This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
Power Efficiency Maximization in Cognitive Radio Networks Deah J. Kadhim, Shimin Gong, Wenfang Xia, Wei Liu, Wenqing Cheng Dept. of Electronics and Information Engineering, Huazhong University of Science and Technology,Wuhan, P.R. China E-mail:
[email protected], deya
[email protected] Abstract— Cognitive radio technology is used to improve spectrum efficiency by having the cognitive radios act as secondary users to access primary frequency bands when they are not currently being used. In general conditions, cognitive secondary users are mobile nodes powered by battery and consuming power is one of the most important problem that facing cognitive networks; therefore, the power consumption is considered as a main constraint. In this paper, we study the performance of cognitive radio networks considering the sensing parameters as well as power constraint. The power constraint is integrated into the objective function named power efficiency which is a combination of the main system parameters of the cognitive network. We prove the existence of optimal combination of parameters such that the power efficiency is maximized. Then we reformulate the objective function to incorporate the throughput. According to different constraints or degree of significance, we may put proper weight to each term so that we could obtain more preferable combination of parameters. Computer simulations have given the optimal solution curve for different weights. We can draw the conclusion that if we put more emphasis on power efficiency, the transmit power is a more critical parameter, however if throughput is more important, the effect of sensing time is significant.
I. Introduction The recent boom in wireless technologies has led to an increasing demand in terms of spectrum resources. However, numerous reports indicate that the spectrum usage experiences significant fluctuations [12]. Often, the unlicensed bands experience heavy spectrum utilization while licensed bands experience low utilization. An example is the TV band ranging from 54MHz to 862MHz. To alleviate the upcoming pressure of high spectrum demands and low utilization, the Federal Communications Commission (FCC) has been investigating new ways to manage RF resources for such a precious resource. Within this setting, the FCC has recently recommended that significantly greater spectral efficiency could be realized by considering cognitive radio [1], [2]. In such scheme, it defines primary users who already posse license to use a particular frequency and the secondary users who could opportunistically access the currently unused frequency bands. In this case, the interference caused by secondary users is therefore based on the detection performance of primary users and adaptive transmission over a wide bandwidth. Some fundamental issues are described in [3], [7]. This work was supported in part by the National Natural Science Foundation of China through the grant 60602029 and 60772088, the Foundation of Hubei Provincial Key Laboratory of Smart Internet Technology under Grant No.HSIT200605 and also supported by the Chenguang Project for Youth of Wuhan City under Grant No. 200750731261.
Cognitive radio systems offer the opportunity to improve spectrum utilization by detecting unoccupied spectrum bands and adapting the transmission to those bands while avoiding the interference to primary users. This novel approach to spectrum access is challenged by the balance between the conflicting goals of minimizing the interference to the primary users and maximizing the performance of the secondary users, which corresponding to minimize the miss detection probability and false alarm probability respectively. Cooperative sensing algorithms [8], [14] are devised to improve the detection performance. Hard combination algorithm was explained in [8] and better soft combination algorithms were proposed in [14]. In [4] and [5], optimization method was introduced to cooperative sensing. The optimization based soft combination algorithm in [4] was proved much better than traditional EGC and MRC algorithms. However, they focus on the probability of detection and false alarm while overlook the time consumption of the sensing process. Work in [13] focus on adaptive power control algorithm based on the reliability of the sensed information. [9], [10] turn their focus on sensing time and scheduling schemes. Paper [10] describes the relationship among probability of detection, sensing time and probability of false alarm, and finds the optimal sensing time to maximize the secondary throughput under certain miss detection probability. However, they didn’t consider the energy constraint in practical cognitive networks. In this paper, we focus on the sensing time consumption and energy constraint of the cognitive radio, which is mobile unit generally powered by battery. We define the power efficiency which is related to sensing time and transmit power of the secondary user. Using energy detector, we prove the existence of such optimal sensing time and transmit power that reach the maximum power efficiency. This paper is organized as follows. In section II, we describe the channel sensing model and energy detector. Section III, gives the details description of our performance analysis. Section IV, provides our computer simulation results. The conclusions are drawn in section V. II. System Model Figure 1 plot our cognitive model, which is the typical Wireless Regional Area Network (WRAN) structure [11]. Similar to the infrastructured 802.11 network, the cognitive network is central controlled by the secondary base-station. All the cognitive radios compete to access the available channel, however, just one transmission is permitted at one time. We
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
Cover range of PS
Energy detector is the most popular channel sensing scheme. The test statistic for energy detector is given by:
PS
PS:Primary Station
Cover range of SS
PU: P rimary User SS:Secondary Station PU
Cognitive Model as WRAN Structure
further consider that all of the cognitive radios are battery powered mobile units. Such energy constraint thus drive us to effectively use every unit of energy. We also assume our system working in a slotted mode shown in Figure 2. The frame length of primary user is divided into sub-slots. In any sub-slot, the secondary user chooses a part of time to sensing and the rest to transmit. frame length
τ
T −τ
T Fig. 2.
