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We study the energy-efficient power allocation techniques for OFDM-based cognitive radio (CR) networks, where a CR transmitter is communicating with CR receivers on a channel borrowed from licensed primary users (PUs). Due to non-orthogonality of the transmitted signals in the adjacent bands, both the PU and the cognitive secondary user (SU) cause mutual-interference. 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. Our goal is to allocate subcarrier power for the SU so that the energy efficiency metric is optimized as well as the mutual-interference on all the active PU bands are below specified bounds. We show that the green power loading problem is a fractional programming problem. We use Charnes-Cooper transformation technique to obtain an equivalent concave optimization problem for what the solution can be readily obtained. We also propose iterative Dinkelbach method using parametric objective function for the fractional program. Numerical results are given to show the effect of different interference parameters, rate and power thresholds, and number of PUs.

The demand for ubiquitous wireless broadband data access and multimedia services is constantly growing in the crowded consumer radio bands while wider spectral ranges of already licensed frequency bands are barely used. To cope with this unequal spectrum access and usage, spectrum pooling is identified as one of the potential techniques that enables public access to licensed frequency bands. The key idea of spectrum pooling is to merge spectral ranges from different spectrum owners into a common pool and the cognitive or secondary users may borrow/rent spectrum from the pool. The coexistence of both the licensed users and cognitive users are realized by filling the time-frequency gaps of the primary network when they are idle.

Orthogonal frequency division multiplexing (OFDM) has been identified as a feasible modulation technique due to its flexible spectral shape that can adaptively fill the idle gaps for such a co-existence scenario. However, due to the non-orthogonality of the transmit signals, both primary and secondary systems introduce mutual interference and it is crucial that the sum of the interference from all the subcarriers does not exceed acceptable limits. In this paper, our goal is to greenwise design a cognitive radio (CR) system that optimizes energy efficiency under probabilistic interference quality of service (QoS) constraints for primary users (PUs), and throughput and power QoS constraints for secondary users (SUs). We assume that each PU has its own statistical interference limits depending on its own QoS requirements. The SU sharing the spectrum has knowledge of all these individual statistical interference limit of the PUs. OFDM has already been deployed in different broadband broadcast wireless standards, such as, Digital Video Broadcasting (DVB), Digital Audio Broadcast (DAB),

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While accessing PU's spectrum, it is crucial to limit interference so that PU's operation is not hampered. Different form of interference limit has been used in the literature, such as, instantaneous hard interference limit, average interference limit, PU outage limit, or soft statistical interference limit. The authors in [

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Energy-efficient green communications techniques and network designs are of special importance for future generation communications in order to reduce carbon dioxide gas emission due to exponential increase on energy consumption in our daily lives [

While wireless handheld devices are playingan ever-increasing integral role in human daily activities, wireless systems as a whole invariably contribute to a significant global carbon footprint. A recent study shows that information and communication technology (ICT) is responsible for about 3%–5% of the worldwide total energy consumptions [

From the discussion above it can be seen that there are two streams of studies for cognitive radio networks in the literature: some authors studied the maximization of capacity with statistical interference constraint, and some authors addressed the maximization of EE without considering statistical interference model. In this paper, we address the deficiencies in both streams by combining them. We address a generalized formulation for green cognitive radio networks. Therefore, although downlink power allocation techniques for wireless broadcast channels exist in the literature, energy-efficient green power allocation technique with statistical interference constraint is not explored yet. Also, most of spectrum access techniques in cognitive radio networks deal with either throughput maximization or power minimization in interweave manner (cognitive user transmit when the primary user is off). In this paper, we addressed EE maximization problem considering three important constraints that are not addressed before together, but for cognitive radio scenario.

