Power control for cognitive relay networks with sensing uncertainties
 Hangqi Li^{1},
 Xiaohui Zhao†^{1}Email author and
 Yongjun Xu^{1}
https://doi.org/10.1186/s1363801606171
© Li et al. 2016
Received: 19 December 2015
Accepted: 19 April 2016
Published: 4 May 2016
Abstract
Power control (PC) is a key solution to enable spectrum sharing between secondary users (SUs) and primary users (PUs). However, previous research lacks sensing uncertainties for the status of PUs. In this article, we focus on the PC problem for a cognitive relay network under the spectrum sensing uncertainties to minimize the total bit error rate (BER) of SUs under the constraints of maximum transmit power budgets, signaltointerferenceandnoise ratio (SINR) constraints, and interference requirements to provide protection for PUs. We first formulate the interference model by taking sensing uncertainties into account, while the worstchannelstateinformation (worstCSI) PC algorithm is introduced to limit the BER of SUs, which only needs to operate the algorithm in one link whose CSI is worst. And a cooperative spectrum sensing (CSS) strategy is considered to optimize the sensing performance. To deal with the optimization problem, the original minmax BER problem is converted into an equivalent maxmin SINR problem solved by Lagrange dual decomposition method. Finally, simulation results are presented to indicate that our proposed algorithm can obtain good BER performance and guarantee quality of service of PU.
Keywords
1 Introduction
The spectrum survey conducted by the Federal Communications Commission has revealed that some frequency bands of the allocated spectrum are heavily used, but others are unused in most of the time with the spectrum utilization ranging only from 15 to 85 % [1]. Cognitive radio (CR) [2] as an intelligent technique for the next generation of wireless communication can significantly improve spectrum utilization and deal with spectrum shortage problem through the spectrum sharing scheme, in which secondary users (SUs) (i.e., unlicensed users or CR users) can opportunistically access to the licensed spectrum bands allocated to primary users (PUs) (i.e., licensed users) [3]. In general CR networks (CRNs), power control (or resource allocation) techniques are used based on perfect channel state information (CSI) and spectrum sensing results. Power control (PC) technology is to obtain a certain ideal goal (e.g., utility maximization, throughout maximization, total power minimization) by adjusting the transmit power of secondary system with no harmful interference for communications of PUs.
In wireless communication, the quality of service (QoS) of users may not be guaranteed when users locate in the edge of networks or the distance between users is far away. Thus, relay technology (i.e., cooperative technology) has been proposed as an effective way to overcome the problem [4]. The earliest emergence of relay networks can be traced back to the late 1970s in [5, 6], Cover and others indicate that the transmission scheme using relays can effectively increase the capacity and coverage of system by ensuring credible communications between users from the viewpoint of information theory. Since cognitive relay networks have more advantages than traditional CRNs (i.e., nonrelay networks) and more suitable for actual communication scenarios (i.e., heterogeneous networks, 5G communications), in this paper, we study the PC problem in cognitive relay networks with a multiuser scenario.
As we know, PC technique as a key solution can improve the performance of CRNs and control the interference power of PUs so that SUs share licensed spectrums opportunistically. In order to obtain good system performance and improve spectral efficiency, PC is based on various network structures such as traditional CRNs, cellular CRNs, and multipleinput multipleoutput (MIMO) CRNs. has been studied in many works [7–9]. In [7], an adaptive PC scheme relying on partial CSI for an underlay CRN is studied to obtain a good tradeoff between the interference introduced by SUs on PUs and SU’s performance. In [8], for an overlay twoway cellular network, a spectrum sharing protocol is proposed for devicetodevice (D2D) communication to maximize the sum rate of both D2D and cellular communication. In [9], based on Euclidean projection, a distributed PC algorithm with QoS requirements is studied to minimize total power consumption of SUs under timevarying channel scenario. In [10], the authors extend the pricing concept to a multichannel MIMO CR scenario and propose two iterative PC and channel allocation algorithms.
Since there are many advantages of flexible spectrum scheduling of orthogonal frequency division multiplexing (OFDM) technology, OFDM has been widely introduced to CRNs [11–13]. In [11], for an OFDMbased multihop CRN, a crosslayer optimization design is proposed to address both aggregate utility maximization and energy consumption minimization. In [12], radio resource allocation in an underlay CRN based on OFDMA is studied to maximize the sum capacity of the secondary service and to find the optimal allocated power, subcarrier, and rate across all subcarriers and different SUs. In [13], the authors propose a robust ergodic resource allocation (ERA) scheme in the framework of an OFDMbased underlay heterogeneous network to maximize the average sum rate while guaranteeing macro network interference requirements with any desired high probability.
Obviously, the articles mentioned above are mainly based on the perfect spectrum sensing information (i.e., without considering spectrum sensing uncertainties). In real communications, due to user’s mobility and timevarying characteristics and fading characteristics of wireless channels, a spectrum detector cannot exactly detect the status of PUs in the spectrum sensing phase. Thus, it is necessary to take sensing uncertainties or the imperfect spectrum sensing information into account since inevitable estimation errors and uncertainties may produce harmful interference to PUs for their communications and make the received signaltointerferenceandnoise ratio (SINR) at SU receiver below the target requirements of SUs. Over the last decade, PC problem with the spectrum sensing uncertainties has been extensively studied for various network structures (e.g., traditional CRNs, OFDMbased CRNs, heterogeneous cellular networks, micro CRNs). Considering traditional CRNs under the spectrum sensing uncertainties, PC problem is studied in [14, 15]. In [14], a joint bandwidth and power allocation is proposed to minimize total power of SUs and guarantee their QoS requirements. In [15], resource allocation problem with the imperfect spectrum sensing is considered to maximize capacity of SU. Considering OFDMbased CRNs under the spectrum sensing uncertainties, PC problem is studied in [16, 17]. In [16], the authors investigate the energy efficient resource allocation strategy to maximize energy efficiency of CR system subject to total transmission power budget and each PU interference constraints. In [17], for an OFDMbased heterogeneous CRN including single network and multihoming network, the resource allocation problem with the imperfect spectrum sensing is solved to maximize system capacity and the joint subcarrier, and PC problem is formulated under total transmission power constraint, interference constraint, and QoS constraint. Considering Femtocell CRNs with the imperfect spectrum sensing in [18], PC in a twotier OFDMbased heterogeneous cellular network to maximize the sum throughput of Femtocell users (FUs) is provided. Considering CRNs with the imperfect spectrum sensing and one primary network (PN) or many micro CRNs in [19], a hybrid spectrum access strategy is proposed to maximize the capacity of the secondary link over the Rayleigh fading channel, which is different from the traditional underlay or the overlay strategy. However, research on PC in cognitive relay networks with the spectrum sensing uncertainties is quite few.

