Distributed Power Control for Cognitive Radio Networks, Based on ...

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

Distributed Power Control for Cognitive Radio Networks, based on Incumbent Outage Information Olasunkanmi Durowoju, Kamran Arshad and Klaus Moessner Centre for Communication Systems Research University of Surrey, United Kingdom E-mail :{O.Durowoju, K.Arshad, K.Moessner}@surrey.ac.uk Abstract—The interference management problem in cognitive radio networks is in this paper, tackled from the transmitter power control perspective so that transmissions by cognitive radios does not violate the interference level thresholds at incumbent users. We modify distributed power control algorithms to suit the cognitive radio framework by exploiting spectrum use and radio environment knowledge for incumbent user location estimation in worst-case scenario. Most literature employs worst-case analysis to guarantee robustness thereby trading off optimality. We therefore, propose a stochastic approach which allows the cognitive radio network, access the extra capacity based on incumbent user outage information with guarantees on interference protection to the incumbent user at all times. This paper therefore shows that the proposed distributed power control strategy is robust with the benefit of increased spectral efficiency compared to its worst case counterpart.

I.

INTRODUCTION

Much literature advocates cognitive radio technology has a viable solution to the impending spectrum underutilization problem [1] leading to significant spectrum gains. However, with such spectrum gains comes the risk of increased interference to the licensed user of the spectrum called the Incumbent user (IU). Therefore ways of appropriate interference mitigation/avoidance techniques to IUs becomes exigent. In this paper we focus on Transmitter Power Control (TPC) for cognitive radios (CRs) as a way of curtailing excessive interference to IUs due to spatial co-existence while maintaining a reasonable quality of service (QoS) within the cognitive radio network (CRN). TPC [2-4] is an age long technique proven viable for interference mitigation in conventional cellular networks. Imperative is therefore the need to modify some of these algorithms to suit the cognitive radio framework [5-7]. Conventional TPC algorithm was first adapted to the CR environment in [5], where a sensor in proxy of the IU reports interference violations to the CRN. Such feedback reporting channel techniques are prone to inherent failures and expose the IUs to transient interference degradations. This anomaly was corrected in [6], where an autonomous power control (PC) algorithm was formulated with the ability of maintaining the IU interference environment unperturbed at all times given stringent interference conditions. Spectrum sensing based prototypes for interference mitigation in TV white space has been investigated and found viable in a series of experiment conducted by FCC [8] without serious degradation in TV signal quality given cognitive radio access. This led to the investigation of power control

algorithms (PCAs) based on spectrum sensing information [9]. In our previous work, we extended the approach presented in [6] for the case of CRN, where multiple CR terminals individually estimate their channel to the worst case IU and coupled with some readily available information to formulate respective TPC algorithm [7]. The algorithm in [7] were fully distributed PCAs with primary protection via spectrum sensing and has the ability of ensuring that the IU environment remains unperturbed at all times with the opportunity of increased number of CR users. The approaches in [5-7] however considered worst case placements of incumbent receivers. Worst case scenarios considers, the aggregate interference contributions by multiple CRs to the nearest co-channel incumbent receiver to it, therefore CRs are denied access to the extra capacity achievable when IU system is able to tolerate more interference or in partial outage due to its planning i.e. grade B or noise limited contours are usually planned to cover 50% of locations, 90% of time following the F(50,90) curve [10], therefore the remaining 50% of locations which may be in outage can therefore be accessed by CRs. Worst case analysis generally trades optimality for robustness, we therefore in this paper eschew such conservative approach and provide a more efficient solution with strict interference consideration to IUs. Worst case analysis requires that the incumbent outage must be greater than 90% before CRs can be allowed to access licensed spectrum. Such power control strategy only provides an upper bound on the total number of CR terminals that can be supported. In this paper, we present a stochastic power control procedure based on incumbent outage information, which allows CRs to access spectrum when the incumbent is not totally in outage. To allow for fully distributed framework, we enable CR terminals with the prerogative of estimating incumbent outage information using spectrum sensing results. We show that even when we eschew worst-case conditions, a degree of CR terminals can still be accommodated depending on incumbent outage probability (IOP) without degrading the interference limit at the nearby receivers. We further advance the model to incorporate shadow fading which was not modeled in [5-7] and assume that fast fading is compensated by using appropriate coding and interleaving process. The benefits of this approach are manifolds: (i) it is a purely distributed approach and therefore very suitable for the CRN (ii) it provides for explicit incumbent protection at all times (iii) it is “optimal” as well as robust since the TPC strategy is formulated based on IOP (iv) it provides for increased

