A new time-hopping/direct-sequence biorthogonal PPM UWB communication system
© Shen et al; licensee Springer. 2011
Received: 7 January 2011
Accepted: 31 October 2011
Published: 31 October 2011
In order to increase the capacity and diminish the multiple access interference (MAI) of an ultra-wideband (UWB) system, we propose a new time-hopping/direct-sequence (TH/DS) scheme using N-ary biorthogonal pulse position modulation (BPPM). In contrast with the conventional TH/DS systems employing fixed partition of the TH slots (Shen and Ueng, Proceedings of the IEEE VTC-Spring, 2010), the proposed TH/DS system can put the start location of the TH slot in any one of Q available pulse positions within the frame. In the proposed TH/DS system, the modulation level of BPPM can be increased and the multiple access capability can be improved without degrading the system performance. Compared with the existing TH-UWB system that employs the whole frame to carry out TH process (Shen et al. IEEE Trans. Veh. Technol. 59(2), 742-753, 2010), the proposed system has the merits of smooth power spectral density and low receiver complexity. In this article, we also derive the probability distribution of MAI for each correlator's output of the proposed TH/DS system based on the analytic characteristic function technique. In order to verify the correctness of the performance analyses and to demonstrate the effectiveness of the proposed TH/DS system, some simulation results are given in both the additive white Gaussian noise channel and the realistic UWB fading channels. From the simulation results, we find that the proposed TH/DS system outperforms the conventional TH/DS scheme.
Owing to the demand of short-range high-speed wireless data communication, the impulse radio ultra-wideband (IR-UWB) transmission which transmits extremely short impulses (referred to as monocycles) becomes an attractive technology recently . The high ratio of transmitted signal bandwidth to data signal bandwidth makes UWB technique useful for multiple access applications. The modulation schemes that consist of pulse amplitude modulation (PAM), pulse position modulation (PPM), and pulse position amplitude modulation (PPAM) are widely adopted in IR-UWB systems. PPM and PAM modulations use the precise position and amplitude of impulses, respectively, to convey data message, while PPAM exploits both the position and amplitude of mono-cycle to carry information. N(= 2M)-ary biorthogonal PPM (BPPM) which combines binary PAM and M-ary PPM is a special case of PPAM. Under the same throughput, N-ary BPPM can provide better performance and less complexity than those of M-ary PPM [2, 3].
The time-hopping (TH) and direct sequence (DS) multiple access schemes are applied in IR-UWB systems. In the conventional TH UWB system, each symbol duration is divided into N s frames, and each frame interval is divided into N c time slots (chips). A data symbol is modulated based on the adopted modulation scheme to transmit one pulse in each frame duration. Afterward, the position of the time slot in each frame on which the modulated pulse is located is selected and hopped from frame to frame according to the pseudorandom TH code. However, the use of PPM and/or PAM signaling in conventional TH system has one disadvantage that the line spectral occurs in the spectrum of the transmitted signals. This is because the same polarity (unipolar) of monocycles are transmitted in a given symbol period. To alleviate the effect of this problem, the conventional TH systems exploiting the randomized polarity (bipolar) of the transmitted pulses, also called the hybrid TH/DS system, are studied in [3, 4]. The selections of the user-specific TH codes, corresponding to the utilized time slots, and the polarity (DS) codes are well designed to mitigate the multiple access interference (MAI) and improve the system capability.
In asynchronous MA environment, the collisions of the received pulses from different users are inevitable because of the randomness of time misalignment among the received signals of all the users. Compared with binary modulation, it is well known that N-ary biorthogonal modulations are able to provide higher throughput and better BER performance, as the modulation level is increased . The benefit of the proposed TH scheme is able to increase the modulation level of N-ary BPPM signaling without decreasing the number of TH slots. Consequently, the proposed TH method employing larger modulation level can carry more information bits in a symbol duration and then improve the system throughput. At the transmitter of the proposed TH/DS system, the TH-coded symbol sequence of each user is first generated according to the specific TH code (hopping pattern) and becomes as the input of N-ary BPPM modulator which also applies specific DS code to randomize the polarity of the modulated pulses. The proposed TH technique has been widely employed in the frequency-hopping (FH) system which combines a larger modulation level of M-ary FSK modulation and provides better performance [6, 7].
