ECE 5233 Satellite Communications

ECE 5233 Satellite Communications Prepared by:

Dr. Ivica Kostanic

Lecture 19: Multiple Access Schemes (4)(Section 6.8)

Spring 2011

Florida Institute of technologies

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CDMA principlesCDMA transmission and receptionDS-SS CDMA capacityExamples

Outline

Important note: Slides present summary of the results. Detailed derivations are given in notes.


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

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well, see youtom orrow

hello, howare youdoing?

bye !

m y salary ,s ir...

wh at?!...ra iseagain?

w ell, see youtom orrow

hello , howare youdoing?

bye !

m y sa lary,s ir...

w ha t?!...ra iseagain?

Hello, howare youdoing?

j!j.

ObAP AHMAJA!

3 PABOJA !!

Common analogies used for the access schemes

FDMA

CDMA

TDMA


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

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CDMA example – 2

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Processing gain (PG) is the ratio of chip and bit rates

x

X

S

X

X

S 1

S 2

C 1C 1

Integra te

Integra te

C 2

= 1

= -1

1 11 1

1 11 1

1 1-1 -1

0 0 2 2

X = S 1C 1+S 2C 2

S 1 C 1x

S 2 C 2x

1 11 1

1 1 -1 -1

1 1 -1 -1

C 2

0 0 2 2

0+0+2+2 = 4 > 0

0 0 -2 -20+0-2-2 = -4 < 0

X C 1x

X C 2x

1 wassent

-1 wassent

Tw o s igna ls coexist intim e and frequency

b

c

RR

PG

Note: codes in this example are synchronized in time


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

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CDMA scheme


PN sequences (AKA M-sequences)

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Have “noise like” auto-correlation properties Generated as output of shift registers that have taps indicated by primitive polynomials

o Taps need to be in “special places”o Location of taps for different code lengths:

http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm

Shift register for generation of binary sequence

Remember:

1 maps into -1

0 maps into 1


M sequences - properties

1. An m-bit register produces an m-sequence of period 2m-1.

2. 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 2m-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.…2m-3 runs of ones and 2m-3 runs of zeros, each of length 1.

6. 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/(2m-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).

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Circular autocorrelation of PN sequence

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N

np Nvnxnx

NvR

1

),mod(1

nxPN sequence of length N:

Circular autocorrelation:

For PN sequences

0,1

0,1

vN

vvRp

Microsoft Office Excel 97-2003 Worksheet

Consider N=15 sequence in the attached spreadsheet

Note: PN sequences are practically orthogonal to their delayed versions


CDMA capacity

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On the ground S/N ratio for a given link (in dB)

b

cSSout R

RNCNS log10//

Consider Q identical earth stations using a transponder in a CDMA mode

b

c

Ti R

RCQN

CNS log101

log10/

For large Q

1log101

log101

log10

QCQ

CCQN

C

T

Therefore

1

log10/QMNS i

Solving for Q

outNS

b

c

RRQ /1.010 Max number of earth

stations


Example

1.Consider DS-CDMA system with processing gain of 1023. 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

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6454.64101023 10/12 Q

2. Example 6.8.1


Homework

Problems 6.5, 6.6 and 6.7

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ECE 5233 Satellite Communications