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     

Optimal Successive Group Decoders for MIMO Multiple-Access Channels

We consider a slow-fading narrowband multiple-input multiple-output (MIMO) multiple-access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) that simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the error exponent of the decodable set of users. An adaptive SGD is derived which not only retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight (in the limit of high signal-to-noise ratio (SNR)) affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacitiy yielded by the OSGD. Limiting expressions for the relevant capacities as the number of users and the number of receive antennas approach infinity are also obtained and it is shown that the OSGD yields symmetric capacity gains commensurate with the decoding complexity allowed. Simulation results with practical low-density parity-check (LDPC) outer codes show that the OSGD offers significantly improved performance at low decoding complexity.      

Outage Capacity for Secondary Users Due to Bandwidth Fluctuations: Multicarrier Versus Single Carrier

In this work we study the channel capacity from the point of view of a secondary user that shares the bandwidth of the channel with a primary user using dynamic spectrum access in cognitive radio.The secondary user sees bandwidth fluctuations (i.e, at any given time the bandwidth can be available or not) that impact its channel capacity. We study the outage capacity for the secondary user considering two scenarios in which the secondary user uses either a single carrier modulation for the case in which bandwidth fluctuates over the complete transmission band, and a multicarrier modulation for the case in which bandwidth fluctuations are over various transmission subbands. We derive expressions for the outage capacity of the secondary user for both single carrier and multicarrier. Results show that: (1) The outage capacity for single carrier can be higher than for multicarrier, but with a higher outage probability for single carrier than for multicarrier. In fact, a low value of outage probability for single carrier requires a duty cycle for the secondary user close to one, but this has the problem that it leaves a very short duty cycle for the primary user. (2) Although for the secondary user the outage capacity for multicarrier is smaller than for single carrier, for multicarrier lower values of the outage probability can be achieved even for short values of the duty cycle of the secondary user, allowing larger duty cycle values of the primary user. (3) For multicarrier, the outage capacity is more sensitive to changes in the duty cycle than to changes in the outage probability. To obtain a larger outage capacity with low values of both the outage probability and the duty cycle, it requires the use of a large number of subbands.     

Optimal power allocation in DS-CDMA with adaptive SIC technique

This paper proposes an optimal power allocation in direct sequence-code division multiple access (DS-CDMA) system. The objective is to minimize total transmit power, while simultaneously meeting the certain sum channel capacity (data transmission rate) and outage probability constraints on Rayleigh fading channel. Then a weighted correlator with an adaptive successive interference cancelation (SIC) scheme is developed using neural network (NN) for an improvement in receiver performance. A closed mathematical form of joint probability of error (JPOE) is derived. This determines the number of active users’ interfering effect that needs to be canceled in order to achieve a desired bit error rate (BER) value. Mathematical analysis shows that better receiver performance can be achieved through large change in weight up-gradation (w) for the strong users with a particular change in learning rate (η). Simulation results in terms of sum capacity as well as weak user’s (users with poor channel gain) capacity, outage probability and BER performance duly support the effectiveness of the proposed scheme over the existing works.     

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.     

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.     

Outage Perforformance of Power Controlled DS-CDMA Wireless Systems with Heterogeneous Traffic Sources

This paper proposes a performance analysis of a Direct Sequence-Code Division Multiple Access (DS-CDMA) wireless system with heterogeneous traffic in terms of second order outage statistics. Imperfections in closed-loop power control are modelled in their first order distribution and autocorrelation function. System capacity and optimal power allocation has been previously derived [7] in the presence of requirements expressed only in terms of signal-to-(noise + interference) ratio and outage probability of every user in the system. Therefore, in this paper the effectiveness of power allocation is evaluated also in terms of average outage rate and average outage duration for the generic user link of each traffic class. This allows to gain insights on the effects of power allocation and feedback control on channel burstiness for each class of users, so that forward error correction and retransmission strategies can be properly tuned. With proper choice of system parameters, the proposed analysis can be applied to both the terrestrial and satellite segments of 3G systems, and integrated scenarios as well. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Adaptive Modulation over Nakagami Fading Channels

We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closed-form solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We then analyze the performance of practical constant-power variable-rate M-QAM schemes over NMF channels. We obtain closed-form expressions for the outage probability, spectral efficiency and average bit-error-rate (BER) assuming perfect channel estimation and negligible time delay between channel estimation and signal set adaptation. We also analyze the impact of time delay on the BER of adaptive M-QAM.     

