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 with Max–Min and Min–Max Fairness for Cognitive Radio Networks with Imperfect CSI

This paper consider the power allocation strategies in the cognitive radio (CR) system in the presence of channel estimation errors. As the user has different channel condition in CR systems, different amount of power resource is required to meets the QoS request. In order to guarantee the fairness of each CR user, ensure the interference from the primary user and other CR users meet the QoS requirement of the CR user and limit the interference that is caused by CR users on primary user within the range into the level that primary user can tolerate, we proposed some new power allocation schemes. The targets are to minimize the maximum power allocated to CR users, to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all CR users and to minimize the maximum outage probability over all CR users. The first power allocation scheme can be formulated using Geometric Programming (GP). Since GP problem is equivalent to the convex optimization problem, we can obtain the optimal solutions for the first scheme. The latter two power allocation schemes are not GP problems. We propose iterative algorithms to solve them. Simulation results show that proposed schemes can efficiently guarantee the fairness of CR users under the QoS constraint of the primary user and CR users.     

Cross-Layer optimal connection admission control for variable bit rate multimedia traffic in packet wireless CDMA networks

Next generation wireless code division multiple access (CDMA) networks are required to support packet multimedia traffic. This paper addresses the connection admission control problem for multiservice packet traffic modeled as Markov modulated Poisson process (MMPP) with the quality of service (QoS) requirements on both physical layer signal-to-interference ratio (SIR) and network layer blocking probability. Optimal linear-programming-based algorithms are presented that take into account of SIR outage probability constraints. By exploiting the MMPP traffic models and introducing a small SIR outage probability, the proposed algorithms can dramatically improve the network utilization. In addition, we propose two reduced complexity algorithms that require less computation and can have satisfactory approximation to the optimal solutions. Numerical examples illustrating the performance of the proposed schemes are presented.     

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     

Utility-based power control with QoS support

This paper addresses the issue of incorporating QoS requirements expressed in terms of some minimum SIR targets into the traditional utility-based power control problem. As suitable projection methods seem to be not amenable to distributed implementation, we first focus on a primal-dual algorithm to solve the utility-based power control problem subject to the SIR requirements. We prove a global convergence of the algorithm for a large class of utility functions and show that it can be implemented in a distributed wireless environment. However, the approach has an important drawback: An optimal solution may not exist as the SIR targets may be infeasible due to, for instance, channel effects. This motivates a reformulation of the problem so that an optimal solution always exists. We consider the possibility of using a barrier method to closely approach the desired SIRs of the users and combine this approach with the conventional utility-based power control problem to incorporate best effort users. We prove relevant properties of optimal solutions and propose a distributed recursive algorithm with global convergence. Finally, the performance of the proposed approaches is verified by simulations.     

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     

Worst-case performance optimization for robust power control in downlink beamforming

In this paper,¹ we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition.     

A novel approach for energy‐efficient resource allocation in double threshold‐based cognitive radio network

This paper mainly focuses on solving the energy efficiency (EE) maximization problem in double threshold‐based soft decision fusion (SDF) cooperative spectrum sensing (CSS) in the cognitive radio network (CRN). The solution to this objective problem starts with the selection of suitable secondary users (SUs) both for the spectrum sensing and data transmission. Here, energy efficiency is maximized under the constraints of interference to the primary user (PU), an acceptable outage of SUs, the transmission power of the SUs and the probability of false alarm. We propose a novel algorithm called iterative Dinkelbach method (IDM) which jointly optimizes the sensing time and transmission power allocation to the SUs. Further, Lagrangian duality theorem is employed to find the exact power assigned to the SUs. Finally, simulation results are carried out to validate the effectiveness of our proposed scheme by comparing with the other existing schemes. The performance is also analyzed for different system parameters.     

Jointly Optimal Congestion and Power Control for Rayleigh-Faded Channels with Outage Constraints

We address the problem of joint congestion control and power control with link outage constraints in Rayleigh fast-fading and multihop wireless networks. Because of packet loss caused by the fast-fading-induced link outage, the data rate received successfully at the destination node (the effective rate) is much lower than the transmission rate at the source node (the injection rate). In this paper, a novel model, i.e., effective network utility maximization with power control (ENUMP), is designed to formulate this scenario. In ENUMP, the network utility is associated with the effective rate, and an effective network utility maximization formulation with link outage constraints is used. Although the original problem is non-convex and non-separable, we can still construct a distributed algorithm by applying appropriate transformations. Since in our model we sufficiently take into account the statistical variations of the signal-to-interference ratio, the power updates do not follow the instantaneous state of the fast-fading channel. Simulation results show that the optimal solution of our algorithm is close to the globally optimal solution. Besides, simulation results also verify that ENUMP achieves significant gains of the effective rate, the network utility, and the network congestion control over an existing famous model.     

