### Modified soft combination scheme for

cooperative SPRT considering i.n.i.d. samples in

## cognitive radio

1

## Mayank Sahu, 2

## Amit Baghel

1

## Research Scholar, 2

## Assistant Professor

Department of Electronics and Telecommunication Engineering

Jabalpur Engineering College, Jabalpur, M.P., India

Abstract: In this paper, a modified soft combination scheme for cooperative sequential probability ratio test

(SPRT), is proposed for cooperative spectrum sensing to reduce the average number of required samples in a

fast fading scenario . This is done to reliably detect primary users activity, in a fast fading environment as the

samples are independent but not identically distributed samples(i.

n.i.d.), with decreased number of samples.

Log-likelihood ratio computation is also studied with respect to fast changing samples, variances of received

signal and noise, considered as random variables. Firstly, the detectability of the conventional generalized log-

likelihood ratio (GLLR) is analyzed considering i.n.i.d. samples caused due to fast fading. Second, we

proposed a modified rule for soft combination of test statistics for performing the cooperative SPRT to

achieve even less number of samples, assuming probability density functions of the received signal and noise

variances are unknown. Finally, it is shown by our simulation results that the proposed cooperative SPRT

with modified soft combination rule performed better in this fast fading environment by reducing average

sample number (ASN), as compared to the conventional GLLR scheme. Also, t he proposed detection rule is

simple to implement and avoids the deterministic knowledge of primary signals.

## I – Introduction

Cognitive radio emerged as a way which enabled secondary users to improve the overall spectrum usage by

exploiting spectrum opportunities in both licensed and unlicensed bands to mitigate the spectrum scarcity problem.

Spectrum sensing is an essential functionality of cognitive radio networks to detect spectrum holes or white spaces,

to exploit spectrum access opportunities by ensuring that cognitive radios do not cause harmful interference to

### primary user networks[1].

Energy detection (ED) is the most commonly used spectrum sensing method, due to its non reliance on any a priori

knowledge of primary signals with less complex implementation. However, for the case of low SNR, ED needs a

large number of the received samples to achieve a detection decision, resulting in long sensing time. Sequential

detection method as proposed by wald, reduces the number of samples required by energy detector through

sequential probability ratio test(SPRT),

In cooperative spectrum sensing, a number of secondary users collaborate to mitigate the effects of shadowing and

fading. Each CR, senses the spectrum for availability of white spaces individually, and then sends the sensed

information (decision or sensing data) to the fusion center which takes the final decision.

The cooperative sequential detection scheme which was well analyzed by[2]; to reduce the average sensing time in

cognitive radio networks by composite hypotheses using the generalized log-likelihood ratio (GLLR) performed

well in for independent and identically distributed (i.i.d.) samples acquired by the detector.

Practically, due to fast fading it is of interest to analyze Spectrum sensing for cognitive radio systems considering

i.n.i.d. samples, signifying fast fading. In [3], it was exhibited that soft combination schemes based cooperative

spectrum sensing, such as equal gain combination (EGC) and maximal ratio combination (MRC), improved

performance in cooperative spectrum sensing.

In this paper, we have used cooperative sequential detection scheme with energy detection. Acquired statistics of the

signal and noise samples depend on the received signal and noise power level, respectively. The network consists of

M cognitive radios that are monitoring the frequency band of interest, as shown in Fig. 1. Here, we modified the soft

combination rule based on a linear weighted combination of local statistics from participating cognitive radios for

the cooperative sequential detector for spectrum sensing when the samples acquired by cognitive radios due to fast

fading are independent but not identically distributed (i.n.i.d.). This is caused by the effect of fast changing channel

characteristics in mobile cognitive radio systems. We have assumed that the received signal statistics and the noise

### statistics to be i.n.i.d..

Figure 1 . Cognitive radio network for spectrum sensing.[1]

## II – System model

Throughout this paper, we adopted a system model similar to that in [4] where M is the number of cognitive radios

and assumed that the nth acquired sample by the mth (m=1,2,. . . ,M) cognitive radio is a zero mean Gaussian

### random variable with v

1 m

(n) , as received signal variance and v

0 m

(n) noise variances ( v

1 m

(n) > v

0 m

(n) i.e.,

H

## i : x m

[n] ~ exp (- ),

w here the two hypotheses are defined as

H

0 : target signal is absent

H

1 : target signal is present.

