MFSK Demodulator Baseband
Demodulate FSKmodulated data
Library
FM, in Digital Baseband sublibrary of Modulation
Description
The MFSK Demodulator Baseband block demodulates a signal that was modulated using the
Mary frequency shift keying method. The input is a baseband representation of the
modulated signal. The input and output for this block are discretetime signals. This
block accepts a scalar value or column vector input signal of type
single
or double
. For information about the
data types each block port supports, see Supported Data Types.
The Mary number parameter, M, is the number of frequencies in the modulated signal. The Frequency separation parameter is the distance, in Hz, between successive frequencies of the modulated signal.
The MFSK Demodulator Baseband block implements a noncoherent energy detector. To obtain the same BER performance as that of coherent FSK demodulation, use the CPFSK Demodulator Baseband block.
IntegerValued Signals and BinaryValued Signals
When you set the Output type parameter to
Integer
, the block outputs integer values in the range
[0
, (M – 1
)]. M
represents the Mary number block parameter.
When you set the Output type parameter
to Bit
, the block outputs binaryvalued
signals that represent integers. The block represents each integer
using a group of K = log_{2}(M)
bits, where K represents the number of bits per
symbol. The output vector length must be an integer multiple of K.
The Symbol set ordering parameter indicates
how the block maps a symbol to a group of K output
bits. When you set the parameter to Binary
,
the block maps the integer, I, to [u(1) u(2) ... u(K)] bits,
where the individual u(i) are given by
$$I\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\displaystyle \sum _{i=1}^{K}u(i){2}^{Ki}}$$
u(1) is the most significant bit.
For example, if M = 8, you set Symbol
set ordering to Binary
, and
the demodulated integer symbol value is 6, then the binary output
word is [1 1 0].
When you set Symbol set ordering to Gray
, the
block assigns bit outputs from points of a predefined Graycoded signal constellation. The
predefined Mary Graycoded signal constellation assigns the bit representation in the pth
row of bit matrix b
to the pth integer, where the leftmost bit is the
most significant bit (MSB).
M = 8; P = [0:M1]'; nBits = log2(M); b = int2bit(bitxor(P,floor(P/2)),nBits); b = reshape(b,[],8)';
The typical Binary to Gray mapping for M = 8 is shown in the following tables.
Binary to Gray Mapping for Bits
Binary Code  Gray Code 

000  000 
001  001 
010  011 
011  010 
100  110 
101  111 
110  101 
111  100 
Binary to Gray Mapping for Integers
Binary Code  Gray Code 

0  0 
1  1 
2  3 
3  2 
4  6 
5  7 
6  5 
7  4 
Whether the output is an integer or a binary representation of an integer, the block maps the highest frequency to the integer 0 and maps the lowest frequency to the integer M1. In baseband simulation, the lowest frequency is the negative frequency with the largest absolute value.
SingleRate Processing
In singlerate processing mode, the input and output signals have the same port sample time. The block implicitly implements the rate change by making a size change at the output when compared to the input. The input width must be an integer multiple of the Samples per symbol parameter value, and the input can be a column vector.
When you set Output type to
Bit
, the output width is K times the number of input symbols and the Mary number value must be a power of two.When you set Output type to
Integer
, the output width is the number of input symbols.
Multirate Processing
In multirate processing mode, the input and output signals have different port sample times. The input must be a scalar. The output symbol time is the product of the input sample time and the Samples per symbol parameter value.
When you set Output type to
Bit
, the output width equals the number of bits per symbol and the Mary number value must be a power of two.When you set Output type to
Integer
, the output is a scalar.
To run the MFSK Demodulator block in multirate mode, clear the Treat each discrete rate as a separate task checkbox (in Simulation > Configuration Parameters > Solver).
Parameters
 Mary number
Number of frequencies in the modulated signal, specified as a positive integer ≥ 2.
 Output type
Determines whether the output consists of integers or groups of bits. If this parameter is set to
Bit
, then the Mary number parameter must be a power of two. Symbol set ordering
Determines how the block maps each integer to a group of output bits.
Note
When you set Symbol set ordering to
Gray
, the Mary number value must be a power of two. Frequency separation (Hz)
The distance between successive frequencies in the modulated signal.
 Samples per symbol
The number of input samples that represent each modulated symbol.
 Rate options
Select the rate processing method for the block.
Enforce singlerate processing
— When you select this option, the input and output signals have the same port sample times. The block implements the rate change by making a size change at the output when compared to the input. The output width is the number of symbols (which is given by dividing the input length by the Samples per symbol parameter value when the Output type parameter is set toInteger
).Allow multirate processing
— When you select this option, the input and output signals have different port sample times. The output period is the same as the symbol period and equals the product of the input period and the Samples per symbol parameter value.
For more information, see SingleRate Processing and Multirate Processing in the Description section of this page.
 Output data type
The output type of the block can be specified here as
boolean
,int8
,uint8
,int16
,uint16
,int32
,uint32
, ordouble
. By default, the block sets this todouble
.
Supported Data Types
Port  Supported Data Types 

Input 

Output 

Pair Block
References
[1] Sklar, Bernard. Digital Communications: Fundamentals and Applications. Upper Saddle River, NJ: PrenticeHall, 2001.
Extended Capabilities
Version History
Introduced before R2006a