Resource Allocation for Relay Assisted CognitiveRadio Networks�

Ammar Zafar∗, Yunfei Chen?, Mohamed-Slim Alouini∗, and Redha M. Radaydeh∗∗Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST)

Thuwal, Mekkah Province, Saudi ArabiaEmails:{ammar.zafar, slim.alouini, redha.radaydeh}@kaust.edu.sa

?School of Engineering, University of WarwickCoventry, UK, CV4 7AL

Email: yunfei.chen@warwick.ac.uk

Abstract—In this paper, we present two optimal resourceallocation schemes that maximize throughput and symbol correctrate (SCR). The throughput and SCR are derived. The derivedthroughput and SCR are optimized with respect to the sensingtime, the source transmission power and the relay transmissionpower. Numerical results show that the optimal sensing timeis dependent on the primary user’s signal-to-noise-ratio (SNR).They also show that SCR increases with increase in the numberof relays.

I. INTRODUCTION

Recent years have seen the employment of cognitive relaysto improve cognitive radio performance [1], [2]. In cognitiverelaying, secondary nodes act as relays for the source. Inthis scenario, the source first looks for “spectral holes” usingspectrum sensing. Upon detection of a “spectral hole”, ittransmits information to the destination and the relays. Therelays then forward the received signal to the destination toachieve diversity gain.

The secondary user has to balance two conflicting objectivesof reducing interference to the primary user and increasing itsown throughput. Hence, the secondary user must efficientlyemploy spectrum sensing so as not to interfere with primaryuser and also not to miss any transmission slot. The trade offbetween probability of detection and probability of false alarmcan be thought of as the trade off between throughput of thesecondary user and the interference to the primary.

In [3], the authors investigated this sensing-throughput tradeoff for a cognitive radio network without relays and optimizedthe sensing time for maximization of the throughput. Powerallocation strategies for relay assisted cognitive radio networkshave been studied in [4]–[6]. However all of these assumeco-existence of the primary and secondary networks withoutspectrum sensing. In other words, the proposed schemes workin an “underlay” setup by keeping a measure of performance,generally the interference experienced by the primary user,below a certain threshold.

In this paper, we consider a relay assisted cognitive radionetwork with opportunistic access to licensed bands. Sensingis performed only at the transmitting secondary user and not

�This work was funded by King Abdullah University of Science andTechnology (KAUST).

at the relays. Two power allocation schemes that maximizethroughput and symbol correct rate (SCR) of the secondarysource employing cognitive relays are considered. The sourcedivides its power between spectrum sensing and transmissionwhereas the relays only use their power for forwarding. Inaddition to individual power constraints, we also consider aglobal power constraint on the whole system. We assumecomplete channel state information (CSI). Finally, we willconsider amplify-and-forward (AF) relays.

Numerical results show that the optimal power allocation isindependent of the number of relays but is dependent on thechannel. They also show that the throughput decreases with thenumber of relays, while the SCR increases. In addition, resultsshow that the optimal sensing time is significantly influencedby the primary user’s signal-to-noise-ratio (SNR).

II. SYSTEM MODEL

Consider a system with a source node and a destinationnode, and m relays between them, as shown in figure 1. Weassume here an orthogonal system. For our discussion, weassume time orthogonality. In the first time slot, the sourcesenses for any primary activity. On detection of a spectral holethe source transmits data to the destination through the relays.The relays amplify the signal from the source and forward itto the destination. Each relay transmission takes place in adifferent time slot. Thus one packet requires a total of m+ 1time slots.

With this setup, there are four possible scenarios: 1) Thesource, with probability of detection Pd, correctly detectstransmission from the primary and will not transmit, 2) Thesource, with probability 1 − Pd, does not detect the trans-mission from the primary and transmits and as such causeinterference, 3) The source, with probability Pf , incorrectlydetects transmission from the primary and stays silent, there-fore missing an opportunity for transmission, 4) The source,with probability 1−Pf , correctly detects a “spectral hole” andtransmits data to the destination through the m relays.

According to these four scenarios, there are two transmittedsignal models.

