Performance Analysis for Bit Error Rate of DS- CDMA SensorNe(2)

166 ISSN: 1693-6930

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.

2. 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]:

( )=∑ m . ( )cos ( ) (1)

Where Pk is the power of the transmitted signal, is the common carrier angular frequency, θk is the phase shift offset, m ( ) and ( ) are the data and spreading signals for the kth 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:

m =∑∞ ∞m ∏( ,( +1) ) (1-a) =∑∞ ∞C ∏( ,( +1) ) (1-b)

where ∏( , ) is a unit rectangular pulse on [t1,t2).

To keep generality on this interesting case, consider ∈[0, ) and ∈[ , ] since the analyses are conducted in the time delays module, T, and phase delays module, 2π. Thus the de-spread demodulated signal Sd(t) can be given as:

M2 Sd(t)= ∑k=2 mk(t- k)c1(t) ck(t- k) cos(wct+θk) coswct + m1(t)coswct + n(t) c1(t)coswct (2)

( )( )( )With using the ME coding, for coding a data and ∈{ 1,1} with = getting

( ) =0 ( =1) 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:

′ = + ( ) (3)

where ( ) is a white Gaussian noise with , spectral density.

The output of the matched filter, with assuming the received signal is matched to transmitter number 1 at = is:

= /2 + ( )

( ) , , + ( ) (4)

( )( )where, =( , ) (4-a)

( ) and, =cos .{ . . + . } (4-b) .

TELKOMNIKA Vol. 10, No. 1, March 2012 : 165 – 170