose a sub‐optimal power control law based on a parametric approach. The proposed power control scheme tries to minimize the packet drop probability by considering the queue length, i.e., reducing the probability of those queue‐length states that will cause full buffer. Simulation results show that our proposed power control scheme reduces the packet drop probability by one or two orders of magnitude, compared to the time domain water filling (TDWF) and the truncated channel inversion (TCI) power control. Copyright © 2010 John Wiley & Sons, Ltd.     

Decode-and-Forward Cooperative Diversity with Power Allocation in Wireless Networks

We study power allocation for the decode-and-forward cooperative diversity protocol in a wireless network under the assumption that only mean channel gains are available at the transmitters. In a Rayleigh fading channel with uniformly distributed node locations, we aim to find the power allocation that minimizes the outage probability under a short-term power constraint, wherein the total power for all nodes is less than a prescribed value during each two-stage transmission. Due to the computational and implementation complexity of the optimal solution, we derived a simple near-optimal solution. In this near-optimal scheme, a fixed fraction of the total power is allocated to the source node in stage I. In stage II, the remaining power is split equally among a set of selected nodes if the selected set is not empty, and otherwise is allocated to the source node. A node is selected if it can decode the message from the source and its mean channel gain to the destination is above a threshold. In this scheme, each node only needs to know its own mean channel gain to the destination and the number of selected nodes. Simulation results show that the proposed scheme achieves an outage probability close to that for the optimal scheme obtained by numerical search, and achieves significant performance gain over other schemes in the literature     

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     

基于中断概率最小化的认知无线网络衰落信道条件下的功率控制

Cognitive radio allows Secondary Users (SUs) to dynamically use the spectrum resource li-censed to Primary Users (PUs ), and significantly improves the efficiency of spectrum utilization and is viewed as a promising technology. In cognitive radio networks, the problem of power control is an important issue. In this paper, we mainly focus on the problem of power control for fading channels in cognitive radio networks. The spectrum sharing un-derlay scenario is considered, where SUs are al-lowed to coexist with PUs on the condition that the outage probability of PUs is below the maximum outage probability threshold limitation due to the interference caused by SUs. Moreover, besides the outage probability threshold which is defined to protect the performance of PUs, we also consider the maximum transmit power constraints for each SU. With such a setup, we emphasize the problem of power control to minimize the outage probability of each SU in fading channels. Then, based on the statistical information of the fading channel, the closed expression for outage probability is given in fading channels. The Dual-Iteration Power Control (DIPC) algorithm is also proposed to minimize the outage probability based on Perron-Frobenius theo-ry and gradient descent method under the constraint condition. Finally, simulation results are illustrated to demonstrate the performance of the proposed scheme.     

Outage-based optimal power control for generalized multiuser fading channels

We address the problem of achieving outage probability constraints on the uplink of a code-division multiple-access (CDMA) system employing power control and linear multiuser detection, where we aim to minimize the total expended power. We propose a generalized framework for solving such problems under modest assumptions on the underlying channel fading distribution. Unlike previous work, which dealt with a Rayleigh fast-fading model, we allow each user to have a different fading distribution. We show how this problem can be formed as an optimization over user transmit powers and linear receivers, and, where the problem is feasible, we provide conceptually simple iterative algorithms that find the minimum power solution while achieving outage specifications with equality. We further generalize a mapping from outage probability specifications to average signal-to-interference-ratio constraints that was previously applicable only to Rayleigh-faded channels. This mapping allows us to develop suboptimal, computationally efficient algorithms to solve the original problem. Numerical results are provided that validate the iterative schemes, showing the closeness of the optimal and mapped solutions, even under circumstances where the map does not guarantee that constraints will be achieved.     

Optimized layered multicast with superposition coding in cellular systems

We consider the problem of optimal power allocation and optimal user selection in a layered multicast transmission over quasi‐static Rayleigh fading channels. A scheme based on superposition coding is proposed in which basic multicast streams and enhanced multicast streams are superimposed and transmitted by a base station, while users with worse channel conditions can only decode basic multicast streams, and users with better channel conditions can decode both basic and enhanced multicast streams. In this paper, subject to fixed user selection ratios, the optimal power allocation for each stream that maximizes average throughput is investigated, and the impact of power allocation on average outage probability is discussed. Finally, subject to fixed transmit power and power allocation, the optimal user selection ratio for enhanced multicast streams is also studied. Numerical results show that the optimized layered multicast scheme outperforms the conventional multicast scheme in terms of average throughput. Copyright © 2010 John Wiley & Sons, Ltd.     

Capacity and optimal resource allocation for fading broadcastchannels .II. Outage capacity

For pt.I see ibid., vol.47, no.3, p.1083-1102 (2002). We study three capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the capacity region with outage. In this paper, we derive the outage capacity regions of fading broadcast channels, assuming that both the transmitter and the receivers have perfect channel side information. These capacity regions and the associate optimal resource allocation policies are obtained for code division (CD) with and without successive decoding, for time division (TD), and for frequency division (FD). We show that in an M-user broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multiuser generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for the different outage capacity regions are obtained for the Nakagami-m (1960) fading model     

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.     

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions     

Performance comparison of different selection combining algorithms in presence of co-channel interference

In this paper, we present a unified approach for the computation of the outage probability, the level crossing rate (LCR), and the average outage duration (AOD) of selection combining (SC) in the presence of multiple cochannel interferences and under both minimum signal-to-interference ratio (SIR) and desired signal power constraints. We consider three selection algorithms, namely: 1) the best signal power algorithm; 2) the best SIR algorithm; and 3) the best total power (desired plus interference) algorithm. As a specific application example, we analyze the three algorithms for a low-complexity dual-branch SC receiver subject to multiple interferers over Rayleigh fading channels. When applicable, the new results are compared to those previously reported in the literature dealing with the outage probability, AOD, and LCR of 1) interference-limited systems and 2) power-limited systems. Numerical examples show that the minimum desired signal power constraint induces a floor to the outage probability, AOD, and LCR performance measures. They also show that the best SIR algorithm provides the best outage probability and AOD performance for low average SIR. On the other hand, the best signal power algorithm and the best S+I algorithm outperform the best SIR algorithm for high average SIR. It is also shown that the best SIR algorithm tends to have more outage level crossings.