Performance of optimum wavelet for DS‐CDMA chip waveform over multi‐path Rayleigh fading channels

Abstract

In this paper, the probability of error ðP e Þ expression of asynchronous direct sequence-code division multiple access (DS-CDMA) signals using band-limited chip waveforms is derived over multi-path Rayleigh fading channels. In receiver, a matched filter-based rake receiver in conjunction with maximum ratio combiner (MRC) is considered. Numerical values for the P e are calculated for various chip waveforms including an optimum wavelet waveform. Analytical results are verified by conducting simulations. Results show that the optimum wavelet-based scheme outperforms time-limited raised cosine, half sine, rectangular and band-limited square-root raised cosine chip waveform-based schemes in terms of the P e and the capacity defined as the number of users per Hertz for a same P e level. of information. Each digit of the spreading codes is encoded by a pulse shaping waveform called chip waveform. Chip waveforms are continuous-time waveforms. It was shown by Lehnert and Geraniotis and Pursley [2, 3] that the multiple access interference (MAI) of DSSS communication systems depended on the actual shape of chip waveform as well as its energy. Besides, the bandwidth of the chip waveform determines the bandwidth of DSSS signals [2]. Since the MAI degrades the probability of error ðP e Þ performance for DS-CDMA-based systems, the performance can be improved by selecting a proper chip waveform. The selection of the chip waveform has become the subject of many researches [2][3][4][5][6][7][8][9][10]. In these works, the time-limited chip waveforms (limited to one chip interval) are considered. For the time-limited chip waveforms, only two neighbour chip waveforms overlap. In such a case, partial crosscorrelation function (PCF) derived by Lehnert and Geraniotis and Pursley [2, 3] is used to determine the MAI and the P e expressions over asynchronous and multi-path fading channels. In a recent work [11], the design of time-limited chip waveforms used with low pass filters at both transmitter and receiver to obtain band-limited transmitted signal is considered. However, nontime-limited (i.e. band-limited) pulse shaping waveforms, the durations of which are greater than one chip interval, are recently considered as chip waveforms: band-limited square root raised cosine (SRRC) chip pulse is used as the chip waveform in standardized wide-band CDMA-based 3G cellular systems [12], and the future systems will also consider such chip waveforms due to their compact bandwidths. For band-limited chip waveforms, the PCF derived by Lehnert and Geraniotis and Pursley [2, 3] cannot be used, because multi-chip waveforms overlap in time. In [13,14], the P e of DS-CDMA signal over asynchronous channels is derived for band-limited chip waveforms. In these works [13,14], the effects of multi-path fading are not considered.Orthogonal wavelets have been used as pulse shaping waveforms of digital symbols in [15][16][17][18][19][20][21]; however, there are few studies for the use of continuous time wavelet waveforms as the chip waveforms of DS-CDMA sign...

Comparisons of various pulse shapes for DS-UWB signals over the UWB channel

“…In bipolar DS-UWB systems, the transmitted signal is similar to that of BPSK/DS-CDMA systems described in Öztürk andŞahin [17], Öztürk [18] except there is no carrier signal, and for a total of U users it is given by…”

“…In this study, the considered receiver is a match filters based Rake receiver similar to that in Öztürk andŞahin [17]. Since the bandwidth of the transmitted signal is UWB, the number of resolvable paths is quite large.…”

“…In the MRC, the branches of rake receiver are weighted for maximum SNR, and decision is made based on the combined signal. Based on the similar assumptions for the Rake receiver in Öztürk andŞahin [17], the SNR γ 1 r at the output of the reference finger r {r ∈ 0, 1, 2, . .…”

“…where the parameters are defined similarly to those in Öztürk andŞahin [17], Öztürk [18]: for all u and n are also i.i.d. equally probable binary real chips {+1, −1}.…”

Performances of DS-UWB signals over the CM1 channel model

“…The MRC combines the L f outputs. Since the bipolar DS-UWB signal in (1) is similar to a BPSK/DS-CDMA signal, the Signal to Noise Ratio (SNR) 1 r γ at the output of the reference path can be derived by following a similar procedure in [12] and obtained as ( ) ( )…”