An OFDMbased cognitive relay network with multiple PUs, SUs, and relays is considered. The BER of the SUs with the spectrum sensing uncertainties is minimized under maximum transmit power constraints, SINR constraints, and interference constraints.

The uncertainties in the spectrum sensing and errors of the reporting channels are considered in order to adapt actual communication environment. The proposed algorithm conducts power allocation and update at secondary user transmitters and relay transmitters, respectively, to satisfy the requirements of device flexible adjustment.

The worstCSI PC algorithm is introduced to limit the total BER of SUs, which only needs to operate the algorithm in one link so that the complexity and convergence time of the algorithm are reduced.
The remainder of this paper is organized as follows. In Section 2, a system model and a spectrum sensing model are described. Section 3 introduces a cooperative spectrum sensing (CSS) scheme and formulates the interference model under the spectrum sensing uncertainties. Then, PC problem is formulated and our proposed algorithm is given in Section 4. Section 5 presents simulation results and performance analysis of the system. Finally, Section 6 provides conclusion of the paper.
2 System model
Important notation in the paper
Symbol  Specification 

\({P_{p}^{n}}\)  Transmit power of the pth PUT on the subcarrier n 
\(P_{l,1}^{n}\)  Transmit power of the lth SUT on the subcarrier n 
\(P_{l,2}^{n}\)  Transmit power of the lth relay on the subcarrier n 
\(h_{l,1}^{n}\)  Channel gain of the firsthop of the lth link on the subcarrier n 
\(h_{l,2}^{n}\)  Channel gain of the secondhop of the lth link on the subcarrier n 
\(h_{l,p,1}^{n}\)  Channel gain of the lth SUT to the pth PUR on the subcarrier n 
\(h_{l,p,2}^{n}\)  Channel gain of the lth relay to the pth PUR on the subcarrier n 
\(g_{p,l,1}^{n}\)  Channel gain of the pth PUT to the lth relay on the subcarrier n 
\(g_{p,l,2}^{n}\)  Channel gain of the pth PUT to the lth SUR on the subcarrier n 
\(z_{p,l}^{n}\)  Sensing channel gain of the pth PUT to the lth SUT on the subcarrier n 
3 Spectrum sensing process
3.1 Cooperative Spectrum Sensing (CSS)
where \(\hat {V}_{p}^{n}\) and \(\hat {O}_{p}^{n}\) denote the sensing result of the sensing node on the subcarrier n unoccupied and occupied by the pth PU, respectively.
where u is equal to f τ/N. \(\chi _{2u}^{2}\) follows a central chisquare distribution with 2u degrees of freedom, and \(\chi _{2u}^{2} ({2\gamma _{p,k}^{n}})\) follows a noncentral chisquare distribution with 2u degrees of freedom and a non centrality parameter \(2\gamma _{p,k}^{n}\) [4]. And \(\gamma _{p,k}^{n}\) is the instantaneous signalnoise ratio (SNR) of the received signal from the pth PU at the kth sensing node on the subcarrier n.
