Keywords

UWB, Probability of error, THPPM modulation, THBPSK modulation 
INTRODUCTION

UWB is a novel technology emerging in recent years as a promising solution for high speed or low power indoor communications. Indeed, this technology offers the potential for robust communications in multipath and multiuser environments, as well as low cost and low complexity implementations. However, the performance of UWB systems is strongly dependant on the multiple accesses and used modulation techniques. 
TH multiple access technique, where users are distinguished by their respective pulse arrival time sequences, is one of the most popular multi access techniques used for an impulse radio system [1]. The combination between time hopping (TH) and pulse position modulation (PPM) is the original modulation type proposed for UWB systems [3][4]. A performance study of this modulation in terms of BER has been mentioned in [5] with an AWGN channel. 
Currently, THPPM and THBPSK UWB systems have the same interest despite the performance difference in terms of bit error rate (BER) especially. Analysis of THBPSK UWB systems was analyzed and studied in [6] [7] [8]. In [9], a performance comparison between different modulation scheme was applied. In this paper, our purpose is to provide an analytical method to evaluate the BER performance of THBPSK with the presence of an AWGN channel. 
This paper is organized as follows. Section II describes the THBPSK UWB system model. In Section III, we elaborate an analytical approach to determine the performance of this modulation scheme and then, we validate the theoretical analysis with simulation results. In Section IV, we compare the performances of THBPSK and THPPM UWB system models using our analytical analysis. Finally, some conclusions are given in section V. 
THBPSK UWB SYSTEM MODEL

In general, the UWB system is formed by short pulses. For the BPSK case, the information depends on the pulses polarities, if dj is the source signal and βi the BPSK signal modulation. This is presented as follows [8], 

From (1), we note that the basic pulse sign’s of THBPSK is modulated according to the data bit where for each user is assigned an unique time hopping random sequence. In our case, we consider a THBPSKUWB system to apply our analytical approach. A typical transmitted THBPSK signal model is given in Fig.1 [10]. 
This modulation type can be modelled as follows for the mth user [8], 

Where SBPSK (k) (t,i) is the signal transmitted by one user corresponding to the ith data bit and p(t) is the transmitted UWB pulse shape. Eb is the total energy of one information bit. Tf is the duration of a frame which can be subdivided into chips of duration Tc. cj (k) ? {0, 1, ..., Nh 1} is the TH sequence related to the kth source where Nh represents the number of hops and satisfies Nh Tc ≤ Tf [11]. As THBPSK UWB modulation is antipodal, di (k) ?{1,1} represents the ith data bit transmitted by the kth source with the same probability. 
ANALYTICAL APPROACH FOR THBPSK UWB SYSTEM MODEL

The performance analysis starts by the reception of the THBPSK system. If we consider the THBPSK performance for one user and one path, (2) becomes, 
..........(3) 
If we suppose that the temporal support is disjoints, we obtain after calculation(4), 
(4) 
With Rw = [T] p2 (t) dt represents the autocorrelation function of the transmitted signal, and determines the noise power. In the noise less case (b(t)=0), we obtain, 
(5) 
The performance study of THBPSK is based on the comparison of the received sequences with the emitted ones. If we suppose that the di are equiprobably distributed, we have then, 
..........(6) 
(7) 
To determine the autocorrelation function, we consider the Gaussian impulse relation as follows, 

Consequently, the autocorrelation function Rw becomes, 

By following this way and replacing Rw(0) by its expression, we obtain the equation (9), which represents the performance of THBPSK UWB system model for one user and one path, 
...........(8) 
Which Eb represents the bit energy, N0 is the power noise and Q is the Marcum function. 
Fig. 2 shows BER curve of THBPSK system in theory case versus simulation with the MATLAB tool. We note, from this figure, that the theoretical and simulated results are approximately similar. This validates the approach using our new analytical analysis. 
PERFORMANCE COMPARISON BETWEEN THE THBPSK AND THPPM UWB SYSTEM MODEL

A.THPPM UWB SYSTEM MODEL

TH.PPM UWB system model is the very popular scheme because it depends to the pulse that will be sent early or late relatively to the data transmitted. In [11], PPM is defined as a modulation type that introduces a shift (δ) to distinguish between the pulses related to the bit “0” and the bit “1”. 
A typical UWB THPPM waveform can be modelled as follows, 

Where wtr is the transmitted pulse shape of duration Tp, Ts is the symbol duration. Tf is the frame period. Ns is the chips number with duration Tc and di ?{0,1} is the data bit transmitted. 
After calculation of the probability of error as the same method as THBPSK UWB system model, we obtain the equation (10) related to the performance of THPPM UWB system model found in [1], 

Fig. 3 shows the performance of THPPM UWB system model found in the theoretical case from (10) compared to the simulation results. 
B.PERFORMANCE COMPARISON

In this part, we compare the performance between the THBPSK and THPPM UWB system models with the results found in (8) and (10). This is given in Fig. 4, which represents the comparison performance between THBPSK and THPPM system models with our analytical approach. 
From this figure, we notice that the THBPSK model is better than the THPPM for all values of SNR. This further validates our analytical approach, as confirmed by the previous studies in this domain [7]. 
While THBPSK is antipodal, this modulation scheme agrees with properties of UWB system which consequently is better than THPPM that’s an orthogonal signal. We can conclude that THBPSK is a good choice for UWB application, but it doesn’t mean that THPPM is not usable. It can be used in many other applications. Additionally, BPSK is able to delete spectral lines which, if existing, could interfere with conventional radio systems. The THBPSK receiver detects the two signal polarities (1 and 1). But for the THPPM case, we have only one phase to detect which may provide more error with noise. 
CONCLUSION

In this paper we have proposed and analyzed bit error probability performance of THBPSK UWB multiple access communication in AWGN channel. We have provided a characteristics mathematical method to calculate the BER. Then, we validate our analytical approach by simulation and comparing with the results found for the THPPM case. 
From this study we can conclude that the UWB THBPSK system model outperforms UWB THPPM for all values of SNR. This result confirms other results find by other authors using different analytical approach. We can consequently choose the THBPSK model as the suitable scheme for UWB communication system design. A natural extension of this work is to include propagation over multipath channels. The proposed analytical approach presented in this article can be extended further to other UWB modulation schemes like THOOK. It may be possible in future research to study the performance of TH Mary Phase Shifting Keying (THMBPSK) and Mary pulse position modulation (THMPPM). 
Figures at a glance





Figure 1 
Figure 2 
Figure 3 
Figure 4 

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