Multiplelevel power allocation strategy for secondary users in cognitive radio networks
 Zhong Chen^{1, 2},
 Feifei Gao^{2}Email author,
 Zhengwei Zhang^{1},
 James CF Li^{3} and
 Ming Lei^{3}
https://doi.org/10.1186/16876180201451
© Chen et al.; licensee Springer. 2014
Received: 15 February 2014
Accepted: 24 March 2014
Published: 14 April 2014
Abstract
In this paper, we propose a new multiplelevel power allocation strategy for the secondary user (SU) in cognitive radio (CR) networks. Different from the conventional strategies, where SU either stays silent or transmit with a constant/binary power depending on the busy/idle status of the primary user (PU), the proposed strategy allows SU to choose different power levels according to a carefully designed function of the receiving energy. The way of the power level selection at SU side is optimized to maximize the achievable rate of SU under the constraints of average transmit power at SU and average interference temperature to PU. Simulation results demonstrate that the proposed strategy can significantly improve the throughput of SU compared to the conventional strategies.
Keywords
Introduction
Cognitive radio (CR) has recently emerged as a promising technology to improve spectrum utilization and to solve the spectrum scarcity problem [1]. Consequently, spectrum sensing and power allocation play as two key functionalities of a CR system, which involves monitoring the spectrum usage and accessing the primary band under given interference constraints.
The earliest spectrum access approach is the opportunistic spectrum access where secondary user (SU) can only access the primary band when it is detected to be idle [2]. The second approach is the underlay where SU is allowed to transmit beneath the primary user (PU) signal, while sensing is not needed as long as the quality of service (QoS) of PU is protected [3]. The recent approach, sensingbased spectrum sharing, performs spectrum sensing to determine the status of PU and then accesses the primary band with a high transmit power if PU is claimed to be absent, or with a low power otherwise [4, 5]. These three approaches adopt either constant or binary power allocation at SU which is too hard’ and limits the performance of SU.
In order to make the power allocation softer,’ we propose a multiplelevel power allocation strategy for SU, where the power level used at SU varies based on its receiving energy during the sensing period. It can be easily known that the conventional constant or binary power allocations are special cases of the proposed strategy. The whole strategy is composed of two phases: (i) sensing phase, where the receiving energy is accumulated and the transmit power of SU is decided; (ii) transmission phase, where SU sends its own data with the corresponding power level.
Under the constraints of the average transmit power at SU and the average interference temperature to PU, the sensing duration, energy threshold, and power levels are optimized to maximize the average achievable rate at SU.
System model
One data frame of CR is divided into the sensing slot with duration τ and the transmission slot with duration T  τ. During the sensing slot, ST listens to the primary channel and obtains its accumulated energy. In the conventional schemes, spectrum sensing is performed in this slot and the decisions on the status (active/idle) of the channels are made. When transmitting, ST accesses the primary band with the optimal power in order to maximize the throughput while at the same time keeping the interference to PR.
where H_{0} and H_{1} denote the hypothesis that PT is absent and present, respectively; ϕ is the instant channel phase that is unknown; n_{ j }is the additive noise which is assumed to follow a circularly symmetric complex Gaussian distribution with zero mean and variance N_{0}, i.e., ${n}_{j}\backsim {\mathcal{N}}_{c}(0,{N}_{0})$; s_{ j }is the j th symbol transmitted from PT. For the purpose of computing the achievable channel rate, the transmitted symbols s_{ j }from the Gaussian constellation are typically assumed [4, 5], i.e., ${s}_{j}\backsim {\mathcal{N}}_{c}(0,{P}_{p})$, where P_{ p }is the symbol power. Without loss of generality, we assume that s_{ j }and n_{ j }are independent of each other.
where Γ (.) is the gamma function defined as $\Gamma \left(x\right)=\underset{0}{\overset{+\infty}{\int}}{t}^{x1}{e}^{t}\mathit{\text{dt}}$. Indeed, f (xH_{0}) and f (xH_{1}) are both variants of the Gamma distribution.
In the conventional CR, ST compares x with a threshold ρ and makes decision according to $x\underset{{H}_{0}}{\overset{{H}_{1}}{\gtrless}}\rho $. Specifically,

In opportunistic spectrum access approach, ST can only access the primary band when x < ρ (it means H_{0}) [7, 8].

In sensingbased spectrum sharing, if x<ρ, ST transmits with one higher power and otherwise with a lower power (binary power) [9].