A. Without Interference

The signal at the destination from the source is

yrt =√ESThrts+ nrt (1)

where s is the zero-mean and unit-energy transmitted symbol,EST is the energy used by the source for transmission, hrtis the known channel response between the source and thedestination and nrt ∼ CN(0, σ2

nrt) is the complex Gaussian

noise. The signal at the ith relay from the source is

yit =√ESThits+ nit (2)

where hit is the known channel response between the sourceand the ith relay and nit ∼ CN(0, σ2

nit) is the complex

Gaussian noise. The relay normalizes the received signal andtransmits it to the destination. The signal transmitted by theith relay is

si =√

EST

EST |hit |2+σ2nit

hits+√

1EST |hit |2+σ2

nit

nit .

Hence the signal at the destination from the ith relay is

yri =√Eihrisi + nri (3)

where hri is the known channel response between the destina-tion and the ith relay, Ei is the energy used for transmission bythe ith relay and nri ∼ CN(0, σ2

nri) is the complex Gaussian

noise. Putting in si, we can write

yri =

√ESTEi

EST |hit |2 + σ2nit

hrihits+ nri (4)

where nri ∼ CN(0, ˜σ2nri

) and

˜σ2nri

=Ei|hri |2σ2

nit

EST |hit |2 + σ2nit

+ σ2nri.

In matrix form one has

y = hs+ n (5)

where

y =

[1

σnrt

yrt1

˜σnr1

yr1 . . . . . . . . .1

˜σnrm

yrm

]T

h =

[√ESTσ2nrt

hrt

√ESTE1

˜σ2nr1

(EST |h1t |2 + σ2n1t

)hr1h1t . . .

√ESTEm

˜σ2nrm

(EST |hmt|2 + σ2

nmt)hrmhmt

]Tand n ∼ CN(0, I).

B. With Interference

Now the signal at the destination from the source is

yrt =√ESThrts+ nrt + yIrt (6)

where yIrt is the interference signal from the primary userdue to missed-detection. The signal received at the ith relaynow becomes

yit =√ESThits+ nit + yIit . (7)

Following the same procedure as before, the received signalfrom the ith relay can be written as

yri =

√ESTEi

EST |hit |2 + σ2nit

hrihits+ nri + ˆyIri (8)

where nri ∼ CN(0, ˆσ2nri

),

ˆσ2nri

=Ei|hri |2σ2

nit

EST |hit |2 + σ2nit

+ σ2nri

and

yIi = yIri +

√Ei

EST |hit |2+σ2nit

hriyIit .

Again, in matrix notation one has

yI = hIs+ nI + YI (9)

where

yI =

[1

σnrt

yrt1

ˆσnr1

yr1 . . . . . . . . .1

ˆσnrm

yrm

]T

hI =

[√ESTσ2nrt

hrt

√ESTE1

ˆσ2nr1

(EST |h1t |2 + σ2n1t

)hr1h1t . . .

√ESTEm

ˆσ2nrm

(EST |hmt |2 + σ2nmt

)hrmhmt

]T

YI =

[1

σnrt

yIrt1

ˆσnr1

yI1 . . . . . . . . .1

ˆσnrm

ˆyIm

]Tand nI ∼ CN(0, I).

C. Spectrum Sensing

Let T denote the duration of one time slot. The source willemploy spectrum sensing for duration of ts < T seconds.Transmission will take place, in the presence of a spectralhole, in the remaining time. An energy detector can be usedfor spectrum sensing. According to [7], the probabilities ofdetection and false alarm are given by

Pd = Q

(λ−N − γ√2(N + 2γ)

)

Pf = Q

(λ−N√

2N

)respectively, where λ is the threshold of the energy detector,N = tsfs is the number of samples, fs is the samplingfrequency, γ equals N times the SNR at the output of thedetector and Q(.) is the Gaussian Q-function.

III. OPTIMIZATION

In this section, we present two optimal resource allocationalgorithms to maximize throughput and SCR. We derive thethroughput and SCR and quantify the constraints on the twooptimization problems.

A. Throughput

Using our assumptions, we can derive the throughput as

C =P (H0) log2(1 + SNR)

(T − ts

T +m(T − ts)

)(1− Pf )+

P (H1) log2(1 + SINR)

(T − ts

T +m(T − ts)

)(1− Pd)

(10)

where SNR is as defined previously, SINR is the signal-to-interference-noise-ratio, P (H0) is the probability that theprimary user is absent, P (H1) = 1−P (H0) is the probabilitythat the primary user is present and T−ts

T+m(T−ts) is introducedas a penalty in throughput because out of the total time ofT + m(T − ts), only T − ts data is transmitted. It can beshown that the SNR can be written as

SNR = a+

m∑i=1

bi˜σ2nri

(11)

where

a =EST |hrt |2

σ2nrt

bi =ESTEi|hri |2|hit |2

EST |hit |2 + σ2nit

.