Outage Probability Based Robust Distributed Beam-Forming in Multi-User Cooperative Networks with Imperfect CSI

In this paper, a new robust problem is proposed for relay beamforming in relay system with stochastic perturbation on channels of multi user and relay network. The robust problem aims to minimize the transmission power of relay nodes while the imperfect channel information (CSI) injects stochastic channel uncertainties to the parameters of optimization problem. In the power minimization framework, the relays amplification weights and phases are optimized assuming the availability of Gaussian channel distribution. The power sum of all relays is minimized while the outage probability of the instantaneous capacity (or SINR) at each link is above the outage capacity (or SINR) for each user. The robust problem is a nonconvex SDP problem with Rank constraint. Due to the nonconvexity of the original problem, three suboptimal problems are proposed. Simulation and numerical results are presented to compare the performance of the three proposed solutions with the existing worst case robust method.     

Approaching V-BLAST Capacity With Adaptive Modulation and LDPC Encoding

This paper presents a practical implementation of the vertical Bell Laboratories layered space-time (V-BLAST) type system, in which the multiple-input multiple-output (MIMO) open-loop capacity can be approached with conventional scalar coding, using adaptive modulation with appropriate channel codes, e.g., low-density parity-check (LDPC) codes and optimum successive detection (OSD). The density evolution (DE) technique is employed to determine the maximal achievable rate of an LDPC code for each transmit antenna for a given channel realization at a given SNR. Numerical results show that the average sum rate of the adaptively modulated LDPC-encoded system is quite close to the V-BLAST capacity with both rate and power adaptations. Considering the performing degradation caused by error propagation due to the imperfect feedback and relatively long decoding delay in the OSD, we use parallel interference cancellation (PIC) followed by minimum mean square error (MMSE) filtering in the bit error rate (BER) performance simulation. Simulation results show that a target BER of 10-5 can be achieved by the optimally designed LDPC codes. To simplify the code design, we replace the LDPC codes optimally designed for each channel realization with rate-compatible punctured LDPC codes, at the cost of a slight sum rate loss. If the fading process is nonergodic, the outage capacity corresponding to a given outage probability is used to measure the channel performance. As an example, we design the LDPC codes for an adaptively modulated 2 × 2 V-BLAST system to approach its outage capacity for a given outage probability.      

基于NOMA的D2D辅助中继系统性能分析与优化

本文针对两阶段NOMA(Non-Orthogonal Multiple Access)-D2D((Device-to-Device)辅助中继场景提出了一种功率优化算法，推导分析了各用户的中断概率。构建了以最大化系统各态历经容量为目标的优化问题，由于一、二两阶段通信用户的差异性，重点优化了对提升系统容量起决定作用的第一阶段功率分配因子，分析证明了原优化问题存在极值点，并利用凸函数性质获得了优化的功率分配因子，并且进一步推导分析了各个用户的中断概率。仿真结果表明，理论推导的中断概率值与仿真结果完全一致，证明了推导的正确性，本文提出的功率优化算法能显著提高系统容量，且降低了中断概率。例如当SNR为35dB时，本文算法可以提高约17.6%的系统容量，而作为辅助中继用户的中断概率大约降低了81.3%。      

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.     

Downlink capacity evaluation of cellular networks with known-interference cancellation

Recently, the capacity region of a multiple-input multiple-output (MIMO) Gaussian broadcast channel, with Gaussian codebooks and known-interference cancellation through dirty paper coding, was shown to equal the union of the capacity regions of a collection of MIMO multiple-access channels. We use this duality result to evaluate the system capacity achievable in a cellular wireless network with multiple antennas at the base station and multiple antennas at each terminal. Some fundamental properties of the rate region are exhibited and algorithms for determining the optimal weighted rate sum and the optimal covariance matrices for achieving a given rate vector on the boundary of the rate region are presented. These algorithms are then used in a simulation study to determine potential capacity enhancements to a cellular system through known-interference cancellation. We study both the circuit data scenario in which each user requires a constant data rate in every frame and the packet data scenario in which users can be assigned a variable rate in each frame so as to maximize the long-term average throughput. In the case of circuit data, the outage probability as a function of the number of active users served at a given rate is determined through simulations. For the packet data case, long-term average throughputs that can be achieved using the proportionally fair scheduling algorithm are determined. We generalize the zero-forcing beamforming technique to the multiple receive antennas case and use this as the baseline for the packet data throughput evaluation.     