where E[·] denotes the expectation and P r(·) is the probability. \(\Gamma \left ({m,\tilde x} \right)\) is the incomplete gamma function given by \(\Gamma \left ({m,\tilde x} \right) = \int _{\tilde x}^{\infty } {{v^{m  1}}{e^{ v}}d} v\), and Γ(m) is the gamma function. \({P_{d,p,k}^{n}}\) and \({P_{fa,p,k}^{n}}\) denote the detection probability and the falsealarm probability. And \({P_{md,p,k}^{n}}\) denotes the probability of missdetection.

Each sensing node (i.e., L SUs and L relays) independently evaluates its own spectrum detection, then makes detection information (i.e., a binary decision on status of PU).

The binary decisions made by all sensing nodes are reported to an AP in the local area network (LAN) or networks.

AP fuses all detection information and makes global decision about the status of PU to determine whether PU is present or not.
3.2 SINR expressions (AF protocol)
where \({N_{l,1}^{n}}\) and \({N_{l,2}^{n}}\) denote the additive noise power at the lth relay and SUR.
3.3 Interference model
Four situations for CSS
Spectrum state  CSS result  Relative probability  CR power 

Occupied (\({O_{p}^{n}}\))  \(\hat {O}_{p}^{n}\)  \(P_{d}^{n}\)  0,0 
Occupied (\({O_{p}^{n}}\))  \(\hat {V}_{p}^{n}\)  \(P_{md}^{n} = 1  {P_{d}^{n}}\)  \(P_{l,1}^{n},P_{l,2}^{n} \) 
Vacant (\({V_{p}^{n}}\))  \(\hat {O}_{p}^{n}\)  \(P_{fa}^{n}\)  0,0 
Vacant (\({V_{p}^{n}}\))  \(\hat {V}_{p}^{n} \)  \(1  P_{fa}^{n}\)  \(P_{l,1}^{n},P_{l,2}^{n}\) 
where \({Pr}(O_{p}^{n})\) is a probability that the subcarrier n is occupied by the pth PU. \(P_{md}^{n}\) is a missdetection probability (i.e., \(Pr(\hat {V}_{p}^{n}{O_{p}^{n}})\)). \(I_{\text {SP}_{p}}\phantom {\dot {i}\!}\) and \(\phantom {\dot {i}\!}{I_{\text {RP}_{p}}}\) are the interference produced by all SU transmitters and all relay transmitters, and they must be limited by the IT constraint.
4 Proposed algorithm
where \(Q\left (\bar {x} \right) = \frac {1}{{\sqrt {2\pi } }}\int _{\bar x}^{\infty } {{e^{ \frac {{{w^{2}}}}{2}}}} dw\) is a Gaussian Qfunction, b=log2M, and M is the number of bits of the modulation symbols.
where [·]^{+}= max(0,·). d denotes the iteration number. β _{1}∼β _{6} are the small step sizes which satisfy β _{ q }>0, q={1,2,3,4,5,6}. Apparently, λ _{ l,1}(d+1), λ _{ l,2}(d+1), \(\lambda _{l,3}^{n}({d + 1})\), and \(\lambda _{l,4}^{n}({d + 1})\) are locally updated, whereas λ _{ p,5}(d+1) and λ _{ p,6}(d+1) are updated through cooperation. In addition, the Lagrange multipliers λ _{ p,5}(d+1) and λ _{ p,6}(d+1) in (50) and (51) can only be updated by obtaining the interference channels information (i.e., \(h_{l,p,1}^{n}\) and \(h_{l,p,2}^{n}\)) about other SUs and relays, respectively.
Finally, taking the optimal solutions \({P_{l,1}^{n}}{~}^{*}\) and \({P_{l,2}^{n}}{~}^{*}\) into (21) and (22), respectively, the optimal BER can be calculated.
Based on the above development, we get our algorithm reaching the optimum control power at SUT and relay for the optimization problem. And the specific power allocation algorithm can be given in Algorithm 1.
5 Simulation results
Maximum BER at SUR for different \(P_{md}^{n}\)
Modulation form  \(P_{md}^{n}=0.08\)  \(P_{md}^{n}=0.10\)  \(P_{md}^{n}=0.12\) 

