Resource Allocation in MU-OFDM Cognitive Radio Systems with Partial Channel State Information
© Dong Huang et al. 2010
Received: 4 March 2010
Accepted: 28 July 2010
Published: 10 August 2010
In wireless communications, the assumption that the transmitter has perfect channel state information (CSI) is often unreasonable, due to feedback delays, estimation errors, and quantization errors. In order to accurately assess system performance, a more careful analysis with imperfect CSI is needed. In this paper, the impact of partial CSI due to feedback delays in a multiuser Orthogonal Frequency Division Multiplexing (MU-OFDM) cognitive radio (CR) system is investigated. The effect of partial CSI on the bit error rate (BER) is analyzed. A relationship between the transmit power and the number of bits loaded on a subcarrier is derived which takes into account the target BER requirement. With this relationship, existing resource allocation schemes which are based on perfect CSI being available can be applied when only partial CSI is available. Simulation results are provided to illustrate how the system performance degrades with increasingly poor CSI.
In performance analyses of wireless communication systems, it is often assumed that perfect channel state information (CSI) is available at the transmitter. This assumption is often not valid due to channel estimation errors and/or feedback delays. To ensure that the system can satisfy target quality of service (QoS) requirements, a careful analysis which takes into account imperfect CSI is required .
Cognitive radio (CR) is a relatively new concept for improving the overall utilization of spectrum bands by allowing unlicensed secondary users (also referred to as CR users or CRUs) to access those frequency bands which are not currently being used by licensed primary users (PUs) in a given geographical area. In order to avoid causing unacceptable levels of interference to PUs, CRUs need to sense the radio environment and rapidly adapt their transmission parameter values [2–6].
Orthogonal frequency division multiplexing (OFDM) is a modulation scheme which is attractive for use in a CR system due to its flexibility in allocating resources among CRUs. The problem of optimal allocation of subcarriers, bits, and transmit powers among users in a multiuser-(MU-) OFDM system is a complex combinatorial optimization problem. In order to reduce the computational complexity, the problem is solved in two steps by many suboptimal algorithms [7–10]: determine the allocation of subcarriers to users and determine the allocation of bits and transmit powers to subcarriers. Resource allocation algorithms for MU-OFDM systems have been studied in [11–14]. These algorithms are designed for non-CR MU-OFDM systems in which there are no PUs.
In an MU-OFDM CR system, mutual interference between PUs and CRUs needs to be considered. The problem of optimal allocation of subcarriers, bits, and transmit powers among users in an MU-OFDM CR system is more complex. It is commonly assumed that perfect CSI is available at the transmitter [15, 16]. As noted earlier, this assumption is often not reasonable. In this paper, we investigate the problem of resource allocation in an MU-OFDM CR system when only partial CSI is available at the CR base station (CRBS). We assume that CSI is acquired perfectly at the CRUs and fed back to the CRBS with a delay of seconds. The channel experiences frequency-selective fading. The objective is to maximize the total bit rate while satisfying BER, transmit power, and mutual interference constraints.
The rest of the paper is organized as follows. The system model is described in Section 2. Based on the system model, a constrained multiuser resource allocation problem is formulated in Section 3. A suboptimal algorithm for solving the problem is discussed in Section 4. Simulation results are presented in Section 5 and the main findings are summarized in Section 6.
2. System Model
We consider the problem of allocating resources on the downlink of an MU-OFDM CR system with one base station (BS) serving one PU and CRUs. The basic system model is the same as that described in  and is summarized here for the convenience of the reader.
The PU channel is Hz wide and the bandwidth of each OFDM subchannel is Hz. On either side of the PU channel, there are OFDM subchannels. The BS has only partial CSI and allocates subcarriers, transmit powers, and bits to the CRUs once every OFDM symbol period. The channel gain of each subcarrier is assumed to be constant during an OFDM symbol duration.
represents the interference factor for subcarrier , is the spectral distance between the center frequency of subcarrier and that of the PU channel, and denotes the normalized baseband power spectral density (PSD) of each subcarrier.
Equation (4) shows the relationship between the transmit power and the number of bits loaded on the subcarrier for a given BER requirement when perfect CSI is available at the transmitter. We now establish an analogous relationship when only partial CSI is available.
The imperfect CSI that is available to the BS is modeled as follows. We assume that perfect CSI is available at the receiver. The channel gain, hnk, for subcarrier n and CRU k is the outcome of an independent complex Gaussian random variable, that is, , corresponding to Rayleigh fading. For clarity, we will denote random variables and their outcomes by uppercase and lowercase letters, respectively.