Slotted Frame Structure.
In the following part, we first present the general model for channel sensing, then review the energy detection scheme and analyze the relation between the probability of detection and probability of false alarm through the time-bandwidth product N. A. General Detection Model We suppose that the secondary users must sense the channel before transmitting through time domain sampling and the sampling frequency is f s , thus the binary hypothesis test for spectrum sensing at the k time instant formulated as follows: H0 : H1 :
x(k) = n(k) x(k) = n(k) + hs(k)
u=
N−1 1 |x(k)|2 N k=0
(2)
According to the central limit theorem, when the number of samples N is large enough, the test statistics u can be approximated by a Gaussian distribution with mean and variance as follows: σ2 H0 E(u) = (3) (1 + γ)σ2 H1
SS
SU
Fig. 1.
B. Energy Detector
(1)
Where s(k) denotes the signal transmitted by the primary user and x(k) is the received signal by the secondary user. The signal s(k) is distorted by the channel gain h, which is assumed to be constant during the detection interval, and is further corrupted by the channel noise n(k). Without loss of generality, s(k) and n(k) are assumed to be independent of each other. In this paper, we consider the case: n(k) is circularly symmetric complex Gaussian(CSCG) noise with zero mean and variance σ2 and s(k) is complex PSK modulated signal with zero mean and variance σ2s .
⎧ ⎪ ⎪ ⎨ Var(u) = ⎪ ⎪ ⎩
σ4 N (1+2γ)σ4 N
H0 H1
(4)
Now the decision rule at each secondary user is decided by (3) and (4) where λ is the corresponding decision threshold and σ2 γ = σ2s is the received S NR of the primary user. Therefore, the secondary user will have the following false alarm and detection probability: λ − E(u|H0 ) P f (λ) = Q √ (5) Var(u|H0 ) λ − E(u|H1 ) Pd (λ) = Q √ (6) Var(u|H1 ) where Q(.) is the complementary cumulative distribution function (CCDF), which calculates the tail probability of a zero mean unit variance Gaussian variable, i.e., 1 Q(x) = √ 2π
+∞ t2 exp(− ) dt 2
(7)
x
According to (3) and (4), we reformulate equation (8) and (9), λ √ P f (λ) = Q − 1 N (8) σ2 ⎛ ⎞ ⎜⎜⎜ λ N ⎟⎟⎟⎟ ⎜ ⎟⎟ Pd (λ) = Q ⎜⎜⎝ 2 − γ − 1 (9) 2γ + 1 ⎠ σ where N is the time bandwidth product, N = f s τ and τ is the sensing time, f s is the sampling frequency. Combine (10), (11) and eliminate the decision threshold λ, we get the relationship among three sensing parameters: P f ,Pd and τ: P f = Q 2γ + 1Q−1 (Pd ) + f s τγ (10) ⎛ ⎞ ⎟⎟ ⎜⎜⎜ 1 −1 Pd = Q ⎜⎜⎝ Q (P f ) − f s τγ ⎟⎟⎟⎠ 2γ + 1
(11)
If we set a value to miss detection probability as Pm = 1 − Pd , then we establish the relationship between sensing time τ and P f , and vice versa.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
III. Power efficiency of Cognitive Radio In the previous section, the relation between probability of detection and probability of false alarm has been established. In this section, we will study the performance metric through the formulation of power efficiency which is a combination of the main system parameters of the cognitive network, and then we analysis the attainability of of an optimal combination of parameters that maximize our objective function. A. Problem Formulation Mobile communications devices and sensors generally derive their power from batteries. A key design consideration in such systems is to reduce the requirement for recharging or replacement of the batteries by reducing the power consumption. This is especially true for sensors deployed in locations where access is not