The core aim of this work is the maximization of the achievable data rate of the secondary user pairs (SU pairs), while ensuring the QoS of primary users (PUs). All users are assumed to be equipped with multiple antennas. It is assumed that when PUs are present, the direct communication between SU pairs introduces intolerable interference to PUs and thereby SUs transmit signal using the cooperation of one of the SUs and avoid transmission in the direct channel. In brief, an adaptive cooperative strategy for MIMO cognitive radio networks is proposed. At the presence of PUs, the issue of joint relay selection and power allocation in underlay MIMO cooperative cognitive radio networks (U-MIMO-CCRN) is addressed. The optimal approach for determining the power allocation and the cooperating SU is proposed. Besides, the outage probability of the proposed system is further derived. Due to high complexity of the optimal approach, a low complexity approach is further proposed and its performance is evaluated using simulations. The simulation results reveal that the performance loss due to the low complexity approach is only about 14%, while the complexity is greatly reduced.
Since the issuance of the report of Federal Communications Commission (FCC) in 2002, which revealed the spectrum inefficiency in the incumbent wireless communication systems, cognitive radio (CR) has been regarded as one potential technology to activate the utilization of spectrum resources in the recent evolution of wireless communication systems [
Cognitive radio (CR), MIMO communications, and cooperative communications are among the most promising solutions to improve spectrum utilization and efficiency. Dynamic and opportunistic spectrum access allows CR nodes to communicate on temporarily idle or underutilized frequencies. MIMO systems boost spectral efficiency by having a multiantenna node that simultaneously transmit multiple data streams. To further enhance the performance of cognitive radio networks, a cooperative relay network can be incorporated. Thus, in the underlay CR system with an interference temperature (IT) limit, the cooperative relay networks can also be applied to have a better capacity and error rate performance, trade-off between achievable rate and network lifetime, maximum signal-to-interference-plus-noise ratio (SINR) at the destination node, better channel utilization by multihop relay, maximum throughput, and reduced interference via beamforming and maximum SINR using cooperative beamforming. A timely issue is to embrace recent innovations of the three technologies into a single system.
Joint problems of relay selection and resource allocation in CR networks (CRNs) have attracted extensive research interests due to its more effective spectrum utilization [
The issue of resource allocation in MIMO CRNs was explored in [
The optimal resource allocation in MIMO cognitive radio networks with heterogeneous secondary users and centralized and distributed users was investigated in [
In this paper, we consider the opportunistic spectrum access in MIMO cognitive radio networks (MIMO-CRN) to ensure the SUs’ continuous transmission and reduce its outage probability without interfering the PUs. The desired link is considered as the MIMO link between two SUs, SU transmitter (SU TX), and SU receiver (SU RX). All the users are assumed to be equipped with multiple antennas. We recruit spectrum sensing technology to detect the presence of the PUs. If the PUs are absent, the SU TX communicates the SU RX straightly. Otherwise, the transmit power of SU TX has to be reduced and SU TX transmits to SU RX using the cooperation of one the existing SUs. The cooperating SU is determined using the best relay selection algorithm. To be more accurate, when a PU transmits signal in the system, the joint problems of opportunistic relay selection and power allocation in the context of MIMO CRN to maximize the end-to-end achievable data rate of MIMO CRN need to be considered. Our focus is on the amplify-and-forward (AF) relay strategy. An obvious reason is that AF has low complexity since no decoding/encoding is needed. This benefit is even more attractive in MIMO-CRN, where decoding multiple data streams could be computationally intensive. Moreover, a more important reason is that AF outperforms decode-and-forward (DF) strategy in terms of network capacity scaling: in general, as the number of relays increases in MIMO-CRN, the effective signal-to-noise ratio (SNR) under AF scales linearly, as opposed to being a constant under DF [
To the best of our knowledge, the joint problems of relay selection and power allocation in MIMO cognitive radio networks has not been explored yet. The main contributions of the paper are as follows. The optimal structure of amplification matrix at the cooperating SU and transmit covariance matrix at the transmitter are determined at the presence of PUs. The optimal approach for solving the problem based on the dual method is presented and then a low complexity suboptimal approach is proposed to solve the joint problems of relay selection and power allocation in underlay MIMO CRN. The outage performance of the desired SU link is analyzed.
The remainder of this paper is organized as follows. Section
We consider a scenario where a secondary network, consisting of
When PU pairs are present, the direct communications between the SU TX and SU RX may impose intolerable interference on the PUs. The cooperation of one of SUs with the desired SU link can provide the possibility of reducing the transmit power of the SUs and thereby less interference is imposed on the PU pairs. This is shown in Figure
System model with the two transmission hops, the desired SU link, and other secondary and primary users.
The selected cooperating SU cannot transmit and receive in the same channel at the same time, due to self-interference. Thus, a transmission from SU TX to SU RX at the presence of PUs takes two time-slots. This is also depicted in Figure
In this paper, we assume that a central controller is available, so that the network channel state information and sensing results can be reliably gathered for centralized processing. Notice that the centralized CRNs are valid in IEEE 802.22 standard [
The received signal at
Hence, solving (
In the first subsection, the structure of the optimal amplification matrix in
For now, we assume that
The optimal amplification matrix of SU
Please refer to the Appendix.
Let the singular value decomposition (SVD) of
According to (
In this subsection, the optimal structure of the transmit covariance matrix of the desired link is determined.
