Performance Analysis for Bit-Error-Rate of DS-CDMA Sensor Network Systems with Source Coding

analisis


Introduction
Recently, wireless sensor network applications are gaining much interest in academia and industry areas.The wireless sensor network technologies have been chosen as one of the most important technologies in the 21th century [1].Sensor networks consist of hundreds to thousands of tiny sensor nodes that can sense data, process, and communicate with each other nods or data sink [2].Designing the wireless sensor network is challenging due to high node density, frequent topology changes, limited battery and computing power and requirement of very low cost nodes [3].Nodes of the sensor networks communicate with each other through wireless media.The multiple access is a serious problem due to high node density, so, the code division multiple access (CDMA) is a promising multiple access scheme for sensor and ad hoc network to its interference averaging properties' [4].The minimum energy (ME) coding combined with direct sequenceCDMA (DS-CDMA) is proposed to address both power saving and multiple access interference (MAI) problems [5,6].ME coding reduces the number of high bit (1 bit) by inserting redundant bits, which results increase in codeword length (bandwidth) with less high bit.Power saving can be achieved by using On-Off-Keying (OOK) because only the high bit is transmitted through the channel.As most of bits in a codeword are zeros the multiple access interference (MAI) is also significantly reduced.Thus, it allows nearby users to co-exist and substantially enhances the bit error rate (BER) performance and specify the (SNR) to number of the receivers (users).In this paper, influence of the bit error rate on the signal to noise ratio for number of receivers is analyzed.Also, amount of energy for receiving bits is investigated for the SNR and BERs.Then, effect number of users on the probability of received bits is studied.The achieved results indicate that the SNR is dependent on the amount ratio of energy per bit to node density in the used field.
The rest of the paper is outlined as follows.Section 2 includes the model for the system and the achieved results are presented in section 3.Then, the conclusions are drawn to section 4.

The System Model
The model for the transmission signal is evolved in this part in order to analyze the system characteristics, represents the general DS-CDMA systems with number of receivers (N).Let the transmitted signal is given by [7,8]: Where P k is the power of the transmitted signal, ߱ is the common carrier angular frequency, θ k is the phase shift offset, m ‫)ݐ(‬ and ‫ܥ‬ ‫)ݐ(‬ are the data and spreading signals for the k th received signal, respectively, and ߬ is a random transmission delay calculated with respect to reference transmitted signal.It is accounting for the lack of synchronization among the users.
The data signal and the spreading signal are given as: where To keep generality on this interesting case, consider ߬ ∈ [0, ܶ) and ߠ ∈ [−ߨ, ߨ] since the analyses are conducted in the time delays module, T, and phase delays module, 2π.Thus the de-spread demodulated signal S d (t) can be given as: With using the ME coding, for coding a data and ‫ܥ‬ ) for all j, k and for some minimum period of the spreading sequence, M.
With taking into account influence of noise in the utilizing channel, we can rewrite Eq. 1 to be as: where ‫)ݐ(݊‬ is a white Gaussian noise with ߛ, spectral density.
The output of the matched filter, with assuming the received signal is matched to transmitter number 1 at ‫ݐ‬ = ܶ is: where, ݉ = (݉ ିଵ () , ݉ The output of the correlation receiver for user 1, at t = T b is= ܹ ଵ + ‫ܪ‬ ଵ + ߛ, where ܹ ଵ is the desired received signal for user number 1, ‫ܪ‬ ଵ is the interference from other users and ߛ is the AWGN term with variance of ߛܶ /2.In other words, the three terms are: The Γ , ሺ߬ ሻ and Γ ା (߬ ) are the continuous -time partial cross correlation function defined as followes: To evaluate the system performance the signal to noise ratio (SNR) is analyzed.The SNR is a perfect index to evaluate the quality of the received signal.So, to find the (SNR), the signal power of the ݉ ଵ ‫)ݐ(‬ is computed as Where ܽ 1 is the percentage of high bits for m 1 (t) during the transmission duration of T second.
The MAI and AWGN powers can be shown to be So, the SNR in the energy-efficient DS-CDMA system can be found as For analyzing influence error probability of a CDMA receiver several schemes have been presented in the literature over the past couple of years.The approach that first appeared in [7] is followed in this study.And, the MAI is assumed sufficiently well represented by an equivalent Gaussian random process with assuming that the power control for all the transmitters signals arrive at the receiver of transmitter high bit for each transmitter are same, i.e., ܽ 1 = ܽ 2 = …= ܽ ݉ .. For such condition Eq. ( 7) can be further simplified as where ‫ܧ‬ is energy per bit and ܰ is the node density.
The bit error usually occurs in moving from high bit signal into a lower bit signal or vice versa.The average error probability of reciver1 for transmitting one bit as: where ܲ is the probability of transmitting "zeros" signals and ܲ ଵ is the probability of transmitting "ones" signals for the first transmitter and δ is the threshold for bit detection.If ݉ ሺ‫ݐ‬ሻ = 0; the output of the integrator can be explained to If m 0 (t) = 1, the output of the integrator can be explained to Let δ=ඥܲ1/2 T b , we have As SNR ME approach constant, ∑ →∞ as M→∞ and P 0 (t)>>P 1 (t) under these condition, under these condition we can simplify P b as:

Results and Analysis
Figure 1 illustrates variation of the SNR to the number of users (receivers).The SNR increases for different values of the percentage of high bits for ݉ ଵ ‫)ݐ(‬ during the transmission duration of T second ( ܽ ଵ ) when the number of users increases the interference with the users are increased.Thus such behavior leads to increase amount of the MAI power and the SNR decreases.

Conclusions
This paper investigated influence using the DS-CDMA with minimum energy (ME) coding for the wireless sensor networks.The achieved results show that the ME DS-CDMA reduce the multiple access interference, save amount of power and improving the system performance; with sending a high bit rate, 1's, the probability of multiple access interference is highly decreases with utilizing the MAI, when a certain probability of multiple channels transmitted signals and identical time are kept.This leads to enhance the total performance of the system.The ME DS-CDMA is important to be chosen for wireless sensor network due to its important role in improving the probability of bit error rate and SNR for saving power with various number of users (receivers).

Figure 1 .
Figure 1.SNR for DS-CDMA energy efficient to the number of users and different values of ܽ ଵ .

Figure 2 Figure 2 .
Figure2shows that when the ‫ܧ‬ ܰ ⁄ is increased, the SNR increases linearly at certain values, following that, the SNR become autonomous of ‫ܧ‬ ܰ ⁄ .This can be illustrated as follows, for minimum amount of ‫ܧ‬ ܰ ⁄ the noise power caused by multiple receivers is trivial.Then, for lower values of ‫ܧ‬ ܰ ⁄ , SNR is associated with ‫ܧ‬ ܰ ⁄ , so the noise power get marginal.Figure3explains variation of the probability of bit error rate to number of users.It is increasing as number of user (M) increases for different levels of ɑ1.The probability reaches to the same value in specific number of users, which leads to the save power in more than specific number of users.

Figure 3 .
Figure 3. probability of error per bit for different number of users (receivers) with different values of ɑ1.