Scramble input signal
The comm.Scrambler object applies multiplicative scrambling to input data.
This schematic shows the multiplicative scrambler operation. The adders operate modulo N, where N is the value specified by the CalculationBase property.
At each time step, the input causes the contents of the registers to shift sequentially. Using the Polynomial property, you specify the on or off state for each switch in the scrambler.
To scramble an input signal:
comm.Scramblerobject and set its properties.
Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?
creates a scrambler
System object. This object scrambles the input data by using a linear feedback shift register
that you specify with the Polynomial property.
scrambler = comm.Scrambler
creates the scrambler object with the CalculationBase property set to
scrambler = comm.Scrambler(
base, the Polynomial property set to
poly, and the InitialConditions property set to
comm.Scrambler(8,'1 + x^-2 + x^-3 + x^-5 + x^-7',[0 3 2 2 5 1
7]) sets the calculation base to
8, and the scrambler polynomial
and initial conditions as specified.
Unless otherwise indicated, properties are nontunable, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
release function unlocks them.
If a property is tunable, you can change its value at any time.
For more information on changing property values, see System Design in MATLAB Using System Objects.
CalculationBase — Range of input data
4 (default) | nonnegative integer
Range of input data used in the scrambler for modulo operations, specified as a
nonnegative integer. The input and output of this object are integers from
Polynomial — Connections for linear feedback shift registers
'1 + x^-1 + x^-2 + x^-4' (default) | character vector | integer vector | binary vector
Connections for linear feedback shift registers in the scrambler, specified as a
character vector, integer vector, or binary vector. The
property defines if each switch in the scrambler is on or off. Specify the polynomial as:
A character vector, such as
'1 + x^-6 + x^-8'. For more details on specifying polynomials in this way, see Representation of Polynomials in Communications Toolbox.
An integer vector, such as
[0 -6 -8], listing the scrambler coefficients in order of descending powers of x-1, where p(x-1) = 1 + p1x-1 + p2x-2 + ...
A binary vector, such as
[1 0 0 0 0 0 1 0 1], listing the powers of x that appear in the polynomial that have a coefficient of 1. In this case, the order of the scramble polynomial is one less than the binary vector length.
'1 + x^-6 + x^-8',
[0 -6 -8], and
[1 0 0 0 0 0 1 0 1] all represent this polynomial:
p(x-1) = 1 + x-6 + x-8
InitialConditionsSource — Initial conditions source
'Property' (default) |
InitialConditions — Initial conditions of scrambler registers
[0 1 2 3] (default) | nonnegative integer vector
Initial conditions of scrambler registers when the simulation starts, specified as a
nonnegative integer vector. The length of
InitialConditions must equal
the order of the Polynomial property. The vector element
values must be integers from
0 to CalculationBase –
This property is available when InitialConditionsSource
is set to
ResetInputPort — Scrambler state reset port
false (default) |
scrambles the input signal. The output is the same data type and length as the input vector.
scrambledOut = scrambler(
signal — Input signal
Input signal, specified as a column vector.
scrambledOut = scrambler([0 1 1 0 1])
initcond — Initial register conditions
nonnegative integer column vector
Initial scrambler register conditions when the simulation starts, specified as a
nonnegative integer column vector. The length of
initcond must equal the
order of the Polynomial property. The vector
element values must be integers from
0 to CalculationBase –
scrambledOut = scrambler(signal,[0 1 1 0]) corresponds to
possible initial register states for a scrambler with a polynomial order of
4 and a calculation base of
reset — Reset initial state of scrambler
Reset the initial state of the scrambler when the simulation starts, specified as a
scalar. When the value of
reset is nonzero, the object is reset before
it is called.
scrambledOut = scrambler(signal,0) scrambles the input signal
without resetting the scrambler states.
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named
Scramble and Descramble Data
Scramble and descramble 8-ary data using
comm.Descrambler System objects™ having a calculation base of 8.
Create scrambler and descrambler objects, specifying the calculation base, polynomial, and initial conditions using input arguments. The scrambler and descrambler polynomials are specified with different but equivalent data formats.