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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 IEEE ICC 2011 proceedings

spectrum efficiency hence more supported CR terminals since worst case analysis is relaxed. We therefore modify conventional distributed TPC algorithms and extend our approach presented in [7] using a novel stochastic power constraint based on IOP for increased spectrum utilisation within the cognitive framework. The rest of the paper is organised as follows: section II provides the model considered and problem formulation. We recap spectrum sensing algorithms and distributed power control algorithms in section III. Afterwards, we formulate in section IV, the explicit derivation of the link gain to the incumbent receiver and the proposed algorithm called distributed power control for CRs with primary protection via spectrum sensing with worst case and non-worst case (stochastic) power control strategies. Simulation results supporting the algorithms are presented in section V followed by conclusion of paper in section VI. II.

becomes un-decodable. Icr is the aggregate interference contribution to the IU by CRs and is modelled as Icr=Σpi g(di) Xc . ξth is therefore the Interference Temperature Limit (ITL) at the grade B incumbent receiver. Therefore, provided the incumbent user is not in outage, the aggregate interference power from all CR transmitters must always be less than the ITL at the incumbent receiver. (2) Signal-to-Interference-Noise Ratio (SINR) for CR user: QoS within CRN can be maintained if SINR for the ith CR is greater than a predefined SINR threshold given as: γ cr , i =

p i g ( ri , i ) X c

≥ γ cr , th

N

∑

p j g ( ri , j ) X c + Ptv g ( D i ) X p + N o

(2)

i ≠ j, j =1

γcr,i is the SINR at the ith CR terminal, γcr,th is the SINR

threshold and No is the noise power at the CR receiver.

MODEL AND PROBLEM FORMULATION

Let us consider the system model of Fig. 1, consisting of an incumbent TV broadcast system, characterised by an effective communication range called the noise limited radius rnl with an effective radiating power Ptv. The CRN consist of N transmit-receive (TX-RX) pairs in a m x m square block with uniform distribution of users. The Euclidean distances between CRs are calculated, hence, the overall gain matrix G of the CRN. Fig.1 depicts two scenarios, (1) is the assumption of worst case placement of an IU just on the incumbent noise limited contour and the second, a non-worst case placement of IUs within the grade B contour. The CRN TX power vector is defined as, P=[p1,,p2,….pN]T for i=1,…,N and bounded by 0≤pi≤pmax where pmax is the peak power transmitted by any CR user. The effective communication range of an ith CR TX-RX pair is denoted as ri,i while the range from jth TX to ith RX is ri,j such that ri,j ≥ ri,i due to the random distribution of CRs and rii ≤ 500m . We consider Di and di as the distance from the ith CR to the TV transmitter and receiver respectively. A pathloss exponent of αp=2 is assumed for the incumbent TX and αc=4 for CRs. We further represent Xp and Xc as the shadow parameter for the incumbent and cognitive system and are assumed to be log-normally distributed with zero mean and variance σp and σc respectively. Link gains are therefore represented in a general case as g(x)=x-α. Our aim is to re-use spectrum on a non-interfering basis to the incumbent network, while maximising opportunistic throughput within the CRN. We therefore formulate the QoS objective for CRN coexistence. Without loss of generality, we consider an adhoc based system for the CR network with duo QoS objectives: (1) Interference Event (IE) at IU: In ensuring that QoS levels is unperturbed due to the CRN operation at the worst case primary receiver, the IE must satisfy the following: I E = P ( Pr ≥ Pn l ) ∩ P ( I c r ≤ ξ th ) (1) where Pr is the received incumbent signal power givens as Pr=Ptv g(rnl) Xp and Pnl is the incumbent signal threshold power at the noise limited contour beyond which TV signal

ri, j

j th TX

ri,i

di Di

III.

