Joint Beamforming and Power Control to Overcome Tradeoff Between Throughput-Sensing in Cognitive

Radio Networks A. Fattah1, M. A. Matin2, and I. Hossain1

1Department of Electrical Engineering and Computer Science North South University, Dhaka

2Department of Electrical and Electronic Engineering, Faculty of Engineering Institut Teknologi Brunei (ITB), Brunei Darussalam

Email: m.a.matin@ieee.org Abstract— Cognitive radio is introduced for efficient spectrum utilization by allowing unlicensed (secondary) users to access licensed frequency bands and to maintain a minimum interference to the licensed (primary) users. A sensing time has been allocated for sensing the licensed frequency bands before data transmission of secondary system and during the sensing time, data transmission is prohibited, which results in the sensing throughput tradeoff problem. To overcome this tradeoff, the authors present join beamforming and power control approach in this paper. The presented modified WLS algorithm minimizes the interference to the primary system as well as overcome the sensing throughput tradeoff problems in cognitive radio. The simulation result shows that the optimal transmit power of secondary user can improve the system throughput.

Index Terms-Cognitive radio, power control, interference, SINR, throughput, sensing time, detection probability.

I.INTRODUCTION

Cognitive radio is a novel approach in the field of wireless communication, which can sense their surrounding radio environment and make necessary decision according to the needs [1]. Researchers of this area have paid much attention in spectrum sensing for cognitive radio [2], [3] and only very few research works have focused on the tradeoff between the sensing capabilities and the throughput of the cognitive system. Spectrum sensing is crucial tasks in cognitive networks, which must be performed before data transmission of secondary system in order to protect the primary users from harmful interference with optimized sensing time [4]. According to the classical detection theory [5-6], higher sensing time leads to better protection of the primary users from harmful interference due to high detection probability. On the other hand, if sensing time is lower, the throughput of cognitive radio will be higher. Therefore, an inherent tradeoff exists between the duration of spectrum sensing and data transmission, hence the throughput of the cognitive radio network. In [7], a novel frame structure is proposed to overcome this problem. In our paper, the same problem is

addressed with a new solution through controlling transmit power of secondary system for a fixed/stable sensing time. The interference to PU is reduced with the power control approach which gives us a high probability of detection as well as a better system performance.

II.SYSTEM MODEL

In our system, N secondary users (SU) coexist with M primary users (PU) that are operating at the same frequency band owned by PUs of the wireless network. Both PUs and SUs have single antenna element where each PU and SU has a single transmitter and a single receiver. A secondary base station is equipped with K uniformly spaced antenna arrays at the center of the coverage region of the cognitive network. To simplify the analysis, we assume frequency flat propagation channel where the secondary BS has all cognitive information about the propagation channel. Secondary system must perform spectrum sensing before access the frequency band in order to protect the primary users from harmful interference. In this paper, we use energy detection scheme which is the most popular spectrum sensing scheme in order to determine the status of the primary user [8]. There will be two hypotheses depending on the spectrum sensing of cognitive system.

; ( )0

; ( )1i

x n PU is absenti iys n PU is presenti

+ Η⎧⎪= ⎨ + Η⎪⎩ (1)

Here, ix is the observed signal of secondary system and is is

the primary user signal and in is the noise signal. It is assumed that (N+M) narrowed signals can impinge upon the secondary BS among which N signals of SUs arrive from

1 2, ,....,θ θ θM

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angles and M signals of the PUs arrive from 1 2, ,....,θ θ θN angles. The array responses to these signals constitutes matrix as-

1 2A= [a( ) a( ).......a( )]K Nθ θ θ + (2)

Where, ( 1)

( ) [1 ... ], 1,2,3,......( );j j Ki ia e e i M Niφ φ

θ− − −

= = + (3)

2 cos ; 1, 2,.....( )d i N Mi iπφ θλ

= = + (4)

We also define the K component channel response vector between the K BS antennas and SUn and between K BS antennas and PUm are given by-

( ) ; 1,2,3,4........,0R G a n Nn n nθ= = (5)