The main contributions of this paper are as follows:

We propose an energy-efficiency maximization framework in a cognitive radio scenario, where the transmitter judiciously allocates total power over multiple subcarriers. The transmitter maintains specified statistical interference limits for the individual PUs and minimum throughput for the SUs. We formulate the resulting problem as a fractional program;

Since the optimal solution of the formulated fractional program may be hard to obtain due to non-concavity of the objective function, we show using Charnes-Cooper Transformation (CCT) technique that the problem is equivalent to a concave optimization problem. Suitable concave optimization solution technique can be used to obtain optimal subcarrier powers for the equivalent concave optimization problem;

We discuss the special structure of the solution analytically and show that the power allocation follows a water-filling type distribution for the special case when the sum rate throughput is greater than the specified threshold;

We propose and study an iterative technique based on Dinkelbach method to obtain

With numerical analysis, we show the performance of the green cognitive radio network with different operational parameters. We also compare the convergence of iterative method with equivalent CCT problem.

The rest of the paper is organized as follows. The system model and problem formulation are presented in Section 2. The transformation technique of the non-linear non-concave problem into a concave problem is discussed in Section 3 and iterative technique based on Dinkelbach method using parametric objective is given in Section 4. Simulation results are presented in Section 5 and conclusion is drawn in Section 6.

We consider a cognitive radio network as shown in a simplified _{i}

Let _{i}^{th}

The channel state between the CR transmitter and the CR receiver varies randomly in both time and frequency domain due to fading, and
^{th} subcarrier. We assume that the channel state information (CSI) of all subcarriers are perfectly estimated at the receiver and are fed back to the transmitter for power loading on the subcarriers. Without losing generality, we assume that the set of achievable rate points for the broadcast channel can be computed using any methods, such as, frequency division, time-division, superposition coding (SPC), _{j}_{j}^{n}^{th} subcarrier, its rate throughput, _{j}^{2} is the additive white Gaussian noise (AWGN) variance and _{ij}^{th} PU transmitter to the ^{th} subcarrier. We assume that the randomly varying interference can be perfectly estimated at the SU receiver and also the estimated interference can be fed back to the transmitter.

The performance of the green radio systems are usually measured in terms of energy-efficiency metric, which is defined as the total achievable rate throughput per unit total transmitter power. Let Γ(_{c}_{ji}^{th} subcarrier to the ^{th} PU;
^{th}_{T}^{th}_{1} ensures that the total interference to a PU is below a specified threshold by a specified probability margin, _{2} ensures the sum rate constraints over all the subcarriers and _{3} ensures that the total allocated power does not exceed the power threshold, _{T}_{4} ensures nonnegative power values in the optimization process.

We assume that the fading channel between the SU transmitter and ^{th}_{ji}_{ji}_{j}_{th}_{ji}^{th}^{th}_{s} is the OFDM symbol duration. Suppose

Note that the terms _{ji}_{ji}_{1} of

The detailed derivation of

The problem in

The fractional programming problem in

Problem _{i}^{n}_{i}

A CFP with affine denominator can be transformed to an equivalent concave program with Charnes-Cooper Transformation (CCT) with the following transformations:

The concave program _{2} is a strictly inequality, we show that the power allocation in the subcarriers has water-filling type policy. We express this by the following theorem:

_{2}_{j}, ϕ_{i} and η_{i} are Lagrange multipliers of the Lagrangian function L(

The proof of Theorem 1 is given in

Another mathematically less cumbersome technique that does not require the transformation is an iterative solution technique of the fractional programming problem based on the Dinkelbach method [_{p}_{∈}_{S}

_{p}_{∈} _{S}

Therefore, the problem formulated in

^{−6}, iteration

_{p}

_{1}to

_{4}of

_{ε}

In this section, we present numerical simulation results for the channel access probability, average energy efficiency and average total transmitted power with different interference parameters, power and rate thresholds, and number of interfering primary users using both the CCT and Dinkelbach formulations. Both the CCT and Dinkelbach formulations give the same optimal values. We conduct Monte Carlo simulations by generating several set of channel samples for Rayleigh fading channel and average the optimal energy efficiency and the optimal total power over the number of set of samples. Unless specified otherwise, the values for different system parameters for the Monte Carlo simulations are as follows: the duration of OFDM symbol, _{s}_{c}^{−6} mW, noise power variance, ^{2} = 0.1 mW, the total transmitter power threshold, _{T}^{th}^{6} bits/sec, interference threshold,
^{−4}.

