Lecture 3. Direct Sequence Spread Spectrum Systems. COMM 907:Spread Spectrum Communications

Transcription

1 COMM 907: Spread Spectrum Communications Lecture 3 Direct Sequence Spread Spectrum Systems

2 Performance of DSSSS with BPSK Modulation in presence of Interference (Jamming) Broadband Interference (Jamming): (1) (2)

3 Then from (1) and (2) the bit energy to interference (Jamming) ratio is given by: (3)

4 Partial band Interference (Jamming) (4) Then from (1) and (4), we have:

5

6 Performance of DSSSS with BPSK Modulation in presence of Interference (Jamming) Sampler every Tb Receiver under consideration The bit Error probability in presence of Broadband jamming is giving by: This bit error probability is plotted versus Eb/Nj in Fig. 1.15

7 The bit Error probability in presence of partial band jamming is giving by:

8 Performance in presence of Broadband Jamming

9 Performance in Presence of Partial band Jamming

10 Spreading Codes The spreading sequence is a sequence of binary digits shared by transmitter and receiver. Spreading consists of multiplying the input data by the spreading sequence, where the bit rate of the spreading sequence is higher than that of the input data. When the signal is received, the spreading is removed by multiplying with the same synchronized spreading code again. Two general categories of spreading sequences have been used: - PN sequences with maximal length (M-sequences) and - Orthogonal codes.

11 PN Sequence PN sequence is a periodic binary sequence with a nearly even balance of 0 s and 1 s that appears to be random. PN Sequences - Generated by algorithm using initial values. - PN sequences, which include the maximal sequences, provide practical spreading sequences because their autocorrelations facilitate code synchronization in the receiver. - Unless algorithm and initial values are known, the sequence is impractical to predict.

12 PN codes can be generated using feedback shift register as shown in the figure: P( x) g r x r g 1 x... g r 1 r 1 x g o

13 Example: m=3

14 PN Sequence Since a linear m-stages feedback shift register has exactly nonzero states, the period of its output sequence cannot exceed A sequence of period generated by a linear feedback shift register is called a maximal or maximal-length sequence (M-sequence). If a linear feedback shift register generates a maximal sequence, then all of its nonzero output sequences are maximal, regardless of the initial states.

15 M-Sequence Normalized autocorrelation function

16 Correlation Function The correlation function of N-element sequence (a) and (b) is defined by:

17 Properties of Cross Correlation The cross correlation between an m-sequence and noise is low. This property is useful to the receiver in filtering out noise. The cross correlation between two different m-sequences is low. This property is useful for CDMA applications Enables a receiver to discriminate among spread spectrum signals generated by different m-sequences

18 Gold Sequences Gold sequences constructed by the XOR of two m-sequences with the same clocking. Codes have well-defined cross correlation properties. Only simple circuitry needed to generate large number of unique codes.

19 Example: Gold Sequences

20 Orthogonal Codes Orthogonal codes Provides zero cross correlation among all users. For CDMA application, each user uses one sequence in the set as a spreading code Example Walsh codes

21 Walsh Codes Set of Walsh codes of length n consists of the following Walsh matrix: Every row is orthogonal to every other row. Requires tight synchronization Cross correlation between different shifts of Walsh sequences is not zero

22 Walsh Codes