( ) ; 1, 2,.......,0R G a m Mm m m nθ= =+ (6)

,0 ,0 n mG G denote path fading from SUn to BS and PUm to BS

respectively. The received signals at M antennas are weighted by using MVB weights. We define, wn as the received weight at beam former output of SUn which given as [9]-

† †21 1

Rnwn K MP R R P R Ri i i n m m mi m

γ=

+ +∑ ∑= =

(7)

Here, 2γ n is the receiver noise power. mP is the transmit power

of PUm. In the paper, a fixed value of mP is used and

iP denotes the total initial received power at base station. Since both the primary and secondary network share the same frequency band, the received signal at the secondary BS is infected by transmission of the primary users. Also the received signal at the PUs receiver is interfered by the signal transmitted by the secondary users. Considering the noise the SINR nξ of the SUn and total interference mδ at PUm are

given respectively as-

2 2w R P

w P Rn n nwn n m

nn n

ξγ

=+

(8)

2,X Pm n m mδ = (9)

Where, Pn is transmit power of SUn in the range of

,max0 n nP P< < and ,

Xn m

is the path fading from primary users

to secondary users. The probability of detection and the probability of false alarm under the energy detection scheme are given from [10]-

Pr 12 1

T fs sQd nNε ξ

ξ

⎛ ⎞⎛ ⎞⎜ ⎟= − −⎜ ⎟⎜ ⎟+⎝ ⎠⎝ ⎠ (10)

Pr 1Q T ffa s sNε⎛ ⎞⎛ ⎞−⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠ (11)

Where, ε is the decision threshold of energy detector and N the number of samples. Under the spectrum sharing access scheme, secondary users and primary users coexist in same frequency band. The primary users could either be missed detected or a false alarm may be occurred. As a result, four different cases can be distinguished regarding the sensing decision and actual status of PUn on frequency band [8]. The following four different instantaneous transmission rates of the SUn on the frequency band occur, where the first index number refers the actual status of PUm ('0' for idle and '1' for active) and the second index number refers the decision of SUn ('0' for absent and '1' for present) can be stated as in [11]-

2

log 100 2P hnc

N

⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟⎝ ⎠

(12)

2

log 101 2P hnc

N

⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟⎝ ⎠

(13)

2

log 110 2 2gm

P hncP N

⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟+⎝ ⎠

(14)

2

log 111 2 2m

P hncP g N

⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟+⎝ ⎠

(15)

Where 2h and 2g are channel power gain between the SUn

transmitter- receiver and PUm tranmitter-receiver respectively.

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The average throuhput of the channel for the sensing based spectrum sharing model can be written as-

( )( ) ( ) ( )( ) ( ) ( )( )

00

1 10 1 11

010Pr 1 Pr Pr 1 Pr

0

Pr 1 Pr Pr 1 Pr

fa

d d

T T c cs f faC

T c cf

H H

H H+

− − + − +=

− −

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟

⎝ ⎠ ⎢ ⎥⎣ ⎦

(16)

Where, r 0P (H ) denotes the probability that the channel is idle

and r 1P (H ) denotes the probability that the channel is active.

Pr f and Prd are respectively denotes the false alarm

probability and detection probability. sT is the sensing time

and fT is the frame duration.

To overcome throughput-sensing tradeoff, we propose a join beamforming and power control approach in this paper. The optimized transmit power minimizes interference to PUm with maintaining a higher SINR rate and also increases probability of detection. The throughput maximization is considered under the following condition- max

. . 0 0

CP

s t andδ δ ξ ξ≤ ≥ (17)

Where, 0δ is interference threshold to PUn and 0ξ is the SINR

threshold of secondary user. III.JOIN BEAMFORMING AND POWER CONTROL APPROACH FOR

THROUGHPUT OPTIMIZATION To reduce the interference to PUn and increase the throughput, modified water filling power control approach is introduced in [4]. In our paper, we propose a different approach which is joint beamforming and modified WLS power control .The proposed approach can further improve the throughput and can guarantee higher SINR rate. The transmission power of SU can be written as below after calculation with (8) and (9) -