easy, such as in battlefields or on tall buildings. CR-based optimal power transmission can reduce the total transmitted power level without significant performance degradation. Thus in a flexible spectral shaping CR system, a given frequency sub-band that experiences signal loss due to fading or interference can be switched off, so that no power is injected and wasted in that unfriendly region of the spectrum. The overall effect would be an increase to the power efficiency of the system. The power efficiency η can be defined as follows, T hroughput η= (12) Power Consumption
the channel. In this case, we can eliminate the interference between secondary users. Then the transmission efficiency can be formulated as follows, L −0.5 N pt oise f (δ) = 1 − e (17) Where pt is the transmit power and Noise represent noise power. We assume the probability of H0 and H1 is P(H0 ) and P(H1 ) (P(H0 ) + P(H1 ) = 1) respectively. Then the total throughput in a time slot is as follows, U(pt , τ) = (T −τ)[P(H0 )(1−P f )R f (δ0 )+P(H1 )Pm R f (δ1 )] (18) The power consumption of the total time slot is also related to the sensing time τ and transmit power pt . The sensing and transmitting stages will both consume energy. More sensing time, more sensing energy consumption while maybe less transmitting energy consumption because we have less time to transmit. Specifically, in sensing stage of duration τ with constant power consumption p0 , the energy consumption is p0 τ; then in the transmitting stage of duration T − τ with transmitting power pt , the total energy consumption would be Pe f f (T − τ), where Pe f f is the equivalent transmitting power when considering the probability of false alarm probability and miss detection probability. Then the total energy consumption can be formulated as follows, Power (pt , τ) = p0 τ + (T − τ)[P(H0 )(1 − P f ) + P(H1 )Pm ]pt (19)
The throughput is comprised of two parts: if there is no primary user and the secondary user correctly detects the absence of primary user, the secondary transmitting will take place. however if the primary user is transmitting while the secondary user miss detects the presence, the congest transmitting will take place. In the former scenario, the secondary user will experience relative better channel condition, while in the last scenario, the secondary and primary users will affect each other so that the data rate will be slow. If the cognitive device prefer to spend more time on sensing, the state of primary user will be more clear and then the device will make a better decision on transmit or not. The following equations mean the throughput benefit in different cases. U0 H0 U= (13) U1 H1 0 Pf U0 = (14) R f (δ0 ) 1 − Pf R f (δ1 ) Pm U1 = (15) 0 1 − Pm
Therefore, the predefined power efficiency η(pt , τ) = is as follows,
Where f (δ) is the transmission efficiency and R is the transmission rate., which is related to the S NR of receiver [6]. L f (δ) = 1 − e(−0.5δ) (16)
where α(0 ≤ α ≤ 1) is the emphasis on power efficiency and k is used for unit conversion.
where δ is the S NR and L is the packet length of the secondary user, In our system model, we consider a center control node who schedules the access to the primary channels. Therefore, at certain time slot there is only one secondary user accessing
In part III-A, we derive the formation of the two dimensional objective function. In this part, we will prove the existence of optimal combination of performance parameters. In equation (17), we give the expression of transmission efficiency.