In underly approach, ST transmits with a constant power for all x according to the interference constraint at PU (constant power). No sensing time slot is needed.
Proposed multiplelevel power allocation strategy
It can be easily realized that the conventional constant or binary power of SU does not fully exploit the capability of the coexisting transmission. Motivated by this, we propose a multiplelevel power allocation strategy for SU to improve the average achievable rate.
Strategy of multiplelevel power allocation
where I_{ A }is the indicating function that I_{ A }= 1 if A is true and I_{ A }= 0 otherwise. Note that the conventional power allocation rules are special cases when M = 1 or 2.
The term $\frac{T\tau}{T}$ means that the power constraints occur in the transmission slot. Note that (11) is nonlinear and nonconvex over τ. Hence, following [4, 10], we will simply use the onedimensional search within the interval [0,T] to find the optimal τ, whose complexity is generally acceptable as known from [11, 12].
The algorithm
The Lloyd’s algorithm is employed here to solve problem (11), where the local convergence has been proved for some cases in onedimensional space. But in general, there is no guarantee that Lloyd’s algorithm will converge to the global optimal [13]. Starting from a feasible solution as the initial value, e.g., subspaces {ℜ_{ i }} satisfying ${p}_{i,0}=\frac{1}{M}$, we repeat the following two steps until the convergence: step 1  determine the power allocations {P_{ i }} given the subspaces {ℜ_{ i }}; step 2  determine the subspaces {ℜ_{ i }} given power allocations {P_{ i }}.
Subspaces design
The following lemma is instrumental to deriving the optimal subspaces {ℜ_{ i }}.
Lemma 1.
For x_{1} < x_{2} < x_{3}, if x_{1} ∈ ℜ_{ i }, x_{2} ∈ ℜ_{ k }and i ≠ k, then x_{3} ∉ ℜ_{ i }must hold.
Proof.
From x_{1} ∈ ℜ_{ i }, x_{2} ∈ ℜ_{ k }and (14), we know that S_{i,k}(x_{1}) > 0 and S_{i,k}(x_{2}) < 0. In (14), the sign of S_{i,k}(x) is decided by $\frac{{a}_{i,k}}{{({N}_{0}+{g}_{2}{P}_{p})}^{\tau {f}_{s}}}{e}^{\frac{x{g}_{2}{P}_{p}}{{N}_{0}({N}_{0}+{g}_{2}{P}_{p})}}+\frac{{b}_{i,k}}{{N}_{0}^{\tau {f}_{s}}}$ which is a strictly monotonic function. Thus, for any x_{3} > x_{2}, there are S_{i,k}(x_{3}) < 0 and x_{3} ∉ ℜ_{ i }.
Proposition 1.
ℜ_{ i },i = 1,…,M are continuous intervals and satisfy $\bigcup _{i=1,\dots ,M}{\Re}_{i}=\phantom{\rule{0.3em}{0ex}}[\phantom{\rule{0.3em}{0ex}}0,\infty ]$.
Proof.
The proof can be easily obtained from the law of contradiction. Assuming that ℜ_{ i }has more than two noncontinuous intervals, it is contradicted with Lemma 1. This proposition is instrumental to obtaining the explicit formulation of ℜ_{ i }.
Algorithm 1 Subspaces design for x given {P _{ i } }
Power allocation
Proposition 2.
The power allocation functions P_{ i }are nonincreasing over i.
Proof.
Similarly, we get that △_{ i }is a decreasing function over i. Thus, from (20), we can conclude that P_{ i } is a nonincreasing function with respect to i.
Remark 1.
. Proposition 2 shows that at smaller x, the probability of PU being busy is smaller, so SU can use higher transmit power to better exploit the primary band. On the other hand, at the larger x, lower transmit power should be used to prevent harmful interference to PU. Thus, the proposed multiplelevel power allocation strategy can also be defined on the probability of PU being busy.
while ${\stackrel{\u0304}{P}}_{i}$ is the optimal power allocation for fixed λ and μ[16]. Finally, we summarize the algorithm that computes the sensing time and multiplelevel power allocations in Algorithm 2.
Algorithm 2 Sensing time and multiplelevel power allocations
Remark 2.
All computations are performed offline and the resulting power control rule is stored in a lookup table for realtime implementation. Thus, the computational complexity is not significant.
