M-PSK Modulator Baseband (Communications Blockset)

Modulate using the M-ary phase shift keying method

Library

PM, in Digital Baseband sublibrary of Modulation

Description

The M-PSK Modulator Baseband block modulates using the M-ary phase shift keying method. The output is a baseband representation of the modulated signal. The M-ary number parameter, M, is the number of points in the signal constellation.

Baseband M-ary phase shift keying modulation with a phase offset of maps an integer m between 0 and M-1 to the complex value

The input and output for this block are discrete-time signals. To use integers between 0 and M-1 as input values, set the Input type parameter to Integer. In this case, the input can be either a scalar or a frame-based column vector.

Alternative configurations of the block determine how the block interprets its input and arranges its output, as explained in the sections below.

Binary Inputs

If the Input type parameter is set to Bit and the M-ary number parameter has the form 2^K for some positive integer K, then the block accepts binary representations of integers between 0 and M-1. It modulates each group of K bits, called a binary word. The input can be either a vector of length K or a frame-based column vector whose length is an integer multiple of K.

In binary input mode, the Constellation ordering parameter indicates how the block maps a group of K input bits to a corresponding integer. Choices are Binary and Gray. For more information, see Binary-Valued and Integer-Valued Signals in Using the Communications Blockset.

If Constellation ordering is set to Gray, then the block uses a Gray-coded signal constellation; as a result, binary representations that differ in more than one bit cannot map to consecutive integers modulo M. The explicit mapping is described in Algorithm below.

Frame-Based Inputs

If the input is a frame-based column vector, then the block processes several integers or several binary words, in each time step. (If the Input type parameter is set to Bit, then a binary word consists of log₂(M) bits.)

For example, the schematics below illustrate how the block processes two 8-ary integers or binary words in one time step. The signals involved are all frame-based column vectors. In both cases, the Phase offset parameter is 0.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The Samples per symbol parameter is the upsampling factor. It must be a positive integer. For more information, see Upsampled Signals and Rate Changes in Using the Communications Blockset.

Dialog Box

M-ary number: The number of points in the signal constellation.
Input type: Indicates whether the input consists of integers or groups of bits. If this parameter is set to Bit, then the M-ary number parameter must be 2^K for some positive integer K.
Constellation ordering: Determines how the block maps each group of input bits to a corresponding integer. This field is active only when Input type is set to Bit.
Phase offset (rad): The phase of the zeroth point of the signal constellation.
Samples per symbol: The number of output samples that the block produces for each integer or binary word in the input.

Algorithm

If the Constellation ordering parameter is set to Gray, then the block internally assigns the binary inputs to points of a predefined Gray-coded signal constellation. The block's predefined M-ary Gray-coded signal constellation assigns the binary representation

de2bi(bitxor(m,floor(m/2)), log2(M),'left-msb')

to the mth phase. The zeroth phase in the constellation is the Phase offset parameter, and successive phases are counted in a counterclockwise direction.

Note This transformation might seem counterintuitive because it constitutes a Gray-to-binary mapping. However, the block must use it to impose a Gray ordering on the signal constellation, which has a natural binary ordering.

In other words, if the block input is the natural binary representation, u, of the integer U, then the block output has phase

where is the Phase offset parameter and m is an integer between 0 and M-1 that satisfies

For example, if M = 8, then the binary representations that correspond to the zeroth through seventh phases are below.

M = 8; m = [0:M-1]';
de2bi(bitxor(m,floor(m/2)), log2(M),'left-msb')

ans =

     0     0     0
     0     0     1
     0     1     1
     0     1     0
     1     1     0
     1     1     1
     1     0     1
     1     0     0

Below is the 8-ary Gray-coded constellation that the block uses if the Phase offset parameter is /8.

Pair Block

M-PSK Demodulator Baseband

M-PSK Demodulator Passband M-PSK Modulator Passband