0 02

0 ,

aPn

I b XN m n

δ ξ

ξ

+=

− +

(18)

,0 ,

2

,2

whereif m n

w Rb n n otherwisew Rn m

=⎧⎪⎪

= ⎨⎪⎪⎩

2†21

2†

Mw w R Pn n n m mma

w Rk k

γ + ∑==

We have to maintain the following condition to optimize the eqn. (18)-

1. ,maxPnβα

≤ (19)

Where, 0I bNα ξ= − and a0β ξ=

2. 1

0b

ξ= (20)

3. 2

, 0Xm nβ δα

≤ (21)

Considering the optimization problem, the eqn. (18) is optimized using modified WLS and can be written as -

† †

† †nP α β

α α

Ω Ω=Ω Ω

(22)

where, ( ),1M ndiag ωΩ = is a diagonal weight matrix of

size (N+K)×(N+K). The power optimization with this solution can give us significant protection to PU and improve spectrum sensing as well as maximize the average throughput of the cognitive system.

IV.SIMULATION AND RESULTS

In order to evaluate the performance of our approach, the following parameters are considered r 0P (H ) 0.8,= r 1P (H ) 0.2,= 10mP dB= , 1N = ,

sf 1MHz,= fT 100ms= . We assume that 3 SUs and 5 Pus are uniformly distributed over the service area centered at a single BS for the cognitive radio network. The BS has 10 antenna elements with carrier frequency of 600 MHz. Receiver noise

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power is -120 dBm. The initial transmit power of all SUs is 10 dB. We choose the SINR threshold for all SUs is 12 dB and maximum tolerable interference to all PUs is -100dBm. Fig.1 presents the throughput of the cognitive user in terms of

sT .The transmit power is optimized with modified WLS algorithms. It is observed that the power optimization with modified WLS algorithm give us significant improvement in the secondary system throughput. In our approach, dP

increases due to high sensing time in addition to high throughput.

Figure 1. The throghput of the cognitive systems versus the sensing time

Figure 2. The throughput of the cognitive radio versus the probability of detection of secondary system

Fig.2 depicts the achievable throughput versus the target detection probability for modified water filling approach and modified WLS approach respectively. It is observed that the achievable throughput under the modified WLS approach is higher in comparison to the convenient approach. The

Proposed approach also provides better protection to the primary users at very high target detection probabilities.

V.CONCLUSION In this paper, we use modified WLS algorithm to reduce the total interference of PUs with higher SINR rate of SUs. It is found that optimized transmit power using modified WLS algorithm improves the throughput of cognitive radio network in compare to the conventional approach. This new approach also ensures better spectrum sensing of secondary system.

REFERENCES

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[4] K. Hamdi, and K. B. Letaief, “Power, sensing time, and throughput tradeoffs in cognitive radio systems: A cross-layer approach,” in Proc WCNC’09,Budapest,Hungary,Apr.2009.

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[6] H. V. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. New York: Springer, Mar. 1998.

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[8] A. Sahai, N. Hoven, and R. Tandra, ‘‘Some fundamental limits on cognitive radio,’’ in Proc. Allerton Conf. on Commununictions, control, and computing, Monticello, Oct. 2004.

[9] U. Habiba, Z. Hossain and M.A.Matin, “A Robust Uplink Power Control for Cognitive Radio Networks”, Seventh internartional conference on wireless and optical communications networks (WOCN), 6-8 sept, 2010, pp. 1-4.

[10] Y.-C. Liang, Y. Zeng, E. C. Y. Peh, and A. T. Hoang, “Sensingthroughput tradeoff for cognitive radio networks,’’ IEEE Trans. Wireless Commun., vol. 7, no. 4, pp. 1326-1337, Apr. 2008.

[11] Stotas, S. ; Nallanathan, A. ,’’Optimal Sensing Time and Power Allocation in Multiband Cognitive Radio Networks’’, IEEE Transactions on Communications, January 2011,vol.59,no.1,pp. 226 – 235

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