PRELIMINARIES

In this section we recap on the spectrum sensing mechanism and DPC schemes as a precursor to the proposed distributed algorithm. A. Spectrum Sensing for Cognitive Radios For CR to effectively limit its TX power to the IU, explicit knowledge of its link gain to the IU is desirable. Unfortunately, CRs do not usually know their channel and range to the Incumbent receiver. We therefore enable the CRs with spectrum sensing capabilities for idle channel identification [7]. We would briefly show how to derive an estimate of the link gain to the IU based on statistical and computational tools available from literature using the energy detector [11] and voting algorithms developed in our earlier work [13] (see [7] for more details). Performance of the energy detector is usually characterised by two well known probabilities, namely, probability of false alarm (Pfa) and probability of detection (Pd) [11, see definitions, therein ]. Of interest is the close form expression of Pd [11] given in (3): λ ⎞ ⎛ Γ ⎜ m − 1, ⎟ 1 2 ⎠ ⎛⎜ ⎝ + 1+ Pd , i = ⎜ Γ ( m − 1) m γ tv , i ⎝ ⎛ ⎛ λ m γ tv , i ⎜ Γ ⎜ m − 1, ⎜ ⎜ 2 ( 1 + m γ tv , i ) × ⎜1 − ⎝ Γ ( m − 1) ⎜ ⎜⎜ ⎝

⎞ ⎟ ⎟ ⎠

λ ⎛ m −1 ⎜ − ⎜ e 2 (1 + m γ tv , i ) ⎜ ⎜ ⎝

⎞ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎟ ⎟ ⎟⎟ ⎠

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

(3)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

Where (γtv,i) is the mean SNR of TV signal at the ith CR receiver, Г(*) and Г(*,*) are complete and incomplete gamma functions with time-bandwidth product m=5(used in this paper) and a decision threshold λ, derived for a suitable Pfa (λ=f-1(Pfa) [11]. It is recommended that all CRs synchronise their quiet periods so that SNR is what is sensed and not the SINR. From (3) [11] we can see that the Pd for the ith CR terminal is a function of received SNR, and hence distances Di as in (4). Pd , i = f ( γ tv , i ) = f ( D i ) (4) Where function f depends on spectrum sensing algorithm. Probability of missed detection at the ith CR (Pm,i) is therefore the probability of declaring the primary signal is vacant when in fact it is occupied and is given by Pm,i=1−Pd,i . B. Distributed Power Control in Wireless Networks Power control is well researched area, in this paper; we focus on distributed power control algorithms since an adhoc CRN is assumed. Since the ith CR TX only knows its channel ri,i to its RX and is oblivious of its channel gain to other CR users , it therefore adjusts its power according to the perceived SINR level (γcr,i) at its receiver, as defined in (5). So from equation (2), the standard Distributed Power Control (DPC) can be defined as: γ cr , th p i ( t + 1) = p i ( t ) , t ∈ {0,1, 2, ....} (5) γ crt , i The DPC algorithm is shown to converge to a power levels that fulfils γcr,th for all users; however, achieved at impractical powers. Since device power can not be arbitrarily large, a constraint is imposed on the power disposable to the CR by defining a maximum power pmax for the CRs. This is fulfilled through the Distributed Constrained Power control (DCPC) algorithm, and is shown to converge faster than the DPC [3]. An improved version of the DCPC is the Generalized Distributed Power Control algorithm, GDPC [4]. In GDPC, devices transmitting at pmax without fulfilling their QoS are made passive. This has the benefit of reducing the interference environment leading to increased number of supported users.