The nth instantaneous sample variances v

0 m

(n) and v

1 m

(n), are under H

0 and H

1 respectively. In fast fading

environment, instantaneous variances, v

0 m

(n) ? V

0 m

## and v

1 m

(n) ? V

1 m

, are unknown and considered to be random

variables for n = 1,2,. . . ,N and m = 1,2,. . . ,M their statistics are determined from the channel characteristics, and

## p ( v

0 m

) and p ( v

1 m

) are the probability density functions of v

0 m

(n) and v

1 m

(n), respectively.

### We assumed, parameter spaces V

0 m

## and V

1 m

## are disjoint, where

V

0 m

= {x| L

0 m

? x ? U

0 m

}

and

V

1 m

= {y| L

1 m

? y ? U

1 m

}

### The distributions of v

i m

(n) (n = 1,2,. . . ,N) are same for same cognitive radio over the long term. But, the

## distributions of v

i m

(n) (m=1,2,. . . ,M) between the other cognitive differ from each other. The distributions of the

### acquired signal at the m th

radio are characterized by the probability density functions p

0 m

( x m

[n]; v

0 m

(n)) and

p

1 m

( x m

[n]; v

1 m

(n)), under H

0 and H

1 , respectively.

Figure 2 . Instantaneous variance as a uniform random variable with L = 0.8 and U = 0.9.

III – Sequential Detection in Fast Fading Environments

### A. Sequential Detection using GLLR

Here we have summarized the related previous work in [4,] for clear understanding of the proposed method. As

explained in previous section, the received signal and noise variances change continuously during sensing. In this

fast fading environment, an ideal sequential probability ratio test (SPRT) must perform the following test:

## i) The m th

(m=1,2,. . . ,M) cognitive radio acquires sample x m

[N] and computes

ii) Base station updates the ideal sequential log-likelihood ratio LLR

## N ideal

## according to

LLR

## N ideal =

LLR

## N-1 ideal

+

### iii) H 0 is accepted, If LLR

## N ideal

? ?

0 ; H 1 is accepted, if LLR

## N ideal

? ?

1 , where ?

0 and ?

1 are conceptual thresholds.

iv) Otherwise, take one more sample is taken and repeat Steps 1) to 3).

## However, v

i m

(n) (i=0,1, m=1,2,. . . ,M, n=1,2,. . . ,N) is a random variable, so an exact computation of LLR

## N ideal

is

impossible. Thus, the SPRT using the GLLR [1] is performed by replacing v

i m

(n) with their maximum likelihood

## estimates. We have,

GLLR

N =

## where v?

0 m,(N)

## and v ?

1 m,(N)

are the maximum likelihood estimates of v

0 m

## and v

1 m

[zou], i.e.,

v

?

0 m,(N)

=

v

?

1 m,(N)

=

In fast fading environments, the maximum likelihood estimates () and () converges to the following values:

## a). Under H 0 , v

?

0 m,(N)

## converges to E { v

0 m

(n)} and v ?

1 m,(N)

## converges to L

1 m

.

## b). Under H 1 , v

?

0 m,(N)

## converges to U

0 m

## and v ?

1 m,(N)

## converges to E { v

1 m

(n)}.