The structure of optimal transmit covariance matrix of SU TX is as follows:
Suppose that
It can be verified that
Then, using the second inequality in (
Also, using the first equality in (
In the previous subsection, we proved that the structure of the optimal amplification matrix in SU
Clearly, the relay channel between the SU TX and SU RX has been decomposed into a set of parallel SISO subchannels. Therefore, the achievable data rates in the desired link, as a result of the cooperation of SU
Suppose that the eigenvalue decomposition of
Then, using (
Moreover, the transmit power constraint of the SU TX and SU
The interference constraint on PUs, due to transmission of SU TX, can be written as
The interference constraint on PUs, due to the cooperation of SU
Let
Note that, without loss of generality, it was assumed in (
Let
In this section, we develop approaches for joint relay selection and power allocation in cooperative cognitive radio networks. At first, we provide an optimal approach and then develop a low complexity suboptimal approach.
Using the Lagrange multipliers method [
The optimal approach performs joint opportunistic relay selection and power allocation and results in the maximum data rate. However, the optimal approach is with very high complexity. Here, we aim to develop an alternate low complexity suboptimal approach for problem (
A comparison between the computational complexity of the optimal and suboptimal methods is presented here. For the optimal solution derived in the previous section,
In order to analyze the outage behaviour of the proposed system, we consider the scenario where the PU transmitters,
In order to facilitate the analysis of outage, we modify the system model as explained below. First of all, we assume that the transmit signal at the SU TX is white and thereby
In the first time-slot, the spectrum sensing is used to detect whether the PUs are absent. When the PUs are absent, SU TX transmits data to SU RX directly. When the PUs are present, the transmit power of SU TX,
We firstly assume that no PU link is transmitting signal. Hence, the SU TX communicates directly with the SU RX and the received signal in the SU RX can be written as
Based on the assumptions expressed at the beginning of this section, the achievable data rates of the desired link using the direct channel are given by
Then, we proceed by considering the distribution of the achievable data rate in the desired link as Gaussian with the pdf given in (
As described in the previous section, when PUs transmit signals, the direct communication in the desired link must be avoided and the cooperation of the best SU is employed instead. The received signal in the SU RX using the cooperation of
Thus, the achievable data rates of the desired link is given by
The coefficient
Note that the coefficient
In this subsection, the outage probability of the system is obtained. However, in the case that the DF cooperation strategy is employed and the PUs are present, another possible case in the system is when no SU can decode the signal from SU TX. This may be due to detrimental effects of fading and path loss in the link from the SU TX to SUs. In this case, the SU TX indispensably transmits data to SU TX directly with limited power
In the following theorem, we derive the outage probability of the desired SU link.
The outage probability of the desired SU link is
Consider the case that the PUs are present. Then, the probability of event
The outage probability of the desired link in the presence of PUs and when the one SUs in the subset
Then, the outage probability of the desired SU link in the presence of the PU signals can be written as
Finally, it can be concluded that the outage probability of the desired link is given by
In this section, the performance of the proposed MIMO cooperative cognitive radio system is evaluated using simulations. More specifically, we evaluate the performance of the proposed low complexity approach and compare it with the optimal approach. For better comprehending the merit of the proposed low complexity approach (LCA), we will also compare the proposed approach with the approaches using random cooperative SU selection with optimal power allocation matrices (transmit covariance matrix and amplification matrix), referred to as RS-OPA (random SU-optimal power allocation) and nonoptimal power allocation; that is, the amplification matrix of the randomly selected SU and the transmit covariance matrix are obtained as described in Section All users are assumed to be equipped with the same number of antennas, denoted by We set interference limits, There exist 5 PU pairs in the system, otherwise stated. The elements of the channel matrices follow a Rayleigh distribution and are independent of each other. The SUs are uniformly located between the SU TX and SU RX. The path-loss exponent is 4, and the standard deviation of shadowing is 6 dB. The number of existing SUs in the system, The level of noise is assumed identical in the system and
The achievable data rate in the desired SU link versus the maximum transmit power of SU TX for different number of antennas and various scenarios is shown in Figure
Achievable data rate in the desired link versus the maximum transmit power of SU TX (
The achievable data rate of the desired SU link versus the maximum transmit power of the cooperating SU (
Achievable data rate in the desired link versus the maximum transmit power of cooperating SU (
As shown in Figure
Achievable data rate in the desired link versus the number of existing SUs.
As a final note, all the simulation results are indicating the undeniable effect of the deploying multiple antennas at the SUs and cooperation of other SUs on the performance of the secondary spectrum access in the cognitive radio networks. The results provided in this paper suggest that it is inevitable to take advantage of MIMO systems and cooperation of other SUs, for the aim of opportunistic and dynamic spectrum access and to achieve larger data rates without inducing intolerable interference on the PUs.
In this work, an adaptive transmission strategy for underlay MIMO cooperative cognitive radio networks was proposed. It is assumed that when the PUs are present, the direct transmission by the SUs introduces intolerable interference on PUs. As a remedy and to maintain the performance quality of the SUs, the cooperation of one of the existing SUs was proposed not only to reduce the imposed interference on PUs but also to maximize the data rates in the desired SU link. Afterwards, the optimal solution of the joint problems of power allocation (both in the SU TX and the cooperating SU) and relay selection was presented. However, due to high complexity of the optimal approach, a suboptimal approach with less complexity was further proposed. Meanwhile, the expected degradation in the system performance due to suboptimal approach was proved to be negligible, using simulations. Finally, an outage probability analysis was provided to examine the performance of the proposed MIMO cooperative cognitive radio network.
Our convention is that all eigenvalues are arranged in descending order. It was shown in [
The authors declare that there is no conflict of interests regarding the publication of this paper.