U(pt ,τ) Power (pt ,τ)
(T − τ)[P(H0 )(1 − P f )R f (δ0 ) + P(H1 )Pm R f (δ1 )] p0 τ + (T − τ)[P(H0 )(1 − P f ) + P(H1 )Pm ]pt (20) In this paper, we formulate the objective function as power efficiency under the constraint of miss detection probability. η(pt , τ) =
max s.t
η(pt , τ) = Pm ≤ Pm
U(pt ,τ) Power (pt ,τ)
(21)
where Pm is predefined miss detection probability, which describes the possible interference to the primary user caused by the channel access of secondary user. Also we can consider the balance between throughput and power efficiency and define the following objective utility function. We put weights on different terms according to different emphasis on power efficiency and throughput. Ψ(pt , τ) = αη(pt , τ) + (1 − α)kU(pt , τ)
(22)
B. Performance Analysis
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
Obviously we have, 1
lim f (δ) = 0
pt →0
0.9
=0
thus, lim η(pt , τ) = 0
pt →0
(23)
and lim η(pt , τ)
pt →∞
= = =
P(H0 )(1 − P f )R f (δ0 ) + P(H1 )Pm R f (δ1 ) pt →∞ [P(H0 )(1 − P f ) + P(H1 )Pm ]pt P(H0 )(1 − P f ) + P(H1 )Pm R f (δ0 ) lim pt →∞ P(H0 )(1 − P f ) + P(H1 )Pm pt R f (δ0 ) lim m pt →∞ pt 0 (24) lim
Since η(pt , τ) is a continuous positive function, from equation (23) and (24), we can derive that there exists certain value for pt (0 < pt < ∞) with τ fixed such that, ∂η(pt , τ) | pt = 0 ∂pt
(25)
In the following part, we derive the existence of optimal sensing time. Before we work on, we use the following substitutes: A B m n
= = = =
P(H0 )R f (δ0 ) P(H1 )Pm R f (δ1 ) P(H0 )pt P(H1 )Pm pt (26)
then, the reduced form of power efficiency is as follows, η(pt , τ) =
(T − τ)[A(1 − P f ) + B] p0 τ + (T − τ)[m(1 − P f ) + n]
(27)
lim P f (τ) = −∞
(29)
lim P f (τ) = Pd 1
(30)
τ→0 τ→0
lim P f (τ) = 0
(31)
lim P f (τ) = 0
(32)
τ→T τ→T
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
1
Sensing Time(Ts) / Slot length(T) Fig. 3.
Probability of false and Sensing time relation.
with respect to τ,
2 2 ∂η −AT P f [m(1 − P f ) + n] + T mP f [A(1 − P f ) + B] ∂τ {T [m(1 − P f ) + n]}2 (33) Assume s = A(1 − P f ) + B, K = m(1 − P f ) + n and refer to equation (29),(30) we get the limitation of equation (33),
2 ∂η T P f (sm − AK) = lim (34) τ→0 ∂τ (T K)2 Refer again to the former substitution equation (26), we get the following result,
sm − AK = mA(1 − P f ) + Bm − Am(1 − P f ) − An = Bm − An = P(H1 )P(H0 )Pm ERpt [ f (δ1 ) − f (δ0 )] < 0 Considering the equation (29) and (34), obviously,
In the next steps, we would like to find the derivative of equation(27). We first deduct some useful conclusions before going on. According to equation(10) (Figure 3 show the graph of this equation), we obtain the following conclusions, √ γ f s − (μ+ fs τγ)2 2 P f (τ) = − √ e (28) 2π τ Obviously,
Probability of false alarm(Pf)
lim f (δ) pt →∞ pt
therefore, we get the simplified partial derivative of η(pt , τ)
∂η >0 (35) τ→0 ∂τ In the other aspect, from equation (31), (32), we derive that, lim
lim
τ→T
(A + B)p0 T ∂η =−
