Wireless Medium Access Control and CDMA-based Communication Lesson 08 Auto-correlation and Barker Codes 1
Coding Methods in CDMA Use distinctive spreading codes to spread the symbols before transmission At the receiving end, a correlator used to despread the original signal Unwanted signals not correlated and, thus, not despread 2
CDMA codes The original data rates are called symbols per second and the code chipping rates are called chip rates These codes uniquely distinguish sets of data from each other 3
CDMA codes Carefully designed sequences of ones and zeros These sequences are produced from the codes as per the chips at rates much higher than those of the symbols (Spread factor > 1) Example: f s = 19.2 ks/s, f chip = 1.2288Mchip/s and spread factor = 64 4
CDMA codes Enable unique identification of signals from different sources and allow different signals to be transmitted through the same space, time, and frequency slots without interference No correlation to other codes or to time shifted versions of themselves 5
Correlation Consider coded symbols of n bits between time interval t 0 and t 0 + (n 1)T, where T is the period between successive bits The sequence at the receiver in the interval between t 0 ' and t 0 '+(n 1)T when (t 0 ' t 0 ) = the propagation delay 6
Correlation between Codes When the receiver attempts to correlate the received coded symbols with respect to any of the codes which it internally generates, it is not able to correlate even when it uses exactly the same code as the one used for transmission 7
Reasons for no correlation Propagation delay The receiver uses the code for extracting symbols within the interval t 0 " and t 0 "+(n 1)T and t 0 " and t 0 do not differ by n.t Inappropriate code The reason can be that the sequence of bits in the code itself is such that correlation is not possible by using a correlation method at the receiver 8
Correlation functions Propagation delay taken care of by the receiver by successively shifting the receiver generated sequence by a period = m. T m = 0, 1, 2, 3,, (n 1) 9
Sum of product (SOP) A code symbol a i for i = 0, 1,..., n 2, n 1 is given by the SOP from i = 0 to n k for all values of k between 1 and n SOP = a i.a i+ k 10
Correlation Method The correlation method is to find the sum of products (SOP) to correlate the sequence of bits between t 0 " + (m. T) and t 0 " + (n 1)T + (m.t) with the received coded signal Vary m till the SOP is maximum Inappropriate code taken care of by using an autocorrelation code 11
Autocorrelation code A multi-bit code which, when used for coding the symbols before a transmission, enables the receiver to automatically correlate and extract the symbols using the correlation method SOP = a i.a i+ k 1 for i = 1 k < n SOP maximum when k = 0 12
Example Barker code Assume that the chipping signal symbol is 1 for +1 and 0 for 1 The Barker code is a sequence of n values (code-symbols) of +1 and 1 {+1, +1, +1, 1, 1, 1, +1, 1, 1, +1, 1} 11-bit Code in 802.11 LAN 13
13-bit Barker code C13 {+1, +1, +1, +1, +1, 1, 1, +1, +1, 1, +1, 1, +1} 14
Good autocorrelation function Gives a large value of sum e i r i when e i = r i A very low value, when e i r i for 0 i < n e i = expected chip symbol and r i = received chip symbol in an i th sequence at the receiver 15
Pseudo-noise (PN) sequence The code appears random and noise-like but is actually not random 16
Sum of the 13 products between the coded and received sequences for n = 13 17
Summary Correlation defined by a large value of sum e i r i when e i = r i and a very low value, when e i r i for 0 i < n Correlation method is to successively shift the code by 1 till e i = r i shown by maximum value of SOP for all values of i Barker code autocorrelation code Pseudo-noise code 18
End of Lesson 08 Auto-correlation and Barker Codes 19