We study the energy-optimal subcarrier power allocation for OFDM-based cognitive radio (CR) networks. A CR transmitter communicates with CR receivers on a channel borrowed from licensed primary users (PUs) when PUs' transmission are detected absence on those channels. Due to non-orthogonality of the transmitted signals in the adjacent bands, both the PU and the secondary user (SU) cause mutual-interference to each other. We assume that the statistical channel state information between the cognitive transmitter and the primary receiver is known. The secondary transmitter maintains a specified statistical mutual-interference limits for all the PUs communicating in the adjacent channels. We propose iterative method based on Dinkelbach theorem using parametric objective function for the fractional programming problem. We show analytically that under a special case, the optimal power allocation follows waterfilling algorithm. Numerical results are given to show the effect of different parameters on the energy-efficiency.

We investigate the optimal allocation of power in the downlink cooperative cognitive radio network using decode and forward (DF) relaying technique. The power allocation in DF relaying for green cooperative cognitive radio with an objective of maximising energy‐efficiency is a constraint non‐linear non‐convex fractional programming problem. The optimisation needs to satisfy the primary users interference constraints and secondary users outage constraints. The authors present the optimal power allocation in DF relaying by transforming the constraint non‐linear non‐convex fractional power allocation problem into a concave fractional programme by using Charnes–Cooper transformation. The authors also present an iterative algorithm that uses parametric transformation and guarantees ε ‐optimal convergence. The convergence of the iterative algorithm is proved and numerical results obtained for cooperative cognitive radio network are presented with different network parameter settings.

The authors study the opportunistic spectrum access techniques for hybrid overlay–underlay cognitive radio networks. A secondary user (SU) chooses a channel, transmission mode and adjusts its power so that the interference limit is not crossed and its throughput is maximised. The authors assume that multiple primary user (PU) channels are available and the SU conducts spectrum sensing to access the channels. The objective is to maximise the throughput by switching between the overlay and underlay transmission modes. Using finite‐horizon partially observable Markov decision process framework, the authors first study the optimal policies, where the PU is assumed to be in busy, concurrent or idle state, and the SU either stays idle or transmits with any of the two designed power levels. Although the PU's states are hidden, their activity statistics, transmission ranges and interference thresholds are assumed to be known. Via Monte Carlo simulation, the authors evaluate the performance of physical layer optimal policy (PLOP) and cross‐layer policy (CLAP) and compare them with a fully observable optimal policy. The beliefs in each slot for both policies are updated using the forward algorithm based technique. Simulation results show that the proposed CLAP is more throughput efficient than the conventional PLOP.

In this paper, we investigate the optimal allocation of the power in the downlink cooperative cognitive radio network using decode and forward (DF) relaying techniques. The power allocation in DF relaying for green cognitive radio with objective of maximizing energy efficiency is a constraint nonlinear nonconvex fractional programming (CNNFP) problem. We present the optimal power allocation in DF relaying by transforming the CNNFP power allocation problem into a concave fractional program by using Charnes-Cooper transformation. We also present an iterative ε-optimal solution for the CNNFP problem using Dinkelbach algorithm. The convergence of the iterative algorithm is proved and numerical solutions obtained using simulations for DF cooperative communications are presented.

In this study, the problem of determining the power allocation that maximises the energy efficiency of cognitive radio network is investigated as a constrained fractional programming problem. The energy‐efficient fractional objective is defined in terms of bits per Joule per Hertz. The proposed constrained fractional programming problem is a non‐linear non‐convex optimisation problem. The authors first transform the energy‐efficient maximisation problem into a parametric optimisation problem and then propose an iterative power allocation algorithm that guarantees ε ‐optimal solution. A proof of convergence is also given for the ε ‐optimal algorithm. The proposed ε ‐optimal algorithm provide a practical solution for power allocation in energy‐efficient cognitive radio networks. In simulation results, the effect of different system parameters (interference threshold level, number of primary users and number of secondary users) on the performance of the proposed algorithms are investigated.

We investigate cross-layer rate adaptation techniques for a secondary user (SU) equipped with a finite buffer in green cognitive radio networks. We assume that the activity statistics of the licensed primary users (PUs) channels are independent and identically distributed, and a SU detects their states using a spectrum sensing method. We formulate the problem as an infinite-horizon partially observable Markov decision process (POMDP). The policy is obtained using maximum-likelihood heuristic policy (MLHP) technique. We assume that the transition probabilities of the PUs and the fading channel between the SU's transmitter and receiver are known, but the exact PU's states are hidden. By tracking belief of the hidden states, the SU takes decision on the rate and corresponding power to minimize energy consumption with constraints on delay and bit error rate. Numerical results are given to show the performance of the proposed MLHP, which is found to perform very close to fully observable optimal policy. We also show pointer to choose design parameter so that the scheduler becomes the most energy-efficient for given quality of service requirements of the application.