BPSK  1.102e−5  1.898e−5  4.412e−5 
QPSK  9.401e−4  1.247e−3  1.936e−3 
16PSK  9.777e−2  1.010e−1  1.064e−1 
2QAM  4.264e−8  9.523e−8  3.309e−7 
4QAM  9.401e−4  1.247e−3  1.936e−3 
16QAM  6.618e−2  6.610e−2  7.367e−2 
Figure 2 shows the convergence of SINRs at relay and SUR of the selected link. And the equivalent SINR of the selected link also quickly converges to a stable point. From Fig. 2, we can see that the SINRs of the link increase first with the increase of iteration number, then they converge to the equilibrium points that satisfy the basic SINR requirements of each hop without outage probability all the time. It indicates that our proposed algorithm can provide SU normal communication. Based on the normal communication of SUs, the minimization of BER of the system is meaningful.
To evaluate the effectiveness and reliability of our proposed algorithm on the BER performance of the SU, we demonstrate the convergence characteristic of the BER in Fig. 3 a and the characteristic curve of the BER versus the equivalent SINR of the selected link in Fig. 3 b. Combining Fig. 3 a with Fig. 3 b, we find that our algorithm can effectively reduce the maximum BER of the system through increasing the SINR of each hop while keeping the interference power at PUR belows the IT level.
Figures 4 and 5 give the comparison of the BER performance of SU and the interference power at PUR between the proposed PC algorithm and the PC algorithm without sensing errors. Figure 4 shows the maximum BER performance of the selected SU link. The BER of proposed algorithm for the given IT level I _{ p,th}=0.01 mW is higher than that of the PC algorithm without sensing errors, which provides the protection of PU when SUs share the spectrum opportunistically. From Fig. 4, we can see that the maximum BER of the proposed algorithm for both MPSK and MQAM modulation quickly converges to the stable point, and the optimization goal is achieved by minimizing the maximum BER of the worstCSI channel to limit the total BER of the SUs. Briefly, the purpose of minimizing the BER of the system is obtained by adjusting the transmit power of SUT and relay transmitter, which improves the performance and ensures the QoS of SUs.
From Fig. 5, we can see that the PC algorithm under the imperfect spectrum sensing can guarantee the interference power at PUR always below the IT level, whereas the PC algorithm without sensing errors fail to keep the actual received interference power at PUR in the allowable region. From Figs. 4 and 5, we conclude that the proposed algorithm can provide well protection for PU at the cost of little BER increases.
Figure 6 shows the characteristics of the interference to PU produced by secondary system for different maximum transmit power budget \(P_{l}^{\text {max} }\) (i.e., \(P_{l,1}^{\text {max} }\)=\(P_{l,2}^{\text {max} }\)=\(P_{l}^{\text {max} }\)) with and without sensing errors in PC algorithm. From Fig. 6, we know that the interference power at PUR of the algorithm without sensing errors is higher than that of our proposed algorithm and exceeds the IT level.
In Fig. 7, we present the maximum BER versus the IT level from I _{ p,th}=−20 dBm to I _{ p,th}=−5 dBm of our proposed algorithm for different \(P_{md}^{n}\) and show the maximum BER performance against the interference threshold I _{ p,th} and the missdetection probability \(P_{md}^{n}\) for MPSK (M=2) and MQAM (M=2) modulation. For \(P_{md}^{n}\)=0.1, the maximum BER of the SUs decreases first with the increasing interference power constraint, then keeps flat because of the maximum transmit power constraints. We find that the BER performance of our proposed algorithm under different \(P_{md}^{n}\) is the same when the interference power constraint is large, for example, when I _{ p,th} is larger than −12 dBm. The BER performance for \(P_{md}^{n}=0.08\) is the best under three modulations when the IT level is low. Since larger \(P_{md}^{n}\) stands for more harmful interference to PU, less transmit power is allocated to provide the protection to PUs for their communications.