For a given set of data and channel realization, all the constraints must satisfy together and they form a region where all the possible solution points lie in. However, for a particular set of channel samples, there may not be any feasible region at all. Meaning, there is no solution point that can simultaneously satisfy all the constraints. For that channel scenario and constraint thresholds, the SU cannot access the channel. One or more thresholds must be relaxed in order to transmit for that channel conditions. The channel access probability is defined as the average number of samples for which a feasible region and hence an optimal solution exists for the problem. First let us see the how the three main constraints,

^{th}^{th}^{th}

In _{T}

The effect of interference probability threshold on the channel access probability, total power and energy efficiency are shown in

In

In this paper, we studied energy-efficient downlink power allocation techniques for OFDM-based green cognitive radio systems. We assumed that the primary and secondary users coexist in adjacent bands. In this scenario, the mutual interference is very important to control. We formulated the problem using a fraction programming technique, where the objective is to maximize the energy efficiency that is defined as the ratio of capacity and transmitted power. We first provided the optimal solution of the problem through Charne-Cooper transformation that gives us concave form of the problem from fractional form. Although the original fractional program is quasi-concave for which global optimal point is not guaranteed, the equivalent concave problem is easier to solve using standard optimization technique and also has only one global optimal point. Therefore, finding a local optimal point is enough. Then we investigated the Dinkelbach method, where the fractional objective function is converted into parametric objective function. We provided the proof of one-to-one relationship of the solution between the fractional programming method and the Dinkelbach method. The resulting parametric problem is solved using iterative techniques and

The authors declare no conflict of interest.

Combining constraint _{1} of

Let us assume that

The Lagrangian function of

Suppose,

Substituting ^{+} is the non-negative function.

Number of primary users (PUs)

_{i}

Bandwidth of ^{th}

Number of subcarriers of the secondary user's (SU's) transmitter

Bandwidth of a subcarrier

Channel fading gain of ^{th} subcarrier

Channel power gain of ^{th} subcarrier

Channel fading gain between SU transmitter and ^{th} PU

Channel power gain between SU transmitter and ^{th} PU

_{j}

Power allocated to ^{th} subcarrier

_{ji}

Interference by ^{th}^{th}

Interference threshold

Interference probability threshold

_{j}

Capacity/Rate of ^{th} subcarrier in bits/sec

^{th}

Capacity/Rate threshold

_{T}

Maximum transmitted power over all subcarriers

_{ij}

Interference by ^{th} PU to ^{th} subcarrier

_{s}

OFDM symbol duration

_{ji}

Spectral distance between ^{th} subcarrier and ^{th} PU

Numerator of fractional program

Denominator of fractional program

=

= ^{−1}, Charnes-Cooper transformation variable

Convergence tolerance parameter in Dinkelbach method

Real-valued parameter so that _{p}

A typical scenario of primary and secondary user communications in a geographic area, where primary and secondary users co-exist in side-by-side bands. They cause adjacent channel interference to each other.

Pictorial view of the optimization objective and all the constraints. The feasible region (common region created by the constraints) and the optimal solution point (solid circle) are also shown. Interference and sum rate constraints are active for this case.

Pictorial view of the optimization objective and all the constraints for different rate constraint. The feasible region and the optimal solution point are also shown in this case. Unlike

The variation of channel access probability with number of primary users for different power thresholds.

The variation of average energy efficiency with number of primary users for different power thresholds.

The variation of average total subcarrier power with number of primary users for different power thresholds.

The effect of number of primary users on channel access probability for different rate thresholds.

Channel access probability

Total power

Average energy efficiency

The effect of interference probability threshold on channel access probability for different number of PUs.

The convergence of Dinkelbach method. Energy efficient