Simulation results
In this section, simulations are performed to evaluate the proposed multiplelevel power allocation strategy in a CR system where the system parameters similar to the references [4, 5, 10] are used. The frame duration is taken as T = 100 ms and the sampling frequency f_{ s }= 1 MHz. The target detection probability is set as 0.9 in the opportunistic spectrum access scheme. We set g_{1} = N_{0} = 0 dB, q_{0} = 0.7, $\u012a={P}_{p}=0.5$, $\stackrel{\u0304}{P}=10$ dB, γ = h = g_{2}=0 dB, unless otherwise mentioned.
Conclusions
In this paper, we propose a novel multiplelevel power allocation strategy for SU in a CR system. The receiving signal energy from PU is divided into different categories and SU transmits with different power for each category. The power levels at SU are obtained by maximizing the average achievable rate under the constraints of the average transmit power at SU and the average interference temperature to PU. Compared with the conventional power allocation strategies, the proposed scheme offers significant rate improvement for SU. Furthermore, we are working on extending the idea to the cases of multiple SUs and statistic channel information and on how to decrease the computational complexity.
Endnote
^{a} Namely, we have multiple thresholds to categorize x rather than only using ρ as did in convention.
Declarations
Acknowledgements
This work was supported in part by the National Basic Research Program of China (973 Program) under Grant 2013CB336600 and Grant 2012CB316102, by the Beijing Natural Science Foundation under Grant 4131003, by the National Natural Science Foundation of China under Grant 61201187, by the Importation and Development of HighCaliber Talents Project of Beijing Municipal Institutions under Grant YETP0110; by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, by the Tsinghua University Initiative Scientific Research Program under Grant 20121088074, and by NEC Research Fund.
Authors’ Affiliations
References
 Q Wu: Spatialtemporal opportunity detection for spectrumheterogeneous cognitive radio networks: twodimensional sensing. IEEE Trans. Wirel. Commun 2013, 12: 516526.View ArticleGoogle Scholar
 S Stotas: On the throughput and spectrum sensing enhancement of opportunistic spectrum access cognitive radio networks. IEEE Trans. Wirel. Commun 2012, 11: 97107.View ArticleGoogle Scholar
 XW Gong: Optimal bandwidth and power allocation for sum ergodic capacity under fading channels in cognitive radio networks. IEEE Trans. Signal Process 2011, 59: 18141826.MathSciNetView ArticleGoogle Scholar
 RF Fan: Joint optimal cooperative sensing and resource allocation in multichannel cognitive radio networks. IEEE Trans. Veh. Technol 2011, 60: 722729.View ArticleGoogle Scholar
 X Kang: Sensingbased spectrum sharing in cognitive radio networks. IEEE Trans. Veh. Technol 2009, 58: 46494654.View ArticleGoogle Scholar
 J Ma: Soft combination and detection for cooperative spectrum sensing in cognitive radio networks. IEEE Trans. Wireless Commun 2008, 7: 45024507.View ArticleGoogle Scholar
 GR Ding: Kernelbased learning for statistical signal processing in cognitive radio networkstheoretical foundations, example applications, and future directions. IEEE Signal Process. Mag 2013, 30: 126136.View ArticleGoogle Scholar
 GR Ding: Spectrum sensing in opportunityheterogeneous cognitive sensor networks: how to cooperate? IEEE Sensors J 2013, 13: 42474255.View ArticleGoogle Scholar
 S Stotas: Optimal sensing time and power allocation in multiband cognitive radio networks. IEEE Trans. Commun 2011, 59: 226235.View ArticleGoogle Scholar
 YY Pei: How much time is needed for wideband spectrum sensing. IEEE Trans. Wirel. Commun 2009, 8: 54665471.View ArticleGoogle Scholar
 RO Schmidt: A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation. Dissertation, Stanford University, 1981Google Scholar
 H Liu: A highefficiency carrier estimator for OFDM communications. IEEE Commun. Lett 1998, 2: 104106.View ArticleGoogle Scholar
 SP Lloyd: Leastsquare quantization in PCM. IEEE Trans. Inform. Theory 1982, IT28: 129137.View ArticleMATHGoogle Scholar
 V Lau: On the design of MIMO blockfading channels with feedbacklink capacity constraint. IEEE Trans. Commun 2004, 52: 6270. 10.1109/TCOMM.2003.822171View ArticleGoogle Scholar
 S Body: Convex Optimization. (Cambridge University, Cambridge, 2005)Google Scholar
 DP Bertsekas: Convex Analysis and Optimization. (Athena Scientific, Massachusetts, 2003)MATHGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.