## Therefore, under H

0 , the corresponding GLLR

N m

is expressed by . Similarly, under H 1 , the

## corresponding GLLR

N m

## is expressed by .

B. Optimal Computation of Log-likelihood Ratio with unknown p ( v

0 m

) and p ( v

1 m

)

Since, we do not use the conventional GLLR scheme; hence, here we define optimal for the SPRT

## where v *

0,m

? V

0 m

## and v *

1,m ? V

1 m

## are set by force.

C. Soft Combination Based on energy detection for Cooperative Spectrum Sensing

The soft combination scheme based on energy detection, as given in [3] was modified by us on the hit and trial

basis, the test statistic is first obtained from the local observations of each cognitive user, and then transmitted to the

fusion center, at the fusion centre a final decision will be made to indicate the absence or presence of primary users

based on the weighted summation of all the received test statistics. The test statistic for m th ( m _ 1 , 2 , _ ,M ) cognitive

## can be expressed as,

MLLR

n m

= ,

where N is the number of samples. With soft decision fusion scheme, fusion center uses the following decision rule:

Y =

## where ?

m are the weighting coefficients, which represent the contribution of the signal from different sensing

cognitive radios. Modifying equal gain combination (EGC) the corresponding weights are respectively given by [5]

?

m =

where M is number of cooperative cognitive users. EGC is an attractive method of soft combination due to the fact

that it doesnt require the estimation of fading amplitudes.

### IV – Simulation and Results

To illustrate the performance of our proposed method, simulations were performed with respect to the average

sample number required to reach a decision. Here, number of cooperative cognitive users were taken as M = 4.

Other simulations parameter are listed in the table I. In this scenario received signal and noise variances were

assumed to have uniform distribution. Extensive monte carlo simulations were performed for both scenarios of H

0

## and H

1 . Detection thresholds are dependent on the pre-defined false alarm and miss detection constraints alpha and

beta and are computed as given in[6]. Simulation results are shown in fig and fig under sequential detection H0 and

H1, respectively. As evident from the figures that our proposed method performed better than the LLR method as

## was proposed in [4].

Figure 3 . Sequential detection in fast fading scenario under H0.

Figure 4 . Sequential detection in fast fading environment under H1.

### Table I. Simulation Parammeters.

L

0 m

U

0 m

L

1 m

U

1 m

v *

0,m v *

1,m

m =1 0.64 0.90 0.90 1.15 0.7465 1.0515

m = 2 0.75 0.87 0.90 1.18 0.7976 1.0526

m = 3 0.72 0.82 0.87 1.02 0.7633 0.9522

m = 4 0.69 0.85 0.86 0.99 0.7575 0.9386

## V Conclusion

We in this paper proposed a modified soft combination rule for cooperative sequential detection in fast fading

environment. In section III, we analyzed how the SPRT using LLR performs with respect to average sample

numbers and a modified method was proposed by us applicable to the same scenario. Our simulations results

exhibited that the proposed modified method for cooperative sequential detection performs better with respect

average sample numbers in fast fading scenario.

## VI References

[1] I. F. Akyildiz, B. F. Lo, and R. Balakrishnan, Cooperative spectrum sensing in cognitive radio networks: a

survey, Physical Commun. J. , vol. 4, no. 1, pp. 4062, Mar. 2011.

[2] Q. Zou, S. Zheng, and A. H. Sayed, Cooperative sensing via sequential detection, IEEE Trans. Signal Process. ,

vol. 58, no. 12, pp. 62666283, Dec. 2010.

[3] X. Zhang, Z. Qiu, D. Mu, A Modified SPRT based Cooperative Spectrum Sensing Scheme in Cognitive Radio,

in Proc.2010 IEEE International Conference on Signal Processing , no. 10 , pp. 1512 1515.

[4] Y. J. Cho, J. H. Lee, A. Heo, and D. J. Park, Smart sensing strategy for SPRT considering fast changing sample

statistics in cognitive radio systems, in Proc. 2012 International Conference on Future Generation Communication

### Technology , no. 9, pp. 18.

[5] J. Ma, and Y. Li, Soft Combination and Detection For Cooperative Spectrum Sensing in Cognitive Radio

Netwroks, Proc. IEEE GLOBECOM , pp. 3139-3143, Nov. 2007.

[6] A. Wald , Sequential Analysis . New York: Wiley, 1947.