The Wavelet Packet (WP) Multicarrier (MC) Multicode (MCD) Code-Division Multiple-Access (CDMA) systems in [1] and [2] uses WPs as subcarrier instead of sinusoidal one. Since WPs have much lower sidelobes with negligible sidelobe energy leakage compared with sinusoid carriers, it can mitigate the problem of inter-carrier interference (ICI) and multiple access interference (MAI). Also, WPs are naturally orthogonal and well localize in both time and frequency domain, which relaxes the requirement of frequency or time guard among different user signals.

It is well known that the inherent processing gain of CDMA system will, in many cases, provide the system with a sufficient degree of narrow-band interference rejection capability. However, if the interference signal is powerful enough, the conventional receiver is ineffective in mitigating this problem. Interference suppression filter (SF) can be employed to reject the narrow-band interference. A wiener-type filter, described in [3] , employs a tapped delay line structure to first predict and then subtract out the narrow-band interference. The technique of diversity combining can provide an attractive means for improving system performance by utilizing the signal components of different uncorrelated paths.

In this paper, the WP-MC/MCD-CDMA overlayed with a narrow-band interference binary phase shift keying (BPSK) waveform is analyzed. It is shown that the system performance is improved when the receiver consists of SF combined with diversity. The performance of the system is compared with the Sinusoidal (Sin) based multicarrier multicode CDMA system denoted as Sin-MC/MCD-CDMA.

The transceiver block diagram for the system under consideration is shown in Figure 1. The transmitter consists of two parts, multicode part and wavelet packet part, while the receiver consists of a bandpass filter (BPF), tap suppression filter, correlators (multicode and wavelet packet) and the diversity combiner. At the transmitting

side for the user, the bit stream with bit duration is serial-to- parallel (S/P) converted into J parallel substreams. To reduce the inter-

substream interference (ISSI) resulting from the interference between the J substreams themselves, each sub-

stream with bit duration is coded by an orthogonal signal, where is the code length and is the chip duration. To maintain orthogonality of the coding signals, the maximum number of substreams J is limited to. The coded substreams are added and the resulting signal is again S/P converted into H superstreams,. The next step is the spreading of the H coded superstream by which is the pseudo-random noise (PN, processing gain) sequence of the user. The length of code and chip duration are and, respectively. Note that, and which are the bits with probabilities. The spreading superstreams will be used to modulate a wavelet packets, where is as given in [1] . The resultant superstreams are summed up and modulated by a sinusoidal

carrier, , before being transmitted. The wavelet packets with different h indices represent different subbands, thus the bandwidth of each subband can be arbitrarily chosen due to flexibility of the wavelet packets. Also, the whole signal spectrum is separated into H disjoint subbands. The partition of subbands are not limited by a minimum frequency distance but is determined by the channel characteristic. Furthermore, the energy of is unity. The transmitted signal for the of the user can be written as [1]

where with period T is the data symbol of user, substream of the superstream. The equivalent impulse response for the channel used in this paper can be written as,

where L is the number of propagation paths, , and are respectively, the path gain, the phase delay and the time delay of path of the user. The phase is assumed to be uniformly distributed over

. The path gain model and distribution function depend on the nature of the channel and the propagation environment. We assume that the channel path gain is Nakagami distributed [4] . The output of the channel

for the user,.

The receiver shown in Figure 1 is assumed to be synchronous, designed to detect the first substream of the first user’s first wavelet packet propagating via the first path. The received signal, , is given by

where and are the inphase part and quadrature part of, respectively, and is the AWGN. The BPSK narrow-band interference jammer, is given by:

where is the jammer power, is the offset between the jammer carrier and the signal carrier and is the jammer phase. The information sequence has a bit rate where denotes the duration of one bit. The interference bandwidth is, we assume. An important quantity is the ratio of the

interference band to system bandwidth. The received signal is first passed through the BPF

having band width equal to the spread spectrum (SS) bandwidth =, which removes the out-of band noise and let the desired signal and inferences pass without distortion. The filtered signal is then passed through

a suppression filter which has an impulse response given by where and

(&) which are represent the number of taps of the filter on the left and right of the center tap [3] . For each tap, the output of the filter is given by:

where K is the total number of users, and is the filtered AWGN.