α cr

pi, w c ≤

DISTRIBUTED POWER CONTROL WITH INCUMBENT PROTECTION VIA SPECTRUM SENSING (DPC-IPSS)

Conventional DCPC and GDPC algorithms do not guarantee incumbent users protection; therefore it becomes imperative to modify these algorithms in order to protect the incumbent users. An autonomous distributed power control algorithm was developed in [6] guaranteeing interference free operation to the incumbent at all times. This algorithm is simple yet effective since CRs communication is possible even at close proximity to the users without raising the interference at the incumbent user beyond limits. If the ITL threshold ξth and the number of transmitting CRs N are known (e.g. using routing protocol described in [12] and executing voting decision algorithm [13]), then a further constraint on the maximum individual cognitive power under worst case analysis can be conditioned as pi,wc (6):

N Xc

i ∈ {1, 2 , ....... N }

(6)

Since each of the CR users is now constrained by (6), the ITL at the IU is never violated at any distance from the worst case (WC) incumbent user. The work in [6] implicitly considered di ≈ dtv for all CRs, so that the same pi,wc constraint would be applied to all N transmitting CRs which is quite conservative. This assumption was relaxed in our earlier work by empowering each CR user with spectrum sensing capabilities so that CR users explicitly determine their respective link gains to the worst case IU and as such compute independent power constraints [7]. This makes the system highly distributed compared to [6] with the benefit of supporting more CR terminals since CR transmitters further away from the m x m block would ideally contribute lesser interference to IUs and can therefore enjoy the benefit of a little more predisposed power to fulfil its QoS objective [7]. We therefore briefly describe the explicit determination of link gains and formulate the transmission power for CRs [7]. A. Explicit Estimation of Distance di In order to estimate distance di each CR performs spectrum sensing using Energy Detector. Each node measures energy Yi in T number of time slots and in each time slot it compares Yi to a threshold λ and calculate I ( Y i k ) such that:

⎧1, Yik ≥ λ I (Yik ) = ⎨ ⎩0, otherwise

i = 1,..., N and k = 1,...., T

(7)

Hence estimated probability of detection Pˆd , i for ith CR is:

1 T Pˆd , i = ∑ I (Y i k ) for i = 1,..., N (8) T k =1 Once the probability of detection is estimated, an estimate on the distance from the ith CR to the primary TX can be derived. Since estimated Pˆd , i ≈ Pd , i , it suffice to say Dˆi ≈ f −1(1 − Pm,i ) . The improved maximum individual CR power constraint based on sensing information is therefore given in (9), pi , wc ≤

IV.

ξ th d i

(

th −1 ξ nl g f −1 (1 − Pm , i ) − rnl

N

)

i ∈ {1, 2,.......N }

(9)

B. Stochastic Power Constraint for CRs The worst case constraint presented in section IV-A projects a quite conservative approach which denies the CRN of extra capacity disposable depending on the IOP. In this section we propose a new constraint for our PCA which depends on the IOP at regions around the grade B contour of a TV system. The left hand side of equation (1) therefore models the outage criterion for an incumbent receiver at a grade B contour. Iout is therefore defined as the probability that the received TV signal at some distance Di falls below Pnl under pathloss and shadowing expressed as Iout=P{Pr ≤ Pnl}. So that: I o u t ≅ 1 − P { Pr ≥ Pn l } (10) We now have Pr =Ptv g(Di) Xp = Ptv (f -1(1-Pm,i))-αp Xp . Notice that the link gain is now a function Di so that the CR terminal

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

has the prerogative of estimating the IOP itself since it is capable of sensing the incumbent signal. The outage probability can be approximated as [14]

(

⎛ −1 1 − Pm , i ⎜ Pnl − Ptv + 10 log f I out = 1 − Q ⎜ σp ⎜⎜ ⎝

(

αP ⎞

))

⎟ ⎟ ⎟⎟ ⎠

(11)

Note that all the elements in Q are expressed in (Log scale). Where Q function is the right tail probability of a standard Gaussian random variable. Following the same analysis, the right hand side of the equation (1) can be modeled. The whole idea is to put a bound on CR TX power so that each TX can not exceed a new non worst case power constraint pi,nwc, at any point in time such that Icr =N pnwc di Xcr ≤ ξth , then: ⎛ ξ − N − pnwc − g (di ) ⎞ P ( Icr ≤ ξth ) = 1 − Q ⎜ th ⎟ σc ⎝ ⎠ ⎛ ξ − N − p − 10log g f −1 (1 − P ) − r nwc m,i nl ⎜ th = 1− Q⎜ σc ⎜ ⎝

(

)

(

) ⎞⎟⎞⎟ ⎟⎟ ⎟⎟ ⎠⎠

⎛ IE ⎞ Pnwc = ξth − N − 10log g f −1 (1 − Pm, i ) − rnl + σ c Q−1 ⎜1 − ⎟ − Iout ⎠ 1 ⎝

)

(

(

)

)

(16)

Where t ∈ {0 ,1, 2 ,....} and pˆ i is an arbitrary power value. V.

