# PERFORMANCE ANALYSIS OF FSK MODULATION WITH LIMITER-DISCRIMINATOR-INTEGRATOR DETECTION OVER HOYT FADING CHANNELS

### Nazih Hajri, Neji Youssef

#### 2008

#### Abstract

The focus of this paper is on the performance analysis of frequency shift keying (FSK) modulation with limiter- discriminator-integrator (LDI) detection over frequency-flat Hoyt (Nakagami-q) fading channels. Specifically, a closed-form expression is derived for the probability density function (PDF) of the phase difference of Hoyt faded FSK signals disturbed by additive white Gaussian noise (AWGN). This newly derived PDF is verified to reduce to known results corresponding to the Rayleigh fading channel as a special case of the Hoyt model. The validity of the expression is further demonstrated by simulation for the case of a Hoyt mobile-to-mobile (M2M) fading channel. The analytical PDF of the phase difference is then applied to determine the bit-error probability (BEP) of the LDI receiver taking into consideration the Doppler effects, the click noise as well as the inter-symbol interference (ISI) caused by the intermediate frequency (IF) pre-detection filter. Numerical examples, assuming a Hoyt M2M channel, are given to illustrate the analysis and examine the effects of the FM system parameters and the fading characteristics on the BEP performance.

#### References

- Akki, A. S. and Haber, F. (1986). A statistical model of mobile-to-mobile land communication channel. IEEE Trans. Veh. Technol, VT-35(1):2-7.
- Ng, C. S. Tjhung,T. T. Adachi, F. and Chin, F. P. S. (1994). Closed-form error probability formula for narrow-band fsk, with limiter-discriminator-integrator detection, in rayleigh fading. IEEE Trans. Commun, 42(10):2795-2802.
- Ropokis,G. A. Rontogiannis, A. A. and Mathiopoulos, P. T. (2007). Performance analysis of space-time block coding over hoyt fading channels. Proc of the IEEE GLOBECOM 2007, pages 3416-3420.
- Gradshteyn, L. S. and Ryzhik, I. M. (1994). Tables of Integrals, Series and Products. New York : Academic, 5th edition.
- Hajri, N. and Youssef, N. (2007). Bit error probability of narrow-band digital fm with limiter-discriminatorintegrator detection in hoyt mobile radio fading channels. Proc. of the 18th Annual IEEE PIMRC 2007, pages 1-5.
- Youssef, N., Wang, C. X. and Paetzold, M. (2005). A study on the second order statistics of nakagami-hoyt mobile fading channels. IEEE Trans. Veh. Technol, 54(4):1259-1265.
- Nakagami, M. (1960). The m-distribution-a general formula of intensity distribution of rapid fading. In Statistical Methods in Radio Wave Propagation, pages 3-36.
- Pawula, R. F. (1981). On the theory of error rates for narrow-band digital fm. IEEE Trans. Commun, COM29(11):1634-1643.
- Rice, S. O. (1945). Mathematical analysis of random noise. Bell Syst. Tech. J, 24:46-156.
- Tjhung, T. T. Lye, K. M. Koh, A. K. and Chang, K. B. (1990). Error rates for narrow-band digital fm with discriminator detection in mobile radio systems. IEEE Trans. Commun, 38(7):999-1005.

#### Paper Citation

#### in Harvard Style

Hajri N. and Youssef N. (2008). **PERFORMANCE ANALYSIS OF FSK MODULATION WITH LIMITER-DISCRIMINATOR-INTEGRATOR DETECTION OVER HOYT FADING CHANNELS** . In *Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2008)* ISBN 978-989-8111-62-3, pages 177-181. DOI: 10.5220/0002025201770181

#### in Bibtex Style

@conference{winsys08,

author={Nazih Hajri and Neji Youssef},

title={PERFORMANCE ANALYSIS OF FSK MODULATION WITH LIMITER-DISCRIMINATOR-INTEGRATOR DETECTION OVER HOYT FADING CHANNELS},

booktitle={Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2008)},

year={2008},

pages={177-181},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002025201770181},

isbn={978-989-8111-62-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2008)

TI - PERFORMANCE ANALYSIS OF FSK MODULATION WITH LIMITER-DISCRIMINATOR-INTEGRATOR DETECTION OVER HOYT FADING CHANNELS

SN - 978-989-8111-62-3

AU - Hajri N.

AU - Youssef N.

PY - 2008

SP - 177

EP - 181

DO - 10.5220/0002025201770181