Space-time turbo multiuser detection for coded MC-CDMA

The system capacity and performance of multicarrier code-division multiple-access (MC-CDMA) communication systems can be significantly enhanced by jointly employing MAP-based multiuser detection (MUD) and channel decoding techniques. In this paper, a group-oriented soft iterative MUD based on the combination of smart antennas and iterative MAP-based MUD is presented. The proposed method is featured as a novel technique for further increasing the system capacity and performance. In this method, all the users are first grouped into several groups according to their impinging direction of arrivals (DOAs). All users with similar DOAs are classified into the same group and then low-complexity MAP-based iterative MUD is employed in each group. Because spatial filtering cannot suppress all the interference between the groups, interference cancellation among the groups is used prior to MUD within each group. It is shown that the proposed group-oriented soft iterative MUD algorithm can significantly reduce the computational complexity compared with the conventional optimal MAP-based MUD schemes. It is also demonstrated that the performance of the proposed algorithm can approach that of a single-user coded MC-CDMA system with an antenna array in additive white Gaussian noise and frequency selective fading channels.     

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.     

Power and rate control with outage constraints in CDMA wireless networks

A radio power control strategy to achieve maximum throughput for the up-link of CDMA wireless systems with variable spreading factor is investigated. The system model includes slow and fast fading, rake receiver, and multi-access interference caused by users with heterogeneous data sources. The quality of the communication is expressed in terms of outage probability, while the throughput is defined as the sum of the users' transmit rates. The outage probability is accounted for by resorting to a lognormal approximation. A mixed integer-real optimization problem P1, where the objective function is the throughput under outage probability constraints, is investigated. Problem P1 is solved in two steps: firstly, we propose a modified problem P2 to provide feasible solutions, and then the optimal solution is obtained with an efficient branch-and-bound search. Numerical results are presented and discussed to assess the validity of our approach.     

Dynamic resource allocation algorithm in multi-user cooperative OFDMA systems: considering QoS and fairness constraints

Wireless transmission systems are constrained by several parameters such as the available spectrum bandwidth, mobile battery energy, transmission channel impairments and users’ minimum quality-of-service. In this paper, a new strategy is investigated that aims at improving the allocation of resources in a dual hop OFDMA cooperative network consisting in multi source–destination pairs and multiple decode-and-forward relays. First, the joint optimization of three types of resources: power, sub-channel and relay nodes, is formulated as a problem of subchannel-relay assignment and power allocation, with the objective of minimizing overall transmission power under the bit-error-rate and data rate constraints. However, the optimal solution to the optimization problem is computationally complex to obtain and may be unfair. Assuming knowledge of the instantaneous channel gains for all links in the entire network, an iterative three-step resource allocation algorithm with low complexity is proposed. In order to guarantee the fairness of users, several fairness criteria are also proposed to provide attractive trade-offs between network performance (i.e. overall transmission power, average network lifetime and average outage probability) and fairness to all users. Numerical studies are conducted to evaluate the performance of the proposed algorithm in two practical scenarios. Simulation results show that the proposed allocation algorithm achieves an efficient trade-off between network performance and fairness among users.     

Control and Data Channel Resource Allocation in OFDMA Heterogeneous Networks

This paper investigates the downlink resource allocation problem in Orthogonal Frequency Division Multiple Access (OFDMA) Heterogeneous Networks (HetNets) consisting of macro cells and small cells sharing the same frequency band. Dense deployment of small cells overlaid by a macro layer is considered to be one of the most promising solutions for providing hotspot coverage in future 5G networks. The focus is to devise an optimised policy for small cells’ access to the shared spectrum, in terms of their transmissions, in order to keep small cell served users sum data rate at high levels while ensuring that certain level of quality of service (QoS) for the macro cell users in the vicinity of small cells is provided. Both data and control channel constraints are considered, to ensure that not only the macro cell users’ data rate demands are met, but also a certain level of Bit Error Rate (BER) is ensured for the control channel information. Control channel reliability is especially important as it holds key information to successfully decode the data channel. The problem is addressed by our proposed linear binary integer programming heuristic algorithm which maximises the small cells utility while ensuring the macro users imposed constraints. To further reduce the computational complexity, we propose a progressive interference aware low complexity heuristic solution. Discussion is also presented for the implementation possibility of our proposed algorithms in a practical network. The performance of both the proposed algorithms is compared with the conventional Reuse-1 scheme under different fading conditions and small cell loads. Results show a negligible drop in small cell performance for our proposed schemes, as a trade-off for ensuring all macro users data rate demands, while Reuse-1 scheme can even lead up to 40 % outage when control region of the small cells in heavily loaded.     