For the conventional TH-UWB systems with binary PAM and/or PPM modulations in asynchronous MA scenarios, the performance analyses have been extensively investigated in [4, 8–15]. For the conventional TH-UWB systems with M-ary orthogonal PPM and N-ary biorthogonal PPM modulations, some relative studies have been reported in [16–20] and [2, 21]. The Gaussian distribution assumption can be adopted to model the MAI statistics to derive some simple theoretical analyses for the binary PPM, M-ary orthogonal PPM and N-ary biorthogonal PPM signaling [2, 8–10, 16]. However, if we consider the medium and high signal-to-noise ratio (SNR) conditions, the Gaussian approximation (GA) fails to model the statistics of MAI precisely [4, 11–13, 18, 20]. The exact expression of the cumulative distribution function (CDF) of the MAI is inconsistent with that obtained by using the GA. Hence, using GA leads to inaccurate error probability analysis and also leads to optimistically overestimate the system performance. By deriving the characteristic functions (CF) of the MAI, the accurate performance analyses of binary PPM/TH, M-ary orthogonal PPM/TH and N-ary BPPM/TH/DS UWB systems were proposed in [3, 12–14, 20]. In this article, the analytic CF expression of the MAI is derived and the performance analyses of the proposed TH/DS-UWB system is then obtained.
The rest of this article is organized as follows. The conventional and the proposed TH/DS systems with N-ary BPPM are described in Section 2. In Section 3, the analytic expression of the probability distributions of MAI and the average symbol error rate (SER) of the proposed TH/DS system is derived. Some numerical examples and discussions for the proposed system are presented in Section 4. Finally, we give some conclusions in Section 5.
2 System model
where Es is the average symbol energy which is assumed to be the same for all the users' signals, N s is the number of transmitted pulses required to represent one symbol of message, is the j th element of the k th user's TH code, and is the j th element of the k th user's random polarity code (or random DS spreading code). To reduce the effect of MAI, it can be well designed to assign the specific random TH code and random polarity (DS) code to the k th user. δ denotes the time shift between two adjacent positions for the BPPM signals and is selected to be the pulse width T p due to the assumption of orthogonal BPPM signaling. Therefore, the chip duration on which a M-ary PPM signal is located is equal to T c = MT p . It is worthy to note that each frame duration is partitioned into N c non-overlapped time (chip) slots, the pulse positions of the N s transmitted BPPM signals in the N s selected chip slots are the same and are illustrated in Figure 1a.
For UWB systems, several pulse waveforms have been proposed. The normalized second-order Gaussian monocycle, p(t) = [1 - 4π (t/τ p )2] exp [-2π (t/τ p )2], which has been widely applied in many studies of the literature is adopted in this article as data bearing waveform. The duration of the normalized second-order Gaussian monocycle is T p . In addition, the normalized autocorrelation function of p(t) is defined as [8, 12].
3 Performance analysis
It is worthy to note that the CF of the MAI component for each correlator's output of the proposed TH/DS receiver is di¤erent from that of the conventional TH/DS system which has been shown in .
3.1 Symbol error rate
If all M - 1 erroneous symbols are equally likely chosen, then the corresponding BER is P b = M · P e /[2 · (M - 1)] .
4 Simulation results
A new TH/DS UWB system employing the whole frame to carry out TH and N-ary BPPM is proposed in this article. According to the derived CF expression of the MAI, a simple SER analysis of the proposed TH/DS system using N-ary BPPM is obtained in the presence of asynchronous MAI and AWGN. The proposed SER performance analysis is shown to be consistent with the simulations. From the simulation results, the proposed TH/DS system is shown to outperform both the conventional TH/DS system and the DS UWB systems.
The authors declare that they have no competing interests.
This study was supported in part by the National Science Council of Taiwan under Contract NSC 99-2221-E-150-042.
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