Soft-Decision Cognitive Radio Power ControlBased on Intelligent Spectrum Sensing

Rajgopal Kannan†, Zhiqiang Wuα, Shuangqing Wei‡ , Vasu Chakravarthyβ , Murali Rangaswamyθ

†Dept. of Computer Science, Louisiana State University, Baton Rouge, LA 70803αDept. of ECE, Wright State University, Dayton, OH 45435

‡Dept. of ECE, Louisiana State University, Baton Rouge, LA 70803βAir Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, OH 45433

θAir Force Research Laboratory, Hanscom Air Force Base, MA 01731

I. ABSTRACT

We formulate an expression for the channel capacity ofa soft-decision cognitive network in which cognitive radiotransmitters can share spectrum usage with primary users de-pending on adaptive interference tolerance limits. We considerthe problem of capacity maximization in this domain andprovide an efficient polynomial time algorithm for cognitiveradio power control. Results obtained using this algorithm willbe useful in soft-decision spectrum allocation for cognitiveradio (CR) transmitters as well as for developing the generalanalytic enabling waveform for soft-decision CR described in[6].

II. MOTIVATION

In current cognitive radio, the transmitter continuously mon-itors the radio spectrum and dynamically identifies frequencybands into two categories: used bands or unused bands [1], [2],[3]. In other words, the cognitive radio makes the usability ofone frequency band by employing a hard decision based onspectrum sensing result. However, the coexistence of UWBtransmission and primary users indicates that all the primaryusers’ transmissions can tolerate some level of interference.Hence, we can further increase the channel capacity of cogni-tive radio by making a soft decision on the usability of everyused band. In particular, if we can determine the interferencetolerance level of each primary user, the cognitive radio cantransmit over both unused and used bands to optimize spec-trum usage and maximize the channel capacity. For example,in previous works [4], [5], a multi-carrier platform that notonly transmits over unused spectrum ”holes”, but transmitsover underused spectrum blocks as well, while minimizinginterference to existing primary narrowband transmissions ispresented.

This work was supported by NSF grants IIS-0329738, ITR-0312632 andby AFRL under contract #F33615-02-D-1283 (sub #05-2D1005.001). Theopinions expressed herein are those of the individual authors and independentof the sponsoring agencies.

III. PROBLEM FORMULATION AND RESULT

Using Shannons well-known channel capacity equation,C = W log (1 + S/N) for transmission over a bandwidthW , we can obtain the channel capacity of cognitive radiotransmission over multiple frequency bands as:

CCR =N∑

k=1

Wuklog

(1 +

ΦCRk

n0

)(1)

where N is the total number of unused bands in the entirebandwidth W , Wuk

is the bandwidth of the kth unusedband, ΦCRk

is the power spectrum density of cognitive radiotransmission on the kth unused band. It is evident that incognitive radio transmission, the total bandwidth exploited isless than the total bandwidth W . However, since (1) there isno interference from primary users to cognitive radio and (2)there is no limit in the cognitive radio transmission powerspectrum density ΦCRk

except the interference temperature,the signal to noise ratio is much improved (compared to UWBtransmission).

Now consider a soft-decision cognitive radio where thetransmitter can transmit over unused as well as underused (byprimary receivers) bands subject to interference constraints.Assume the interference tolerance level (the maximum allowedinterference power spectrum density) of the ith used bandis Ii. Current cognitive radio assumes that Ii = 0, i.e., notransmission is allowed if the band is being used. Employingknowledge of the interference tolerance level Ii, the channelcapacity of such a proposed system, assuming only oneCognitive Radio transmitter per band, is given by,

Cnew =N∑

i=1

Wuilog

(1 +

ΦCR1i

n0

)+

M∑i=1

Wpilog

(1 +

ΦCR2i

n0 + Φpi

)(2)

where the first sum term stands for the rate achievable overthe bands without primary users, while the second termis the achievable rate when cognitive radio transmits over

1-4244-1276-5/07/$25.00©2007 IEEE 193 2007 Waveform Diversity & Design

those bands already occupied by primary users. ΦCR1iis the

cognitive radio transmission power spectrum density on the ith

unused band, and ΦCR2iis the cognitive radio transmission

power spectrum density on the ith used band. Φpiis the power

spectral density of the primary user over the bandwidth Wpi.