We investigate the spectrum access and power adaptation techniques in a cognitive radio network to optimize throughput of a secondary user with specified sensing error limit. Using partially observable Markov decision process framework, we first study the optimal policies, where the primary user is assumed to be in busy, concurrent or idle state, and the secondary user either stay idle or transmits with any of the two designed power level. The collision is avoided with proper reward choices. Although the primary user's states are hidden, their activity statistics, ranges of transmission, and interference thresholds are assumed to be known. The instantaneous optimal policy for each time-slot is then obtained for the current belief of the states obtained through channel sensing. We also propose a forward algorithm based technique that updates belief using the sensor output in the first slot and then using the acknowledgment feedback in the subsequent time-slots in a frame. Simulation results show that the proposed cross-layer technique is more throughput efficient than the physical layer optimal case, specially when the primary user activity is slowly varying and/or frame size is smaller.

Adaptive modulation and antenna diversity are two important enabling techniques for future wireless network to meet the demand for high data rate transmission. We study a Markov decision process based cross-layer design of optimal adaptation policy over selection-combining and maximal-ratiocombining Nakagami-m fading channel for Markov modulated Poisson process traffic. Unlike most of the channel-dependent adaptation policies in the literature, proposed policy chooses modulation constellation dynamically depending on incoming traffic state and buffer state in addition to channel state. Because the channel-dependent policy is physical layer optimized, it does not guarantee upper-layer delay and overflow requirements. Furthermore, the throughput predicted in physical layer analysis without considering buffer and traffic is over-optimistic than the actual system-level throughput. Proposed cross-layer dynamic adaptation policy minimizes transmission power and also guarantees target bit error rate, delay and packet overflow rate requirements for specific application being considered.

Adaptive modulation and antenna diversity are two important enabling techniques for future wireless network to meet demand for high data rate transmission. We study a Markov decision process based cross-layer design of optimal adaptation policy over selection-combining Nakagami-m fading channel for Markov modulated Poisson process (MMPP) traffic. Unlike most of the channel-dependent adaptation policy in the literature, proposed policy chooses modulation constellation dynamically depending on the traffic and buffer states in addition to channel state. Proposed cross-layer dynamic adaptation policy minimizes transmission power, maximizes throughput, and also guarantees target bit error rate, delay and packet overflow rate requirements for the application being considered.

Incremental-redundancy hybrid automatic repeat- request (IR-HARQ) schemes are proposed in several wireless standards for increased throughput-efficiency and greater reliability. We investigate transmit power and modulation order adaptation strategies for the IR-HARQ schemes over correlated Rayleigh fading channels using semi-Markov decision process-based model. In order to jointly analyze physical layer and link layer, transmitter model incorporates a finite-size buffer that receives randomly varying traffic from a higher layer application. It is assumed that channel variations can be modeled with a first-order Markov chain. We show that the optimal transmission power and rate adaptation laws under buffering delay and packet overflow constraints can be obtained using the framework of semi-Markov decision process. We discuss three different adaptation models for the IR-HARQ schemes and compare their performances with the non-adaptive scheme. It is shown that unique optimal policy exists for each case and it can be computed using linear programming approach. This optimal policy is then applied for realistic channel fading and incoming traffic samples to evaluate its performance for both hard-decision and soft-decision decoding. Simulation results in general point out that substantial power savings can be achieved using adaptation and also if the transmission-delay requirements are relaxed.

We study coding and modulation rate adaptation problem for HARQ systems with partially observable state from cross-layer viewpoint. The rate of convolutionally coded M-QAM is adapted jointly with buffer state and channel state. We assume that perfect channel state information is not known at the transmitter, but it can be estimated from previous actions and observations. POMDP-based approach is utilized to formulate the problem, where average throughput is maximized, and average delay, packet error rate and overflows are minimized. To solve the cross-layer adaptation problem approximately, we discuss two heuristic-based methods and compare their applicability with completely observable channel state case by simulation results.

We study a cross-layer optimization problem of a rate-adaptive MQAM system that maximizes throughput, and minimizes packet error rate, delay and overflow using the framework of Markov decision process. We consider finite size buffer and random incoming traffic arrivals. The fading channel is assumed to be Nakagami-m and modeled with a finite state Markov channel, and transmit diversity is achieved with orthogonal space-time block code. To schedule packets, the transmitter depends on both buffer state and channel state information, and selective-repeat ARQ is used at the data link layer for error detection. Simulation results show that the throughput maximization depends not only on the received SNR but also on the number of actions and incoming traffic statistics.

We investigate transmit power adaptation strategy for IR-HARQ scheme over correlated fading channels. In order to jointly analyze physical and link layers, the transmitter model incorporates a finite-size buffer that receives randomly varying traffic from a higher layer application. It is assumed that channel variations can be modeled with first order Markov chain. We show that the optimal power adaptation law under buffer delay and packet overflow constraints can be obtained using the framework of semi-Markov decision processes. The optimal policy is computed using the linear programming approach. Simulation results show that substantial power savings can be achieved if the transmission delay requirements are relaxed.