Table 3 shows the maximum BER versus different missdetection probabilities \(P_{md}^{n}\) for I _{ p,th}=0.01 mW, the transmission data for MPSK (M=2,4, and 16) and MQAM (M=2, 4, and 16) modulation. From Table 3, we find that the spectrum sensing requirement is improved from \(P_{md}^{n}=0.12\) to \(P_{md}^{n}=0.08\) for the given modulation, and the maximum BER of the system decreases accordingly. This implies that, with the improved spectrum sensing requirement, a spectrum hole is accurately detected, thus less interference occurs between the primary network and the secondary network, resulting in decreased BER for the secondary transmission. Furthermore, we also find that the maximum BER of the system increases with the increase of the number of bits of modulation symbols. Since the decision region of the corresponding received signal decreases with the increase of M, when the signal suffers to the interference and the damage caused by noise, the error probability of the received signal will be bigger.
Figure 8 shows the maximum BER performance of our proposed algorithm against I _{ p,th} under different maximum transmit power budgets \(P_{l}^{\text {max} }\). In Fig. 8, for the given transmit power budget \(P_{l}^{\text {max} }=1.5\) mW, the maximum BER decreases first then keeps flat when I _{ p,th} increases. We find that the BER performance of our proposed PC algorithm under different maximum transmit power budgets is almost the same when the interference power constraint is low, and the BER performance for \(P_{l}^{\text {max} }=1.6\) mW is significant when the interference power constraint is large, for example, larger than −12 dBm. In fact, from another perspective, the interference power constraints represent the distance, with the increasing distance between the SU and the PU, more transmit power is allocated to achieve a lower BER.
In order to further specify the effect of the sensing uncertainties on the PU, we demonstrate the characteristic of the interference to the PU produced by a secondary system in Fig. 9. And the characteristics of the interference is versus the IT level from I _{ p,th}=−20 dBm to I _{ p,th}=−5 dBm of our proposed algorithm for different \(P_{md}^{n}\). From Fig. 9, we find that the interference power at PUR of our proposed algorithm increases with the increasing missdetection probability from \(P_{md}^{n}=0.06\) to \(P_{md}^{n}=0.12\). For the given missdetection probability \(P_{md}^{n}=0.1\), the interference power at PUR of the proposed algorithm increases first then keeps constant when I _{ p,th} increases because of the maximum transmit power constraints. As emphasized, the larger the missdetection probability \(P_{md}^{n}\) is, the more the concurrent transmission of the PUs and SUs and the greater the harmful interference to PU. In conclusion, the sensing uncertainties should be considered to adapt actual communication scenarios and provide better protection for the communication of the PU.
6 Conclusions
This paper studies the PC problem in a cognitive relay network under the spectrum sensing uncertainties. We propose a PC algorithm under maximum transmit power constraints, SINR constraints and interference constraints to minimize the total BER for all SUs according to the actual situations. The worstCSI PC algorithm and minmax criteria formulation are applied to the optimization problem converted into the maxmin equivalent SINR problem solved by the Lagrangian duality theory. Compared with the PC algorithm without the spectrum sensing uncertainties, simulation results show the advantages of our proposed PC algorithm which can well protect the communication of the PU though there is a little BER increase of the secondary system at the expense. We also find that the BER of the secondary system decreases as the probability of missdetection decreases in our proposed algorithm. In our future research, the PC optimization problem with the introduction of more complicated channels in the underlay cognitive relay networks will be conducted.
Declarations
Acknowledgements
The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. The work of this paper is supported by the National Natural Science Foundation of China under grant no. 61571209.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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