In a companion paper [6], we design an enabling waveformthat combines the overlay and underlay waveforms for the un-used and underused portions of the cognitive radio spectrum,respectively. This general spectral coded waveform supportsthe soft-decision cognitive radio concept just described. Inorder to develop this waveform, we need to determine themaximum available channel capacity for a transmitter underthe soft-decision cognitive framework. Maximizing the chan-nel capacity of the proposed system leads to the followingoptimization problem:

max Cnew, s.t

ΦCR2i≤ Ii,∀i (3)

ΦCR1i≤ φi,∀i (4)

N∑i=1

ΦCR1iWui

+M∑i=1

ΦCR2iWpi

≤ S (5)

where φi is the maximum allowed transmission power spec-trum density (e.g., FCC mandated interference temperature) atthe ith unused band and S the total transmission power.

In this paper, we present a fast polynomial time algorithmfor solving this optimization. Results obtained using thisalgorithm will be useful in soft-decision spectrum allocationfor cognitive radio transmitters as well as for developingthe general analytic enabling waveform for soft-decision CRdescribed in [6]. Assuming Φpi

, the power spectral density ofthe primary is fixed, the solution to the above optimization isas follows:

1) Initialize all values ΦCR2j= 0 and ΦCR1j

= 0i,∀j.2) Construct the two lists

L1 = {Wuilog

(1 +

1Wui

n0

)}, i = 1, . . . , N

and

L2 = {Wpilog

(1 +

1Wpi

(n0 + Φpi)

)}, i = 1, . . . , M

for unused and used bands respectively.3) Sort L1 and L2 in non-increasing order and merge the

two lists. Let L = {l1, l2, . . . , lN+M be the resultantsorted list.

4) Starting from the front of list L, (i.e j = 1, 2 . . .), forthe jth element set ΦCR2j

= Ij if lj corresponds to aused band or set ΦCR1j

= φi if lj corresponds to an

unused band. Compute S′ =j∑

i=1

ΦCRiWi, where ΦCRi

and Wi are chosen appropriately depending on whetherli is a used or unused band.

5) If S′ < S, then choose j = j +1 and go back to step 4.6) If S′ ≥ S, reduce ΦCRj

such that S′ = S, set ΦCRk=

0,∀j < k ≤ N + M and exit.

REFERENCES

[1] FCC Spectrum Policy Task Force, Rep. ET Docket no. 02-1935, 2002.[2] SPTF, ”Report of the Spectrum Efficiency Working Group”, November,

2002.[3] J. Mitola, ”Cognitive Radio: An Integrated Agent Architecture for

Software Defined Radio”, Ph.D. dissertation, KTH Royal Institute ofTechnology, Stockholm, Sweden, 2000.

[4] S. Hijazi, B. Natarajan, M. Michelini, Z. Wu, ”Flexible Spectrum Useand Better Coexistence at the Physical Layer of Future Wireless Systemsvia a Multicarrier Platform”, IEEE Wireless Communications, April2004, Vol.11, No. 2, pp. 64-71.

[5] Z. Wu and C. R. Nassar, ”Narrowband Interference Rejection in OFDMvia Carrier Interferometry Spreading Codes”, IEEE Transactions onWireless Communications, Vol.4., No.4, pp. 1491-1505, July 2005.

[6] V. Chakravarthy et al, ”A General Overlay/Underlay Analytic Expres-sion Representing Cognitive Radio Waveform”, in 2007 InternationalWaveform Diversity and Design Conference, Italy, June 2007.

1-4244-1276-5/07/$25.00©2007 IEEE 194 2007 Waveform Diversity & Design