Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2008, Article ID 346730, 9 pagesdoi:10.1155/2008/346730

Research ArticleAnalysis of Coded FHSS Systems with Multiple AccessInterference over Generalized Fading Channels

Salam A. Zummo

Department of Electrical Engineering, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia

Correspondence should be addressed to Salam A. Zummo, zummo@kfupm.edu.sa

Received 14 April 2008; Revised 30 June 2008; Accepted 11 August 2008

Recommended by Ibrahim Develi

We study the effect of interference on the performance of coded FHSS systems. This is achieved by modeling the physical channelin these systems as a block fading channel. In the derivation of the bit error probability over Nakagami fading channels, we use theexact statistics of the multiple access interference (MAI) in FHSS systems. Due to the mathematically intractable expression of theRician distribution, we use the Gaussian approximation to derive the error probability of coded FHSS over Rician fading channel.The effect of pilot-aided channel estimation is studied for Rician fading channels using the Gaussian approximation. From this,the optimal hopping rate in coded FHSS is approximated. Results show that the performance loss due to interference increases asthe hopping rate decreases.

Copyright 2008 Salam A. Zummo. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

A serious challenge to having good communication qualityin wireless networks is the time-varying multipath fadingenvironments, which causes the received signal-to-noiseratio (SNR) to vary randomly. One solution to fading is theuse of spread spectrum (SS) techniques, which randomizesthe fading effect over a wide frequency band. The main typesof SS are the direct sequence SS (DSSS) and the frequencyhopping SS (FHSS). FHSS is the transmission technique inBluetooth, GSM, and the IEEE802.11 standard.

In FHSS, each user starts transmitting his data over anarrow band during a time slot (called dwell time), and thenhops to other bands in the subsequent time slots accordingto a pseudorandom (PN) code (sequence) assigned to theuser [1]. Thus, the transmission in FHSS takes place overthe wideband sequentially in time. The main advantage ofFHSS is the robust performance under multipath fading,interference, and jamming conditions. In addition, FHSSposses inherent frequency diversity, which improves thesystem performance significantly over fading channels [1].Furthermore, data sent over a deeply faded frequency bandcan be easily corrected by employing error correcting codeswith FHSS systems [1]. In particular, convolutional codesare considered to be practical for short-delay applications

because the performance is not affected significantly by theframe size.

In cellular networks, multiple access interference (MAI)may arise when more than one user transmit over the samefrequency band at the same time in the uplink. This happenswhen users in closely located cells are assigned PN codesthat are not perfectly orthogonal. In this case, a collisionoccurs when two users transmit over the same frequencyband simultaneously, which degrades the performance ofboth users significantly. Also, MAI may be due to the lack ofsynchronization between users transmitting in the same cell[24]. In this case, the borders of time slots used by differentusers to hop between frequency bands are not aligned, that is,a user hops before or after other users. This case is referred toas asynchronous FHSS. The performance of channel codingwith fast FHSS and partial-band interference is well studiedin the literature as in [58]. However, not much work wasdone to investigate the performance of coding with slowFHSS and partial-band interference.

In this paper, we derive a new union bound on thebit error probability of coded FHSS systems with MAI. Weconsider FHSS systems with perfect channel estimation andpilot-aided channel estimation over Rician and Nakagamifading channels. The derivation is based on modeling theFHSS effective channel as a block interference channel

2 EURASIP Journal on Wireless Communications and Networking

U SEncoder

Channelinterleaver

Binarymodulator

FHSS

Figure 1: Block diagram of a coded FHSS transmitter.

[9]. Then, the pairwise error probability (PEP) is derivedby conditioning over the number of interfering users inthe network and then by averaging over this number. Inmodelling the MAI, we consider the exact statistics in the caseof perfect channel state information (CSI) and Nakagamifading, as well as the Gaussian approximation in the caseof imperfect CSI and Rician fading. We investigate thatthe tradeoff between channel estimation and diversity inFHSS systems is studied in order to approximate the optimalhopping rate in FHSS systems with MAI, defined as the hoperate at which the performance of the FHSS system is the bestcompared to its performance using different hopping rates.