We address the issue of optimal packet scheduling over correlated fading channels which trades off between minimization of three goals: average transmission power, average delay and average packet dropping probability. We show that the problem forms a weakly communicating Markov decision process and formulate the problem as both unconstrained and constrained problem. Relative value iteration (RVI) algorithm is used to find optimal deterministic policy for unconstrained problem, while optimal randomized policy for constrained problem is obtained using linear programming (LP) technique. Whereas with RVI only a finite number of scheduling policies can be obtained over the feasible delay region, LP can produce policies for all feasible delays with a fixed dropping probability and is computationally faster than the RVI. We show the structure of optimal deterministic policy in terms of the channel and buffer state and form a simple log functional suboptimal scheduler that approximately follows the optimal structure. Performance results are given for both constant and bursty Poisson arrivals, and the proposed suboptimal scheduler is compared with the optimal and channel threshold scheduler. Our suboptimal scheduler performs close to the optimal scheduler for every feasible delay and is robust to different channel parameters, number of actions and incoming traffic distributions.

We address the issue of optimal coding rate scheduling for adaptive type-I hybrid automatic repeat request wireless systems. In this scheme, the coding rate is varied depending on channel, buffer and incoming traffic conditions. In general, we consider the hidden Markov model for both time-varying flat fading channel and bursty correlated incoming traffic. It is shown that the appropriate framework for computing the optimal coding rate allocation policies is partially observable Markov decision process (POMDP). In this framework, the optimal coding rate allocation policy maximizes the reward function, which is a weighted sum of throughput and buffer occupancy with appropriate sign. Since polynomial amount of space is needed to calculate the optimal policy even for a simple POMDP problem, we investigate maximum-likelihood, voting and Q-MDP policy heuristic approaches for the purpose of efficient and real-time solution. Our results show that three heuristics perform close to completely observable system state case if the fading and/or traffic state mixing rate is slow. On the other hand, when the channel fading is fast, Q-MDP heuristic is the most throughput-efficient among considered heuristics. Also, its performance is close to the optimal coding rate allocation policy of fully observable system state case. We also explore the performances of the proposed heuristics in the bursty correlated traffic case and show that maximum-likelihood and voting heuristics consistently outperform the non-adaptive case

We study two cross-layer optimization problems for M-QAM systems that adapt transmission rate with channel state and buffer occupancy. We formulate both problems as constrained Markov decision process problem and give linear programming technique based solutions. In first problem, our objective is to minimize average transmission power under constraint on average delay and packet dropping probability. We minimize average bit error rate (BER) with average delay and packet dropping probability constraints in second problem. The Nakagami-m fading channel with diversity-combining is described as finite state Markov channel. Simulation results show that the system performances can be improved by adapting rate with buffer state and hence delaying packet in the buffer in addition to employing diversity-combining at the receiver.

We present a cross-layer optimization problem where the coding rate of hybrid ARQ systems is adapted with channel, buffer, and input traffic state to minimize packet errors as well as buffer delay. Representing both the incoming traffic and the time-varying wireless channel as a finite state Markov chain, it is shown that the problem forms a partially observable Markov decision process (POMDP) problem. Since finding optimal policy is PSPACE complete, we investigate two policy-heuristic approaches for the purpose of efficient and real time solving of our formulated POMDP problem. Numerical results reveal that the performances of these two heuristic are almost same as the case when channel states are fully observable.

We present a general Markov decision process based framework for the identification of optimal delay-constrained rate adaptation for MQAM systems and power adaptation for type-I hybrid ARQ systems. This framework can be applied to adaptive resource allocation over correlated fading channels. It is shown that the optimal rate and power control can be obtained by solving the appropriately formulated Markov decision processes using linear programming techniques. In the case of adaptive MQAM systems, the optimal rate allocation policy is dependent on the current buffer occupancy and the channel state. For hybrid ARQ systems the power control law can be formulated as being dependent on the current buffer occupancy and the history record of channel and action observations. The results of this paper are of importance for the development of modern wireless standards that support delay sensitive multimedia traffic.

This paper explores optimal and suboptimal packet schedulers for time-varying flat fading channels that trade-off between minimization of the average delay and the average transmitted power. Both uncorrelated and correlated block fading channels are investigated. Extending a previous work, we formulate the trade-off as a unconstrained Markov decision processes and find the stationary deterministic optimal policy using both relative value iteration and policy iteration algorithm. As well, we present constrained Markov decision processes formulation of the problem and linear programming algorithm to solve it and show that optimal schedulers are randomized in this case. In order to alleviate the computational complexity needed, to determine the optimal scheduling policy we propose a suboptimal log-scheduling policy that has performance close to that of the optimal scheduler. The proposed policy is also robust to different channel models. It is demonstrated that log-policy is favorable to the water-filling policy for very slow fading channels.