The SINR can be expressed as

SINR =

(a+

∑mi=1

biˆσ2nri

)2

a+∑mi=1

biˆσ2nri

+ acσ2nrt

+∑mi=1

diˆσ2nri

biˆσ2nri

(12)

wherec = E[|yIrt |

2]

di = E[|yIi |2]

E[|yIi |2] = E[|yIri |2] + E[|yIit |

2]

(Ei

EST |hit |2+σ2nit

|hri |2).

Substituting (11) and (12) in (10), gives the throughput as

C = P (H0) log2

(1 + a+

m∑i=1

bi˜σ2nri

)(T − ts

T +m(T − ts)

)×(1−Q

(λ−N√

2N

))+ P (H1)

(T − ts

T +m(T − ts)

)×

log2

1 +

(a+

∑mi=1

biˆσ2nri

)2

a+∑mi=1

biˆσ2nri

+ acσ2nrt

+∑mi=1

diˆσ2nri

biˆσ2nri

×

(1−Q

(λ−N − γ√2(N + 2γ)

)).

(13)

Assuming unit symbol time, EST and Ei can be thought ofas source and relay power, respectively. The constraints on theproblem are therefore given by

0 ≤ EST ≤ ET , 0 ≤ Ei ≤ Emaxi ,

EST +

m∑i=1

Ei ≤ Etotal and Pd ≥ P thd (14)

where P thd specifies the constraint on Pd, ET is the poweravailable at the source, Emaxi is the power available at therelays and Etotal is the total power available to the wholesystem. We have put a constraint on Pd to restrict interferenceto the primary user.

B. SCR

To optimize the SCR, the value of symbol time, Ts, is alsoconsidered as a variable of optimization since the SNR andSINR depend on the symbol time. As such, in order to havea trade off between sensing time and SCR, Ts must be varied.The signal energies can now be written as

EST = pSTTs and Ei = piTS (15)

where pST and pis are the source and relay powers, respec-tively. The SCR is given by

SCR = P (H0)(1−Q(√kSNR))(1− Pf )+

P (H1)(1−Q(√kSINR))(1− Pd)

(16)

where the constant k depends on the constellation used.Putting (11), (12) and (15) into (16) gives

SCR = P (H0)

1−Q

√√√√k

(α+

m∑i=1

βi˜σ2nri

)×(1−Q

(λ−N√

2N

))+ P (H1)

(1−Q

(λ−N − γ√2(N + 2γ)

))1−Q

√√√√√√√ k

(α+

∑mi=1

βi

ˆσ2nri

)2

α+∑mi=1

βi

ˆσ2nri

+ αcσ2nrt

+∑mi=1

diˆσ2nri

βi

ˆσ2nri

(17)

where

α =pSTTs|hrt |2

σ2nrt

βi =pST piT

2s |hri |2|hit |2

pSTTs|hit |2 + σ2nit

.

We have the same power constraints as we had in the thethroughput case discussed in the (14). In addition, we put aconstraint on the bit rate, i.e. that at least R symbols shouldbe sent in one T ms time slot. Now the constraints on theproblem are given by

0 ≤ pST ≤ ET , 0 ≤ pi ≤ Emaxi , Pd ≥ P thd (18)

pST +

m∑i=1

pi ≤ Etotal, Ts ≤T

Rand RTs + ts ≤ T.

.

.

PU PU

S D

R1

R2

Rm

hrt

Primary Network

Secondary Network

Fig. 1: Primary and secondary networks.

0 1 2 3 4 5

x 104

0

0.05

0.1

0.15

0.2

0.25

Thr

ough

put (

bits

per

Cha

nnel

use

)

Number of Samples (N)

γ=−10 dBγ=−15 dBγ=−20 dB

Fig. 2: Sensing-throughput trade off for different values of γat m = 4.