The output of the filter, , is demodulated by a local oscillator, despread by a user specific code sequence, multiplied by the wavelet packets and correlated over a period T to recover the super bit stream. The resulting data is then parallel-to-serial (P/S) converted again, despread by the code correlated over a period T, and then combined by diversity combiner. Finally, each combiner output for J substreams is P/S converted to recover. The output of the first correlator in the wavelet packet part denoted as can be written as

where is the desired signal, is the self interference, is the multipath interference, is the multicode interference, is the wavelet packets interference, is the multiuser interference,

is suppressed correlated AWGN and is the suppressed narrowband interference. The output signal of first converter for the first user's may be written as

The output for the first correlator in the multicode part is given by

After evaluation it can be shown that

and

where , ,

are the previous data bit and current data bit, respectively; with for inphase part, for quadrature part. is the discrete-time aperiodic cross-correlation function defined in [5] and is given by

The value of the four components, , and can be written as given in ( [1] , Chapter 4) as follows:

where

where, are the partial cross-correlation functions;, are the inphase part of previous data bit and current data bit, respectively;, are the quadrature component

of previous data bit and current data bit, respectively. Following the definition in [5] and [6] , the partial cross-correlation functions and, can be written as follows:

Also and are the partial cross-correlation functions defined in [5] as follows

The suppressed correlated AWGN component is given by

and the suppressed narrow-band interference is given by

To find the signal-to-noise plus interference ratio (SNIR), we need to find the desired signal power, interfer- ences, noise and jamming variances. From (8), the desired inphase signal power S is given by

To calculate the variances, it is assumed that all the interferences, noise and jamming terms are zero mean independent random variables (RV). The process of computing the variances for the different interference terms

is quite involved. Fortunately, the variances, , , and for a system without sup-

pression filter have been computed in [1, Chapter 4]. Without loss of generality, we invoke the result in [1] and [3] for the above variances with suppression filter, which is given by

where

with for QPSK and for BPSK, , Q represents the sum of amplitude levels of all multipath components, is the mean received symbol energy. Note that in the derivation of the

variances it is assumed that the variation in and is very small and can be ignored for all K users and L paths; and that the variances are independent of k, h and j. The variance for the inphase self interference is given by

Assuming that is a zero means RV uniformly distributed in

Also, it is evident that

And from [3]

According to this, (19) become

where for QPSK and BPSK.

From (15), the inphase component of the narrow jamming signal is given by

The variance can be evaluated as follows:

After certain evaluation it can be shown that

where is given in (19) [3] by

given that (ratio of the offset of interference carrier frequency to half SS bandwidth) and or zero for or, respectively. Accordingly, the total variance for noise and inter- ference is given by

where

and. Therefore, the output SNIR, , can be written as

It is shown in [3] that the coefficients of the suppression filter can be determined using

is a lowpass autocorrelation function consists of three components

where is the lowpass version of the desired signal, is due to noise and is due to narrowband interference. The is given by

Since when or. Further more

then

The and are given in [3] by

where is defined as the integer part of x and. Therefore from (28), (29) and (30), one obtains

From (25) and (31), we can obtain the coefficients.

A common method used to measure the performance for communication systems is, the average bit error rate,. It is obtained by averaging the instantaneous bit error rate (BER) of SNIR, over the channel fading functions.

In practical applications, in order to correctly detect a transmitted signal, the error probability of the received signal must not exceed a specified value. The output SNIR, must be above a certain specified threshold, say. This is quantified by the outage probability, which represents the probability of unsatisfactory reception of the signal over the intended coverage area. In this paper, we define the as the probability that falls

below ( [7] , p. 5), i.e..

and depend on the method of diversity combining employed, as shown below.

In this section, using the above analytical results, the BER performance and the of the system in the presence of narrow-band interference are presented. The effects of changing the system parameters such as the numbers of SF taps, q, p, D, m and the length of code are investigated. Finally, the BER performances of the system and Sin-MC/MCD-CDMA system are compared. Unless otherwise mentioned the parameters listed in Table 1 are used for the simulation in this section by means of the MATLAB program.

The BER and outage performance of a WP-MC/MCD system overlaying a narrow-band BPSK waveform and employing SF in the receiver has been evaluated. It is found that the performance is improved by using SF and diversity. The double-sided SF is superior to single-sided SF for the same number of total taps. The MRC has

better performance than SD and EGC. The performance of the system is improved by increasing the diversity order and the fading parameter. The performance of the system is improved when p increased. The system has the best BER when. Our system uses SF and diversity to suppress the narrow-band interference and MAI, respectively, more efficiently than does the Sin-MC/MCD-CDMA system.

The authors are grateful to Applied Science Private University, Amman, Jordan for financial support granted to cover publication fee of this research article.