**Abstract.** The dependency of an average
probability of correct detection upon the parameters of the multipath fading
channel is studied on the example of an energy-based scheme for white space
detection in cognitive radio systems. The *k-**μ* and *
η-µ* composite channel models (which are
the generalization of a wide variety of existing models, like Rayleigh, Rice,
Nakagami, Hoyt, log-normal, one sided normal, etc) are used. For the case of integer-valued
parameters we obtained closed analytical expression for averaged probability of
detection. This expression was obtained on the base of earlier solution for
more general channel model which takes into account possible loss of visibility
(shadow effects). A numerical analysis (with subsequent physical interpretation)
is carried out for the dependence of signal-to-noise ratio, which is required for
correct detection probability on the 0.9 level, upon the parameters of the considered
models: the number of multipath clusters *µ* (which represents multipath
clustering effects) and the ratio between the total power of the dominant
components and the total power of the scattered waves *k* for *k-**μ*; the ratio between in-phase and
quadrature components *η* and the number of multipath clusters *µ*
for *η-µ*; number of degrees of freedom *u* (a parameter of the
energy-based detection scheme). The performed study of the parameters’ joined
influence upon the channel characteristics can be used at the channel
estimation stage (for further compensation or equalization).

**Key words: **
energy detection,
probability of detection, multipath fading

1. Guryanov I.O. Cognitive
radio: new approaches in providing with a radio-frequency resource of perspective
radio technologies *ELEKTROSVYAZ*, 2012, No. 8, pp. 5-8. (In Russian)

2. Axell E., Leus G., Larsson
E.G., Poor H.V. Spectrum Sensing for Cognitive Radio: State-of-the-Art and
Recent Advances IEEE Signal Processing Magazine, 2012, Vol.29, No. 3,
pp.101-116. DOI: 10.1109/MSP.2012.2183771

3. Wang W. Cognitive Radio
Systems, In-Tech, 2009. 340 p. DOI: 10.5772/7842

4. Zeng Y., Liang Y.-Ch.,
Hoang A.T., Zhang R. A Review on SpectrumSensing for Cognitive Radio:
Challenges and Solutions *EURASIP* *Journal on Advances in Signal
Processing*, 2010, Vol. 2010, No. 1, pp.101-116. DOI: 10.1155/2010/381465

5. Khatib M. Advanced Trends
in Wireless Communications, In-Tech, 2011. 520 p. DOI: 10.5772/15028

6. Yacoub M. D. The *α-μ*
distribution: A physical fading model for the Stacy distribution *IEEE Transactions
on Vehicular Technology*, 2007, Vol. 56, No 1, pp. 27-34. DOI**: **10.1109/TVT.2006.883753

7. Yacoub M. D. The *κ-µ* distribution and the *η-µ* distribution *IEEE Antennas and
Propagation Magazine*, 2007, Vol. 49, No. 1, pp. 68-81. DOI: 10.1109/MAP.2007.370983

8. Yilmaz F., Alouini M.-S.
Product of the powers of generalized nakagami-m variates and performance of
cascaded fading channels *Proceedings of IEEE Global Telecommunications
Conference. *Honolulu, Hawaii, US. Nov. 30 – Dec.
04, 2009. Pp. 1–8. DOI: 10.1109/GLOCOM.2009.5426254

9. Sofotasios P. C., Freear
S. *The k-μ/gamma composite fading model Proceedings of IEEE
International Conference on Wireless Information Technology and Systems
(ICWITS)*. Hawaii, USA. Aug. 28 – Sept. 3, 2010. DOI:
10.1109/ICWITS.2010.5611885

10.Rabelo G. S., Yacoub M. D.
The *k-μ* Extreme Distribution* IEEE Transactions on Communications*,
2011, Vol. 59, No. 10, pp. 2776–2785. DOI: 10.1109/TCOMM.2011.081211.090747

11.Urkuwitz H. Energy
Detection of Unknown Deterministic Signals *Proceedings of the IEEE*,
1967, Vol. 55, No. 4, pp. 523-531. DOI:
10.1109/PROC.1967.5573

12.Shahtarin B.I.
Obnaruzhenie signalov: uchebnoe posobie dlya vuzov. [Signal
detection: university text edition]. Moscow, Goryachaya Liniya –
Telecom Publ. 2014. 526 p. (In Russian)

13.Shellhammer S. Performance
of the Power Detector IEEE 802.22-06/0075r0, May, 2006.