The outline of this paper is as follows. The coded FHSSsystem model is described in Section 2. In Section 3, aunion bound on the bit error probability for coded FHSSsystems is derived for different fading statistics and channelestimation assumptions. Results are discussed in Section 4and conclusions are presented in Section 5.

2. SYSTEMMODEL

The general block diagram of a coded FHSS transmitteris shown in Figure 1. The transmitter consists of a binaryencoder (e.g., convolutional or turbo), an interleaver, amodulator, and an FHSS block. Time is divided into framesof duration NT , where T is the transmission interval of abit. Each frame is encoded using a rate Rc encoder, andeach coded bit is modulated using BPSK. Then, each frameis transmitted using FHSS, where the transmitter hops Jtimes during the transmission of a frame. Thus, the frameundergoes J independent fading realizations, where blocksof m = N/J bits undergo the same fading. In the FHSScontext, the transmission duration of m bits represents thedwell time of the system. Effectively, each packet undergoesa block fading channel [9]. Note that the frame is bit-interleaved prior to the FHSS transmission in order to spreadburst errors in the decoder.

We consider a multiple-access FHSS network of K users.The frequency band is divided into Q bands and userstransmit their data by hopping randomly from one band toanother. When more than one user transmit over the sameband simultaneously, a hit (or collision) occurs. Throughoutthis paper, we assume synchronous transmission with a hitprobability given by ph = 1/Q. Given that only k users(among the total of K users operating in the network)interfere with the user of interest, the matched filter sampledoutput at time l in the jth hop is given by

yj,l =Eshjs j,l + zj,l +

k

f=1

EIh f , j s f , j,l, (1)

where Es is the average received energy, s j,l = (1)cj,l : cj,lis the corresponding coded bit out of the channel encoder,

and zj,l is a noise sample modeled as independent zero-mean Gaussian random variable with a variance of N0/2.The coefficient hj is the channel gain in hop jwhich can bewritten as hj = aj exp( j j), where j is uniformly distributedin [0, 2) and aj is the channel amplitude.

If a line-of-site (LOS) exists between the transmitter andthe receiver, the channel amplitude is modeled as a Ricianrandom variable [10]. In this model, the received signalconsists of a specular component due to the LOS and adiffuse component due to multipath. Hence, the channelgain in each hop is modeled as CN (b, 1), where b representsthe specular component. Thus, the SNR pdf of a Ricianfading is given by

f(x) = (1 + )

exp[ (1 + )x

]

I02

(1 + )x

, x 0,

(2)

where = b2 is the energy of the specular componentand I0() is the zero-order modified Bessel function ofthe first kind. In this context, denotes the specular-to-diffuse component ratio. Another fading distribution is theNakagami distribution, which was shown to fit a large varietyof channel measurements. In Nakagami fading channels, thepdf of the received SNR [11] is given by

f(x) =(

) x1()

exp( x

), x > 0, > 0.5,

(3)

where () is the Gamma function and = 2/Var[] isthe Nakagami parameter that indicates the fading severity.

The term EI in (1) is the average received energy for eachof interfering user and s f , j,l is the signal of the f th interferinguser in the jth hop. The term h f , j denotes the channel gainaffecting the f th interfering user in hop j and modeled asCN (0, 1). We define the signal-to-interference ratio (SIR) asthe ratio = Es/EI . The SIR indicates the relative receivedenergy of each of the interfering signals to the received energyof the desired signal. The average signal-to-interference-and-noise ratio (SINR) given k interfering users is defined as

(k) = EsN0/2 + kEI

= Rcb1/2 + k

(b/

) , (4)

where b = Es/RcN0 is the SNR per information bit.The receiver employs maximum likelihood (ML)

sequence decoding which is optimal for minimizingthe frame error probability. If perfect CSI is availableat the receiver, the decoder chooses the codewordS = {s j,l, j = 1, . . . , J , l = 1, . . . ,m} that maximizesthe metric:

m(Y, S | H) =J

j=1

m

l=1Re

{yj,lh j s j,l

}, (5)

where Y = {yj,l, j = 1, . . . , J , l = 1, . . . ,m}. The metricused in the case of imperfect CSI is presented in Section 3.2in details.

Salam A. Zummo 3

3. BIT ERROR PROBABILITY

For linear convolutional codes with r input bits, the bit errorp