N = 8; scrambler = comm.Scrambler(N,'1 + x^-2 + x^-3 + x^-5 + x^-7', ... [0 3 2 2 5 1 7]); descrambler = comm.Descrambler(N,[1 0 1 1 0 1 0 1], ... [0 3 2 2 5 1 7]);
Scramble and descramble random integers. Display the original data, scrambled data, and descrambled data sequences.
data = randi([0 N-1],5,1); scrData = scrambler(data); deScrData = descrambler(scrData); [data scrData deScrData]
ans = 5×3 6 7 6 7 5 7 1 7 1 7 0 7 5 3 5
Verify that the descrambled data matches the original data.
ans = logical 1
Scramble and Descramble Data with Changing Initial Conditions
Scramble and descramble quaternary data while changing the initial conditions between function calls.
Create scrambler and descrambler System objects having a calculation base of 4. Set the
InitialConditionsSource property to
'Input port' so you can set the initial conditions as an argument to the object.
N = 4; scrambler = comm.Scrambler( ... N,'1 + z^-3', ... 'InitialConditionsSource','Input port'); descrambler = comm.Descrambler( ... N,'1 + z^-3', ... 'InitialConditionsSource','Input port');
Preallocate memory for the error vector which will be used to store errors output by the
errVec = zeros(10,1);
Scramble and descramble random integers while changing the initial conditions,
initCond, each time the loop executes. Use the
symerr function to determine if the scrambling and descrambling operations result in symbol errors.
for k = 1:10 initCond = randperm(3)'; data = randi([0 N-1],5,1); scrData = scrambler(data,initCond); deScrData = descrambler(scrData,initCond); errVec(k) = symerr(data,deScrData); end
errVec to verify that the output from the descrambler matches the original data.
errVec = 10×1 0 0 0 0 0 0 0 0 0 0
Additive Scrambling of Input Data
Digital communications systems commonly use additive scrambling to randomize input data to aid in timing synchronization and power spectral requirements. The
comm.Scrambler System object™ implements multiplicative scrambling but does not support additive scrambling. To perform additive scrambling you can use the
comm.PNSequence System object. This example implements the additive scrambling specified in IEEE 802.11™ by scrambling input data with an output sequence generated by the comm.PNSequence System object. For a Simulink® model that implements a similar workflow, see the Additive Scrambling of Input Data in Simulink example.
This figure shows an additive scrambler, that uses the generator polynomial , as specified in figure 17-7 of IEEE 802.11 Section 126.96.36.199 .
Comparing the shift register specified in 802.11 with the shift register implementated using a comm.PNSequence System object, note that the two shift register schematics are mirror images of each other. Therefore, when configuring the comm.PNSequence System object to implement an additive scrambler, you must reverse values for the generator polynomial, the initial states, and the mask output. To take the output of the register from the leading end, specify a shift value of 7.
Define variables for the generator polynomial, shift value for the output, an initial shift register state, a frame of input data, and a variable containing the 127-bit scrambler sequence specified in section 188.8.131.52 of the IEEE 802.11 standard. Create a PN sequence object that initializes the registers by using an input argument.
genPoly = 'x^7 + x^3 + 1'; % Generator polynomial shift = 7; % Shift value for output spf = 127; % Samples per frame initState = [1 1 1 1 1 1 1]; % Initial shift register state dataIn = randi([0 1],spf,1); ieee802_11_scram_seq = logical([ ... 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 ... 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 ... 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 ... 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 ... 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 ... 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1])'; pnSeq = comm.PNSequence( ... Polynomial=genPoly, ... InitialConditionsSource="Input Port", ... Mask=shift, ... SamplesPerFrame=spf, ... OutputDataType="logical"); pnsequence = pnSeq(initState);
Compare the PN sequence object output to the IEEE 802.11 127-bit scrambler sequence to confirm the generated PN sequence matches the 802.11 specified sequence.
ans = logical 1
Scramble input data according to the 802.11 specified additive scrambler by modulo-adding input data with the PN sequence output.
scrambledOut = xor(dataIn,pnSeq(initState));
Descramble the scrambled data by applying the same scrambler and initial conditions to the scrambled data.
descrambledData = xor(scrambledOut,pnSeq(initState));
Verify that the descrambled data matches the input data.
ans = logical 1
 IEEE Std 802.11™-2020 (Revision of IEEE Std 802.11™-2016). "Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications." IEEE Standard for Information technology — Telecommunications and information exchange between systems. Local and metropolitan area networks — Specific requirements.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).
Introduced in R2012a