ISSN 0032-9460, Problems of Information Transmission, 2008, Vol. 44, No. 2, pp. 91–98.
Pleiades Publishing, Inc., 2008.
Original Russian Text
V.V. Zyablov, D.S. Osipov, 2008, published in Problemy Peredachi Informatsii, 2008, Vol. 44, No. 2, pp. 23–31.
On the Optimum Choice of a Threshold
in a Frequency Hopping OFDMA System
V. V. Zyablov and D. S. Osipov
Kharkevich Institute for Information Transmission Problems, RAS, Moscow
Received November 20, 2007; in ﬁnal form, February 7, 2008
Abstract—We consider a frequency hopping orthogonal frequency-division multiple access
(FH OFDMA) system diﬀerent from those previously described. To ﬁnd the probability density
function of the variable used by the detector, we propose an approach based on the characteristic
function method and Bessel function technique. Based on this approach, we obtain an expres-
sion for the desired density function (in the most probable case of a collision of multiplicity two)
and an expression for the optimum threshold value, which enables us to compute it to any de-
sired degree of accuracy. Eﬃciency of our approach is justiﬁed by simulation results.
Owing to the rapid progress in telecommunication, multiple access systems are presently widely
studied. One of the most eﬃcient user separation methods in multiple access systems is frequency
hopping in an OFDM system . In the present paper we use a data transmission method similar
to that used in . A distinction from  is that here we consider a system using not amplitude
modulation but frequency shift keying. Frequency hopping (assigning subcarriers to users) can be
either coordinated (this means that when choosing a code sequence for each user, we use knowledge
about other users; therefore, this scheme is mostly used for transmission from a base station to
users) or uncoordinated. The uncoordinated frequency hopping has a number of advantages (allows
to realize random multiple access, is well protected from eavesdropping or malicious silencing, and
does not require elaborated protocols, which are inevitable in a system with centralized subcarrier
assignment) and is used, as a rule, for transmission from a user to a base station.
We shall consider transmission to a base station, and hence uncoordinated subcarrier assignment
strategies. In turn, these strategies can be divided into two groups. Methods of the ﬁrst group
exploit code sequences specially designed for multiple access systems and conforming to certain
requirements. The second group includes methods where subcarrier numbers are assigned to users
pseudorandomly. A detailed description of a variant of such a scheme is given in . In this
system, each user randomly chooses q subcarriers of the whole set of Q subcarriers available to
users. If at some time instant a subcarrier is simultaneously used by more than one user, this
subcarrier is regarded as “faulty” at that instant. As is seen from simulation results presented
in , this scheme realizes multiple access with high average transmission rate.
In the present paper, we consider a multiple access system where user separation is based on
using random sequences of orthogonal frequencies; it is diﬀerent from the above-mentioned ones
and can be viewed as a development of ideas underlying the system described in . In Section 2
Research done under State Contract no. 02.514.11.4025 of May 1, 2007.