Communications Blockset

Components of the Gray Coding Demo

This section discusses the purpose, behavior, and relevant parameters of each top-level component within the demo model. This section covers components in the order in which they process data in the simulation.

Random Integer Generator

The Random Integer Generator block produces random data that is used as the information in this simulation. This block generates one 100-symbol frame of integers in the range 0 to M-1 every Tsym seconds.

Integer-to-Bit Conversion

The Integer to Bit Converter block converts integer symbols to their equivalent binary representations. Its parameter is the number of bits in each integer.

Gray Coded M-PSK Modulation

The M-PSK Modulator Baseband block:

• Accepts binary-valued inputs that represent integers between 0 and M-1
• Maps binary representations to constellation points using a Gray-coded ordering
• Produces unit-magnitude complex phasor outputs, with evenly spaced phases between 0 and 2(M-1)/M

The table indicates which binary representations in the input correspond to which phasors in the output. The second column of the table is an intermediate representation that the block uses in its computations.

Modulator Input	Gray-Coded Ordering	Modulator Output
000	0
001	1
010	3
011	2
100	7
101	6
110	4
111	5

The table below sorts the first two columns of the table above, according to the output values. This sorting makes it clearer that the overall effect of this subsystem is a Gray code mapping as shown in the figure below. Notice that the numbers in the second column of the table below appear in counterclockwise order in the figure.

Modulator Output	Modulator Input
	000
	001
	011
	010
	110
	111
	101
	100

AWGN Channel

The AWGN Channel library block simulates transmission over a noisy channel. Its Signal to noise ratio (Es/No) mode uses these quantities to determine the variance:

• E_s/N_o, the ratio of energy per symbol to noise power spectral density
• The input signal power
• The symbol period

  

The values for these parameters are chosen as follows:

• The Es/No parameter is computed from the workspace variables EbNodB and M. The conversion from bit energy to symbol energy reflects the fact that each symbol carries log2(M) bits of information.
• The signal power is 1 watt because the M-PSK Modulator Baseband block produces unit power signals.
• The symbol period of the channel is set to Tsym.

Gray Coded MPSK Demodulation

The M-PSK Demodulator Baseband block mirrors the Gray-coded modulation process. Notice that corresponding parameters in the modulator and demodulator blocks have the same values.

Bit-to-Integer Conversion

The Bit to Integer Converter block converts binary representations of symbols to their integer equivalents. Its parameter is the number of bits in each integer.

Error Rate Calculation

The Error Rate Calculation block compares demodulated symbols to original source symbols to compute the error rate. This model uses two Error Rate Calculation blocks, one to compute the symbol error rate and the other to compute the bit error rate. Both blocks use the parameter values shown below.

Symbol Error Details and Bit Error Details

Simulink's Display block shows the running error statistics throughout the simulation. Each Display block in the diagram lists three numbers, which represent:

• The symbol or bit error rate
• The total number of errors
• The total number of comparisons that the Error Rate Calculation block made

Sending Data to the MATLAB Workspace

Simulink's To Workspace block sends the complete set of error statistics to the MATLAB workspace. When the simulation ends, the MATLAB variables SER and BER are both three-column matrices whose columns represent these quantities at each time step:

• The symbol or bit error rate
• The total number of errors
• The total number of comparisons that the Error Rate Calculation block made

Variables in the Model

Learning More About the Gray Coding Demo