3. Formulation of the Multiuser Resource Allocation Problem
denotes the total bit rate achieved by CRU . Constraint (11) ensures that the average BER for each subcarrier is below the given BER target. Constraint (12) states that the total power allocated to all CRUs cannot exceed , while constraint (14) ensures that the interference power to the PU is maintained below an acceptable level . Constraint (15) results from the assumption that each subcarrier can be assigned to at most one CRU. Constraint (17) ensures that the bit rate achieved by a CRU satisfies a proportional fairness condition.
From (20), an explicit relationship between minimum transmit power and number of transmitted bits cannot be easily derived. However, since in (20) is a monotonically decreasing function of , we obtain the minimum power requirement while satisfying the constraint in (11) by setting .
4. Resource Allocation with Partial Csi
Note that the joint subcarrier, bit, and power allocation problem in (10)–(17) belongs to the mixed integer nonlinear programming (MINP) class . For brevity, we use the term "bit allocation" to denote both bit and power allocation. Since the optimization problem in (10)–(17) is generally computationally complex, we first use a suboptimal algorithm, which is based on a greedy approach, to solve the subcarrier allocation problem in Section 4.1. After subcarriers are allocated to CRUs, we apply a memetic algorithm (MA) to solve the bit allocation problem in Section 4.2.
4.1. Subcarrier Allocation
From (17), it can be seen that the subcarrier allocation depends not only on the channel gains, but also on the number of bits allocated to each subcarrier. Moreover, allocation of subcarriers close to the PU band should be avoided in order to reduce the interference power to the PU to a tolerable level. Therefore, we use a threshold scheme to select subcarriers for CRUs.
where is the total transmit power allocated to all subcarriers and is the total interference power experienced by the PU due to CRU signals. The subcarrier allocation problem in (29)–(32) can be solved using the SA algorithm proposed in . Note that we need to make use of (24) in the SA algorithm if only partial CSI is available. A pseudocode listing for the SA algorithm is shown in Pseudocode 1. The algorithm has a relatively low computational complexity . After subcarriers are allocated to CRUs, we then determine the number, , of bits allocated to subcarrier .
4.2. Bit Allocation
Memetic algorithm (MAs) are evolutionary algorithms which have been shown to be more efficient than standard genetic algorithms (GAs) for many combinatorial optimization problems [25–27]. Using (24), the bit allocation problem can be solved using the MA algorithm proposed in . It should be noted that the chosen genetic operators and local search methods greatly influence the performance of MAs. The selection of these parameters for the given optimization problem is based on the results in . A pseudocode listing of the proposed memetic algorithm is shown in Pseudocode 2.
Crossover: suppose that . Let denote the crossover probability, and let , denote the outcome of an independent random variable which is uniformly distributed in , then is selected as a candidate for crossover if and only if . Suppose that we have such candidates, we then form disjoint pairs of candidates (parents).
Mutation: let denote the mutation probability. For each chromosome in , we generate , where denotes the outcome of an independent random variable which is uniformly distributed in . Then for each component for which , we substitute the value with a randomly chosen admissible value.
In this section, performance results for the proposed algorithm described in Section 4 are presented. In the simulation, the parameters of the MA algorithm were chosen as follows: population size, ; number of generations = 20; crossover probability, ; mutation probability, .
We consider a system with one PU and CRUs. The total available bandwidth for CRUs is 5 MHz and supports 16 subcarriers with MHz. We assume that and an OFDM symbol duration, of s. In order to understand the impact of the fair bit rate constraint in (17) on the total bit rate, three cases of user bit rate requirements with were considered. In addition, three cases of partial CSI with were studied. It is assumed that the subcarrier gains and , for are outcomes of independent identically distributed (i.i.d.) Rayleigh-distributed random variables (rvs) with mean square value . The additive white Gaussian noise (AWGN) PSD, , was set to W/Hz. The PSD, , of the PU signal was assumed to be that of an elliptically filtered white noise process. The total CRU bit rate, , results were obtained by averaging over 10,000 channel realizations. The confidence intervals for the simulated results are within of the average values shown.
The assumption of perfect CSI being available at the transmitter is often unreasonable in a wireless communication system. In this paper, we studied an MU-OFDM CR system in which the available partial CSI is due to a delay in the feedback channel. The effect of partial CSI on the BER was investigated; a relationship between transmit power, number of bits loaded, and BER was derived. This relationship was used to study the performance of a resource allocation scheme when only partial CSI is available. It is found that the performance varies greatly with the quality of the partial CSI.
Pseudocode 1: Pseudocode for subcarrier allocation algorithm.
Using (25), calculate the number of bits loaded on
Pseudocode 2: Pseudocode for the memetic algorithm.
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