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USRP Implementation of Max-Min SNR Signal Energy basedSpectrum Sensing Algorithms for Cognitive Radio Networks

Tadilo Endeshaw Bogale and Luc Vandendorpe

ICTEAM Institute, Universit catholique de Louvain, Belgium

Email: {tadilo.bogale, luc.vandendorpe}@uclouvain.be

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Abstract: This paper presents the USRP experimental results of the Max-Min signal

SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks

which is recently proposed in [1]. Extensive experiments are performed for different set of

parameters. In particular, the effects of SNR, number of samples and roll-off factor on the

detection performances of the latter algorithms are examined briefly. We have observed

that the experimental results fit well with those of the theory. We also confirm that these

algorithms are indeed robust against carrier frequency offset, symbol timing offset and

noise variance uncertainty.

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SUMMARYOFTHEALGORITHMIN [1]

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A pulse shaped transmitted signal x(t) in baseband form is expressed as

x(t) =

∞∑k=−∞

skg(t− kPs)

In AWGN channel, the received signal in baseband form becomes

r(t) =∞∑

k=−∞

skh(t− kPs) +

∫ ∞

−∞f⋆(τ)w(t− τ)dτ

where Ps =period, w(t) =noise, g(t)(f∗(t)) = Tx(Rx) filter, h(t) =∫∞−∞ f∗(τ)g(t − τ)dτ .

The objective of the work of [1] is to decide between H0 and H1, where

r(t) =

∫ ∞

−∞f⋆(τ)w(t− τ)dτ, H0

=∞∑

k=−∞

skh(t− kPs) +

∫ ∞

−∞f⋆(τ)w(t− τ)dτ, H1

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Key detection idea of [1]

Introduce linear combination variables {αi}L−1i=0 to get two sets of samples having min and

max SNR. By doing so define y[n] as

y[n] ,L−1∑i=0

αir((n− 1)Ps + ti)

=

∞∑k=−∞

sk

L−1∑i=0

αih((n− 1)Ps + ti − kPs) +

L−1∑i=0

αi

∫ ∞

−∞f⋆(τ)w((n− 1)Ps + ti − τ)dτ

where {αi}L−1i=0 are the introduced variables, L is over-sampling factor and {ti}L−1

i=0 are set

ensuring tL − t0 = Ps (Symbol period). For given t0 and f(t), compute {αi}L−1i=0 by

minαmin

αHmin(A+B)αmin

αHminBαmin

, maxαmax

αHmax(A+B)αmax

αHmaxBαmax

where A(i+1,j+1) =∑∞

k′=−∞ h(k′Ps + ti)h⋆(k′Ps + tj), B(i+1,j+1) =

∫∞−∞ f⋆(τ)f(ti − tj +

τ)dτ . Then, the following test statistics is used

T =√N(

T − 1)

where

T =

∑Nn=1 |y[n]|2αmax∑Nn=1 |y[n]|2αmin

,∑N

n=1 |z[n]|2∑Nn=1 |e[n]|2

, Ma2z

Ma2e

Ma2z =1

N

N∑n=1

|z[n]|2, Ma2e =1

N

N∑n=1

|e[n]|2

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Probability of detection and false alarm

Using asymptotic analysis Pf and Pd are given as

Pf (λ) = Pr{T > λ|H0} = Q

(λ

σH0

), Pd(λ) = Pr{T > λ|H1} = Q

(λ− µ

σH1

)where λ is the threshold, µ =

√N γd

1+γmin, γmin(γmax) corresponds to min and max SNR,

σ2H0(σ

2H1) is variance of T under H0(H1), γd = γmax − γmin and Q(.) is Q-function.

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Possible designs

The best Pd is achieved when t0 is known perfectly at the CR receiver. This is possible

when the primary Tx and CR Rx is synchronized (which will never happen in practice).

For practically relevant asynchronous Rx scenario, there are two possible designs

1. With estimation of t0: As there are L possible values of T , choosing

T = max{Ti}Li=1 will likely correspond to the correct t0 (Pd and Pf differ slightly)

2. Without estimation of t0: This design uses T = Ti with arbitrary i, (e.g., i=1)

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Experimental environment

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Parameter Value

Fc (ISM band Europe) 433MHz

Hardware kit NI-USRP

Software Matlab + LabVIEW

Channel BW 625 KHz

FFT size (NFFT ) 256 (QPSK)

Used sub-carrier index {-120 to 1 & 1 to 120}

Cyclic prefix (CP) ratio 1/8

N 215

Pulse shaping filter SRRCF (rolloff = β)

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Experimental environment and parameters

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EXPERIMENT.

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−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−80

−70

−60

−50

−40

−30

−20

−10

0

Frequency (in Fs)

PS

D (

in d

B)

Normalized Power Spectral Density

Desired band

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−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−80

−70

−60

−50

−40

−30

−20

−10

0

Frequency (in Fs)

PS

D (

in d

B)

Normalized Power Spectral Density

New position of the desired band

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⋄ Noise power is not white (Left figure):

Potential Reasons:

1. Phase noise, Local oscillator leakage

2. Non-flat filter transfer function

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⋄ Simple approach to remedy non white effect (Right figure):

Desired band has only Fs

L Hz width (due to oversampling)

1. Choose the desired band such that it is almost flat

2. Rotate the spectrum to move the desired band to DC

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Sample power spectrum

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....

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Threshold ( λ)

Pf

Async w/o est (The)Async w/o est (Exp)Async with est (The)Async with est (Exp)

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Theory vs Experiment Pf (β = 0.2)

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−19 −18 −17 −16 −15 −140.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

Pd

Async w/o est (Exp)Async with est (Exp)

Async w/o est (Sim AWGN ∆σ2=0)

Async with est (Sim AWGN ∆σ2=0)

Async w/o est (Sim AWGN ∆σ2=2dB)

Async with est (Sim AWGN ∆σ2=2dB)

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Effect of SNR (β = 0.2, Pf = 0.1)

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1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Number of samples (in N)

Pf (

Pd)

Pd (Async w/o est)Pd (Async with est)Pf (Async w/o est)Pf (Async with est)Target P

f

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Effect of N (β = 0.2, Pf = 0.1)

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0.2 0.25 0.3 0.35

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

Rolloff factor

Pd(P

f)

Pd (Async w/o est)Pd (Async with est)Pf (Async w/o est)Pf (Async with est)Target P

f

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Effect of β (Pf=0.1)

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Experimental results

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CONCLUSIONS

• Perfect match between theory and experiment.

• Better performance is achieved by Asyn with est t0 algorithm.

• The algorithm of [1] does not experience SNR wall (i.e., for any Pf > 0, Pd → 1 as

N → ∞).

• The algorithm of [1] is also robust against carrier frequency and symbol timing offsets.

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REFERENCES

1 T. E. Bogale and L. Vandendorpe, ”Max-Min SNR Signal Energy based Spectrum

Sensing Algorithms for Cognitive Radio Networks with Noise Variance Uncertainty”,

IEEE Trans. Wireless. Commun., Jan. 2014.

2 H. Kim, C. Cordeiro, K. Challapali, and K. G. Shin, ”An experimental approach to

spectrum sensing in cognitive radio networks with off-the-shelf” in IEEE 802.11

Devices, in IEEE Workshop on Cognitive Radio Networks, 2007.

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ICC 12 June 2014, Sydney, Australia