Capacity assessment of a cellular radio system using a narrowband multiuser detector

With a narrowband multiuser detector (MUD), multiple users can simultaneously share the same channel without using a bandwidth-expanding signature code when sufficient power differences at the receiver are maintained. In this paper, we assess the capacity gain that can be achieved in a hypothetical cellular system with centralized power control, using a narrowband MUD based on successive cancellation. The power-control algorithm is adapted to multiple users per channel in a cell. Simulation results are presented for two heuristic carrier-to-interference ratio-based channel-assignment schemes. The MUD allows for a substantial capacity gain due to a tighter packing of users in a channel. The observed gain compared with a conventional single user-per-channel system, ranges from 1.4 to 5 for cluster sizes C = 1 and 7, respectively.     

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.      

Practical Multiuser Diversity With Outdated Channel Feedback

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a multiple access wireless setting. Considering a channel-assigning strategy that assigns the channel only to the user with the best instantaneous SNR [3], our emphasis is on the effects of channel feedback delay in downlink transmissions. A finite set of M-ary quadrature amplitude modulation (M-QAM) constellations is adopted and a constant transmit power is assumed in this practical multiuser adaptive modulation scheme. Based on the closed-form expressions for average bit error rate (BER) and average data rate, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. Simple and accurate asymptotic approximations are also provided in the limit of large numbers of users. Focusing on different applications, we propose two optimization criteria for the switching thresholds, based on either an average BER, or an outage probability constraint. Two novel constant power, variable rate M-QAM schemes that are less sensitive to feedback delay are proposed using the optimal switching thresholds, which are derived to maximize the average data rate subject to these two constraints, respectively. To obtain a certain degree of fairness among the users, we also consider a fair channel-assigning strategy that assigns the channel to only the user with the greatest normalized SNR.     

Hierarchical SIR and rate control on the forward link for CDMA datausers under delay and error constraints

We study the signal-to-interference ratio (SIR) and rate control for code division multiple access (CDMA) data users on the forward link under average or peak power constraints. The quality of service (QoS) for data users is specified by delay and error rate constraints as well as a family of utility functions representing the throughput and fairness among the data users. It is found that the optimal SIR and rate control algorithm has a hierarchical structure which can be easily implemented in a distributed manner. The SIR targets can be adjusted independently by the mobiles using information specific to the individual users. The data rates can be adjusted jointly by the base station based on limited feedback from the mobiles. We also propose a two-level iteration algorithm for both the mobile and the base station to efficiently compute the SIR and data rates. Our results show that a flexible tradeoff between total system throughput (sum of rates achieved) and fairness (similarity in data rates) can be achieved by choosing appropriate utility functions used in this scheme     

Two-way cooperative communications with statistical channel knowledge

We consider the problem of distributed beamforming for a two-way relay network which consists of two transceivers and multiple relay nodes. The main assumption in this work, which differentiates it from previously reported results, is that one of the transceivers is assumed to have only statistical information about channels between the other transceiver and the relay nodes. This assumption imposes less stringent restrictions on the bandwidth required to obtain channel state information via training. Based on this statistical modeling, we propose to use a chance-constrained programming approach to design a distributed beamforming algorithm. In this approach, we aim to minimize the total transmit power (consumed in the entire network) as perceived by one of the transceivers, subject to two probabilistic constraints. These constraints guarantee that the outage probability of the transceivers' received SNRs, as perceived by the master transceiver, is not less than certain given thresholds. We prove rigorously that such an approach leads to a relay selection algorithm where the relay with the strongest channel coefficient to the master transceiver participates in relaying and the remaining relays are shut off. As such, the optimal distributed beamforming algorithm is simplified to a power control solution. Closed-form solution to this problem is obtained and its performance is evaluated through numerical examples.     

Performance of a Cooperative Algorithm for power control in cellular systems with a time‐varying link gain matrix

A new version of the Cooperative Algorithm is proposed for distributed power control in time‐varying cellular environment. Unlike other approaches which assume a fixed link gain matrix, we consider a time‐varying model for shadow fading. We consider the performance of three schemes, namely, instantaneous SIR balancing, slow path loss compensation and the Cooperative Algorithm. Analytical results are obtained for the case where there are two cochannel users. We have shown that the sequence of signal‐to‐interference ratio (SIR) converges in distribution. The outage probability in steady state is obtained. It is shown that when the power control sampling period is small, the performance of the Cooperative Algorithm approaches that of instantaneous SIR balancing. For more than two users, a detailed simulation is performed. This revised version was published online in July 2006 with corrections to the Cover Date.