SIMULATION AND RESULTS

Simulation parameters are given in Table 1. For ease of presenting our results, we normalise the estimated distances: 1 dˆ = N

N

∑ Dˆ i − rnl

i = 1,..., N

(17)

i =1

Simulation Parameters

(12)

(13)

So that the new non worst case power constraint Pnwc is as:

(

γ cr,th ⎧γ cr, th pi (t ) ≤ min pi, nwc , pmax ⎪ t pi (t ), if γ γ crt , i ⎪⎪ cr , i pi (t + 1) = ⎨ γ cr,th ⎪ pˆ , if pi (t ) > min pi, nwc , pmax ⎪ i γ crt , i ⎪⎩

Table 1: Simulation parameters for fully distributed CRN ⎞ ⎟ ⎟ ⎟ ⎠

From equation (1) these two conditions therefore occur independently of each other hence assume statically independence and therefore can be solved in a joint probability sense: ⎛ ⎛ ξ − N − p −10log g f −1(1− P ) − r nwc m,i nl ⎜ ⎜ th IE = (1− Iout )*⎜1− Q ⎜ σc ⎜ ⎜ ⎝ ⎝

Fig. 5. The power updating rule for GDPC-IPSS under nonworst case IU placement is as in equation (16).

(14)

We can now modify the DCPC/GDPC-IPSS algorithms by giving a power bound based on our new stochastic power constraint and call them DCPC/GDPC-IPSS with Incumbent Protection via Spectrum Sensing under stochastic power constraint. We can easily see that when Iout≥0.9, the stochastic power constraint (14) reduces to worst case constraint (9). C. DCPC-IPSS under Non-worst case Power Constraint The iterative power updating process is therefore written as: ⎧γ ⎫ ⎪ cr,th ⎪ pi (t +1) = min ⎨ pi , min ( pi, nwc , pmax ) ⎬, t ∈{0,1,,..} (15) t ⎪⎩ γ cr,i ⎪⎭ The DCPC-IPSS algorithm advanced here implements spectrum sensing to estimate its distance to the incumbent receiver. When the CRs are sufficiently far from the IU system, equation (14) would tend to increase making {pi,nwc,pi,wc}≥ pmax, hence (15) ensures that the CR never exceeds its maximum power, therefore equation (15) reduces to the convention DCPC algorithm as di becomes large. D. GDPC-IPSS under Non-worst case Power Constraint Akin to conventional GDPC algorithm, GDPC-IPSS has the ability to support an increased number of CR transmitters compared to the DCPC-IPSS with obvious reduction in the incumbent interference environment as evident in Fig. 3 and

TV Transmit Power (Ptv) Effective Coverage range of TV station (rnl) Noise power for 8MHz UK TV channel Interference level at rnl Number of CR Transmitters (N) CR maximum terminal power (pmax) CR coverage area Pathloss exponent for Incumbent (αp) Pathloss exponent for CR transmitter (αcr) Distribution of CR terminals Probability of false alarm (Pfa) Arbitrary power Pˆ No of time slots for sensing operation Interference event probability (IE) Variance of shadowing(σp,σc)

Values 80dBm 70Km -105dBm -100dBm 50 20dBm 2000m x 2000m 2 4 Random( ri,i≥ri,j ) 0.01 0dBm 1000 0.05 (6 , 3.6)

In worst case (WC) scenarios, CRs are only allowed to access spectrum where an outage exist for the IU i.e. Iout≥0.9, this results in a tight bound on the number of supported CRs at any distance d from the IU contour as in Fig. 2. With our nonworst case (NWC) analysis, it is evident from Fig.4 that an appreciable number of CR users can be supported even when the incumbent system is not in total outage i.e. Iout