Analytical Mathematical Expression for the Channel Capacity of a Power and Rate Simultaneous Adaptive Cellular DS/FFH-CDMA Systemin a Rayleigh Fading Channel

In this paper, an accurate theoretical analysis for the achievable average channel capacity (in the Shannon sense) per user of a hybrid cellular direct-sequence/fast frequency hopping code-division multiple-access (DS/FFH-CDMA) system operating in a Rayleigh fading environment is presented. The analysis covers the downlink operation and leads to the derivation of an exact mathematical expression between the normalized average channel capacity available to each system-s user, under simultaneous optimal power and rate adaptation and the system-s parameters, as the number of hops per bit, the processing gain applied, the number of users per cell and the received signal-tonoise power ratio over the signal bandwidth. Finally, numerical results are presented to illustrate the proposed mathematical analysis.

• P.Varzakas

• Shannon capacity
• adaptive systems
• code-division multiple access
• fading channels.

[1] A.J.Goldsmith, "The Capacity of Downlink Fading Channels with
Variable Rate and Power", IEEE Trans. on Veh. Technology, vol.
46, no. 3, pp. 569-580, Aug. 1997.
[2] M.K.Simon and M.S.Alouini, Digital Communication over Fading
Channels: A Unified Approach to Performance Analysis, New
York: John Wiley, 2000.
[3] A. Goldsmith and P. Varaiya, "Capacity of fading channels with
channel side information", IEEE Trans. on Inform. Theory, vol. 43,
no.6, pp. 1986-1992, Nov. 1997.
[4] P.Varzakas and G.S.Tombras, "Spectral efficiency for a hybrid
DS/FH CDMA system in cellular mobile radio", IEEE Trans. on
Vehicular Technology, vol. 50, no.6, pp. 1321-1327, Nov. 2001.
[5] M. S. Alencar and I.F. Blake, "The capacity for a discrete-state
Code Division Multiple Access Channel", IEEE J. Select. Areas
Commun., vol. 12, no.5, pp. 925-937, June 1994.
[6] N.Livneh, R.Meidan, M.Ritz and G.Silbershatz, "Frequency hopping
CDMA for cellular radio", Proc. International Commsphere
Symposium, Herzilya, Israel, pp.10.5.1-10.5.6, Dec. 1991.
[7] R.G.Gallager, Information Theory and Reliable Communication,
John Wiley & Sons, 1968.
[8] C.D-Amours and A.Yongacoglu, "Hybrid DS/FH-CDMA System
Employing MT-FSK Modulation for Mobile Radio", PIMRC-95,
pp. 164-168, Sept. 27-29, Toronto, Canada.
[9] K.S.Gilhousen, I.M.Jacobs, R.Padovani, A.Viterbi, L.A.Weaver
and C.E.Wheatley, "On the capacity of a cellular CDMA system",
IEEE Trans. on Veh. Technology, vol. 40, pp.303-312, 1991.
[10] J.G.Proakis, ÔÇÿDigital Communications-, 4th Edit., McGraw-Hill,
2001.
[11] P.Varzakas and G.S.Tombras, "Average channel capacity for
RAKE receivers", IEE Electronics Letters, vol. 38, no.10, pp. 475-
476, May 2002.
[12] Y.Murata, R.Esmailzadeh, K.Takakusaki, E.Sourour and
M.Nakagawa, "Path diversity for FFH/PSK spread-spectrum com
munication systems", IEEE J. Sel. Areas in Commun., vol. 12,
no.5, pp. 970-975, June 1994.
[13] W.C.Y.Lee., Mobile Communications Design Fundamentals, 2th
Edit., New York: Wiley, 1993.