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     

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.     

Power Allocation and Control in Multimedia CDMA Wireless Systems

This paper proposes an analysis of outage performance of a Direct Sequence-Code Division Multiple Access (DS-CDMA) wireless system with heterogeneous traffic. Imperfections in closed-loop power control and the activity characteristics of any traffic source in the system are taken into account. For given requirements of signal-to-(noise + interference) ratio and outage probability of every user in the system, the system capacity is derived in terms of the maximum number of users of each class that can be accomodated. The optimization problem is explicitly solved for a system consisting of a single cell and an approach is outlined for solving the optimization problem in a multi-cell system. The analysis is carried out by resorting to various approximations of Multiple Access Interference (MAI), that require different methods for solving the optimization problem and yield different degrees of accuracy. From numerical results it is seen that optimal power allocation is essential to limit the effects of power control imperfections, mainly in the case of non uniform amplitudes of residual power fluctuations. In the second part of the paper, a performance study of fixed step closed-loop power control algorithms is presented. A detailed simulation of the power control loop evidences that fast fading phenomena can not be easily tracked, even at moderate Doppler spread. Statistics of residual power fluctuations are estimated and can be used to support the assumptions in the first part of the paper. Furthermore, second order statistics of the controlled channel are estimated, and second order outage statistics (average rate and duration of outage events) are derived as a quantitative measure of residual channel burstiness.     

System capacity of F-TDMA cellular systems

We study the system capacity of cellular systems with time-division multiple access, slow time-frequency hopping (F-TDMA), and conventional single-user processing at the receivers. System capacity is formally defined as the maximum of the product of the number of users per cell times the user spectral efficiency for a given maximum outage probability. We adopt an information-theoretic definition of outage as the event that the mutual information of the block-interference channel resulting from a finite number of signal bursts spanned by the transmission of a user code word falls below the actual code rate, because of fading, shadowing, and interference. Starting from this definition, we develop a general framework which naturally takes into account many different aspects of F-TDMA cellular systems like channel reuse, channel utilization, waveform design, time-frequency hopping, voice activity exploitation, handoff, and power control strategies. Most importantly, our analysis does not rely on the choice of a particular coding scheme and can be applied to a very large class of systems in order to find guidelines for capacity-maximizing system design. A numerical example based on a typical urban mobile environment shows that there is a considerable capacity gap between actual F-TDMA systems and the limits predicted by our analysis. However, this gap can be filled by carefully designed (practical) systems, which make use of conventional single-user processing and simple coded modulation schemes     

Investigation on outage capacity of spectrum sharing system using CSI and SSI under received power constraints

In this paper, we have investigated the outage capacity of secondary user for opportunistic spectrum sharing under the joint peak and average received power constraints for Rayleigh fading environment. Under this communication scenario, on detecting the licensed primary user inactive, the secondary unlicensed users transmit data/information in the licensed frequency band such that no or minimum interference may be experienced by the primary user. The soft sensing information (SSI) and secondary user’s channel state information is used to obtain the closed form expressions for the ergodic and outage capacity using truncated channel inversion with fixed rate technique under the joint peak and average received power constraints. Numerically simulated results are provided to demonstrate the improvement in outage capacity of secondary user under the proposed spectrum sharing scheme. Moreover, the proposed scheme is also compared with other conventional spectrum sharing schemes to illustrate the benefits of SSI and received power constraints on the outage capacity of secondary user.

     

Performance analysis of multiuser selection diversity in SIMO spectrum sharing systems

In this paper, a performance analysis is presented for user selection schemes in a single‐input multiple‐output spectrum sharing system. In the considered system, multiple secondary users try to use the licensed spectrum of a primary user in an opportunistic manner, in which an interference constraint for the primary user is satisfied. In this paper, we first use 2 conventional user selection schemes for single‐input multiple‐output spectrum sharing system and analyze the system performance for each scheme. We then propose a new user selection scheme that can overcome the limitations of those 2 conventional user selection schemes. As for the performance analysis, the average channel capacity, the outage probability, and the bit error rate performances of the system using the presented user selection schemes are analyzed and mathematical closed‐form expressions for the outage probability are derived. The performances of the system are evaluated using the derived mathematical formulas in different cases. In addition, Monte Carlo simulation results are also provided to show the accuracy and correctness of the performed analysis.