IV. NUMERICAL RESULTS AND DISCUSSION

In this section, we provide some selected numerical resultsfor the optimization problems. We consider different systemparameters and show that there exist optimal values for thesensing time and powers for maximizing throughput and SCR.All noise variances are set at 1. ET and Emaxi are 2, whileEtotal is set at 4 except when results are shown against m,where it is set at 2 + 1.5m. All the channel coefficients werealso taken to be one unless stated otherwise. The total frameduration T is set as 100 ms. We set P thd = 0.9, and R = 100.For SCR, we assume binary phase shift keying (BPSK) signal.As there is a linear relationship between the number of samplesand the sensing time, we here plot the number of samples

0 1 2 3 4 5 6 7 80.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Number of Relays (m)

Max

imum

Thr

ough

put (

bits

per

Cha

nnel

use

)

γ=−10 dBγ=−30 dB

Fig. 3: Maximum achievable throughput as a function of thenumber of relays for different values of γ.

instead of the sensing time.Figure 2 shows the achievable throughput as a function

of the number of samples N for different values of theprimary SNR, γ. As one sees, there is an optimal value ofN where the achievable throughput is maximized. If N is toolow Pf will increase, hence reduced throughput. If it is toohigh, the fraction of time for transmission will decrease, thusreducing throughput. The optimal value of the N increaseswith decreasing γ. This is due to the fact that for a smaller γ,to achieve the same probability of detection larger number ofsamples is required. The maximum value of throughput alsodecreases as more time is spent on sensing, leaving less timefor transmission.

The effect of the number of relays, m, on the maximumachievable throughput and optimal value of N and the optimalsource power is shown in Figures 3 and 4respectively. Asexpected, the throughput decreases with an increase in thenumber of relays as more time is required in sending oneframe. The throughput also decreases with decreasing γ aslower value of γ implies greater sensing time and less trans-mission time. The optimal number of samples increases as thenumber of relays is increased as can be seen from Figure 4.This is due to the T−ts

T+m(T−ts) term. As m is increased, thedenominator increases. Hence, to compensate for this increase,the sensing time increases, i.e. N increases, to reduce thedenominator.

Figure 5 shows the optimal power allocation as a functionof the channel response. The better the channel response, morepower is allocated to it. The source power is the greatest asnoted. The source power reaches its peak above a certain valueof the channel coefficient. Figure 5 also shows that relay powerallocation is more dependent on the channel between the relayand the source than the channel between the relay and thedestination.

Figure 6 shows the trade-off in SER as a function of thesymbol time Ts,. This trade-off exists due to the constraint

0 1 2 3 4 5 6 7 81

1.5

2

2.5

3

3.5

4

4.5

5x 10

5

Number of Relays (m)

Opt

imal

Num

ber

of S

ampl

es (

N)

γ=−20 dB

γ=−17 dB

Fig. 4: Optimal number of samples as a function number ofrelays.

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Channel

Pow

er

Sourceh

it

hri

Fig. 5: Optimal power allocation versus Channel.

relating ts and Ts.In Figure 7, we show the variation of the SCR with m.

The figure shows a small increase in SCR with larger m. Thisis due to increase in SNR and SINR with increasing m.An important point to note here is that the SCR and symbolerror rate (SER) are not linearly related. Thus increase in SCRdoes not imply an equivalent decrease in SER. The SCR alsoincreases with increasing γ, as higher γ implies greater Ts.

V. CONCLUSIONS

Two optimal resource allocation schemes that maximizethroughput and SCR have been proposed. Numerical Resultsshow that optimal values of the sensing time, source power,and relay powers exist that maximize the targeted parameters.It has also been shown that the optimal power allocationis independent of the primary SNR, γ and the number ofrelays, m but is dependent on the channel between sourceand destination, source and relays, relays and destination. Inaddition, in power allocation for relays, the channel betweenthe relay and source is of greater significance than the channelbetween relay and destination.

0 0.2 0.4 0.6 0.8 1

10−0.8

10−0.7

10−0.6

10−0.5

10−0.4

10−0.3

10−0.2

Symbol Time (ms)

SC

R

γ=−10 dB

γ=−15 dB

γ=−20 dB

Fig. 6: Variation in SCR with respect to the symbol time withm = 4.

0 1 2 3 4 5 6 7 80.69

0.695

0.7

0.705

0.71

0.715

0.72

0.725

0.73

0.735

Number of Relays (m)

Opt

imal

SC

R

γ=−10dB

γ=−15 dB

Fig. 7: Optimal SCR as a function of number of relays.

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