ECE 5233 Satellite Communications Prepared by: Dr. Ivica Kostanic Lecture 19: Multiple Access Schemes (4) (Section 6.8) Spring 2011

Florida Institute of technologies Page 2  CDMA principles  CDMA transmission and reception  DS-SS CDMA capacity  Examples Outline Important note: Slides present summary of the results. Detailed derivations are given in notes.

Florida Institute of technologies CDMA – basic principle  Code Division Multiple Access (CDMA)  Users are transmitting co-time and co-frequency  The signals from different users are separated by codes Page 3 Common analogies used for the access schemes FDMA CDMA TDMA

Florida Institute of technologies CDMA TXC and RX (single link)  At the TX - signal multiplied by a spreading sequence  Spreading sequence – code with higher data rate and god autocorrelation properties  Spread signal send to satellite and received by all earth stations  Received signal correlated with the same spreading code Page 4

Florida Institute of technologies CDMA example – 2 Page 5 Processing gain (PG) is the ratio of chip and bit rates Note: codes in this example are synchronized in time

Florida Institute of technologies CDMA access  Signals from different earth stations are co-spectrum and co time  Signals are spread using codes that are orthogonal even when not synchronized  All signals are amplified by the transponder and send towards the ground  Transmission from the earth stations must me power managed so that the product of processing gain and power is constant – for all earth stations  If the earth stations have same processing gain – they should be received at the same power Page 6 CDMA scheme

Florida Institute of technologies PN sequences (AKA M-sequences) Page 7  Have “noise like” auto-correlation properties  Generated as output of shift registers that have taps indicated by primitive polynomials oTaps need to be in “special places” oLocation of taps for different code lengths: ck_shift_register_lfsr.htm Shift register for generation of binary sequence Remember: 1 maps into -1 0 maps into 1

Florida Institute of technologies M sequences - properties 1. An m-bit register produces an m-sequence of period 2 m An m-sequence contains exactly 2 (m-1) ones and 2 (m-1) -1 zeros. 3. The modulo-2 sum of an m-sequence and another phase (i.e. time-delayed version) of the same sequence yields yet a third phase of the sequence. 3a. (A corollary of 3.) Each stage of an m-sequence generator runs through some phase of the sequence. (While this is obvious with a Fibonacci LFSR, it may not be with a Galois LFSR.) 4. A sliding window of length m, passed along an m-sequence for 2 m -1 positions, will span every possible m- bit number, except all zeros, once and only once. That is, every state of an m-bit state register will be encountered, with the exception of all zeros. 5. Define a run of length r to be a sequence of r consecutive identical numbers, bracketed by non-equal numbers. Then in any m-sequence there are: 1 run of ones of length m. 1 run of zeros of length m-1. 1 run of ones and 1 run of zeros, each of length m-2. 2 runs of ones and 2 runs of zeros, each of length m-3. 4 runs of ones and 4 runs of zeros, each of length m-4. … 2 m-3 runs of ones and 2 m-3 runs of zeros, each of length If an m-sequence is mapped to an analog time-varying waveform, by mapping each binary zero to 1 and each binary one to -1, then the autocorrelation function for the resulting waveform will be unity for zero delay, and -1/(2 m -1) for any delay greater that one bit, either positive or negative in time. The shape of the autocorrelation function between -1 bit and +1 bit will be triangular, centered around time 0. That is, the function will rise linearly from time = -(one-bit) to time 0, and then decline linearly from time 0 to time = +(one-bit). Page 8

Florida Institute of technologies Circular autocorrelation of PN sequence Page 9 PN sequence of length N : Circular autocorrelation: For PN sequences Consider N=15 sequence in the attached spreadsheet Note: PN sequences are practically orthogonal to their delayed versions

Florida Institute of technologies CDMA capacity Page 10 On the ground S/N ratio for a given link (in dB) Consider Q identical earth stations using a transponder in a CDMA mode For large Q Therefore Solving for Q Max number of earth stations

Florida Institute of technologies Example 1.Consider DS-CDMA system with processing gain of Required S/N at the output of the earth station receive is 12dB. Estimate the number of the earth stations that can be supported in the system Page Example 6.8.1

Florida Institute of technologies Homework Problems 6.5, 6.6 and 6.7 Page 12