PN Sequence Generator
Generate pseudonoise sequence
 Library:
Communications Toolbox / Comm Sources / Sequence Generators
Communications Toolbox HDL Support / Comm Sources
Description
The PN Sequence Generator block generates a sequence of pseudorandom binary numbers using a linearfeedback shift register (LFSR). Pseudonoise sequences are typically used for pseudorandom scrambling, and in directsequence spreadspectrum systems. For more information, see More About.
These icons shows the block with all ports enabled.
Ports
Input
Mask
— Output mask
binary vector
Output mask to delay the PN sequence from initial time, specified as a binary vector with N elements. N is the degree of the generator polynomial.
Dependencies
To enable this port, set Output mask source to
Input port
.
Data Types: double
 uint8
 ufix1
oSiz
— Output size
integer
Output size for variablesize output signals, specified as an integer. For information about variablesize signals, see VariableSize Signal Basics (Simulink).
Dependencies
To enable this port, select Output variablesize signals
and set Maximum output size source to Dialog
parameter
.
Data Types: double
Ref
— Reference input
column vector
Reference input, specified as a column vector that determines the maximum and current output sequence length. The Ref input must be a variablesize signal. For information about variablesize signals, see VariableSize Signal Basics (Simulink).
Dependencies
To enable this port, select Output variablesize signals
and set Maximum output size source to Inherit from
reference input
.
Data Types: double
Rst
— Reset sequence generator
0  1
Reset sequence generator, specified as 0
or
1
. For more information, see Reset Behavior.
Dependencies
To enable this port, select Reset on nonzero input.
Data Types: Boolean
Output
Out
— Pseudorandom noise sequence
binary vector
PN sequence, returned as a binary vector.
Parameters
Generator polynomial
— Generator polynomial
'z^6 + z + 1'
(default)  character vector  string scalar  binary row vector
Generator polynomial that determines the feedback connections of the shift register, specified as one of these options:
Character vector or string scalar of a polynomial whose constant term is
1
. For more information, see Representation of Polynomials in Communications Toolbox.Binaryvalued row vector that represents the coefficients of the polynomial in order of descending powers. The length of this vector must be N + 1, where N is the degree of the polynomial. The first and last entries must be
1
, indicating the leading term with degree N and a constant term of 1.Integervalued row vector of elements that represent the exponents for the nonzero terms of the polynomial in order of descending powers. The last entry must be
0
, indicating a constant term of 1.
For more information, see Simple Shift Register Generator.
Example: 'z^8 + z^2 + 1'
, [1 0 0 0 0 0 1 0 1]
,
and [8 2 0]
represent the same polynomial,
p(z) = z
^{8} + z
^{2} + 1.
Data Types: double
 char
Initial states
— Initial shift register states
[0 0 0 0 0 1]
(default)  binary row vector
Initial shift register states of the PN sequence generator when the simulation starts, specified as a binaryvalued row vector. The length of the vector must equal the degree of the generator polynomial specified by the Generator polynomial. For more information, see Simple Shift Register Generator.
Note
For the block to generate a nonzero sequence, the Initial states vector must contain at least one nonzero element.
Data Types: double
Output mask source
— Output mask source
Dialog parameter
(default)  Input port
Output mask source that indicates how the output mask information is given to the block, specified as one of these:
Dialog parameter
to use theOutput mask vector (or scalar shift value)
parameter setting.Input port
to add and use theMask
input port.
Output mask vector (or scalar shift value)
— Output mask vector or scalar shift value
0 (default)  integer scalar  binary vector
Output mask vector or scalar shift value, specified as an integer scalar or binary row vector of length N, where N is the degree of the generator polynomial. This parameter determines the delay of the PN sequence from the initial time. For more information, see Shifting PN Sequence Starting Point.
Dependencies
To enable this parameter, set Output mask source to
Dialog parameter
.
Data Types: double
Output variablesize signals
— Option to output variablelength signals
off
(default)  on
Select this parameter to enable variablelength output sequences during simulation. When you clear this parameter, the block outputs fixedlength sequences. When you select this parameter, the block can output variablelength sequences. For information about variablesize signals, see VariableSize Signal Basics (Simulink).
Maximum output size source
— Maximum output size source
Dialog parameter
(default)  Inherit from reference port
Select how to specify the maximum sequence output size.
Dialog parameter
— Select this value to configure the block to use the Maximum output size parameter setting as the maximum permitted output sequence length. The oSiz input port specifies the current size of the output signal, and the block output inherits the sample time from the input signal. The input value of oSiz must be less than or equal to the Maximum output size parameter.Inherit from reference port
— Select this value to enable the Ref input port and configure the block to inherit the sample time, maximum size, and current output size from the variablesized signal at the Ref input port. These set the maximum permitted output sequence length.
Dependencies
To enable this parameter, select Output variablesize signals.
Maximum output size
— Maximum output size
[10 1]
(default)  vector of the form [n 1]
Specify the maximum output size for the block. n is a positive scalar.
Example: [10 1]
specifies a 10by1 maximum size for the output
signal.
Dependencies
To enable this parameter, and set Maximum output size source
to Dialog parameter
.
Data Types: double
Sample time
— Output sample time
1
(default)  1  positive scalar
Positive scalars specify the time in seconds between each
sample of the output signal. If you set the Sample time to
1
, the output signal inherits the sample time from downstream. For
information on the relationship between the Sample time and
Samples per frame parameters, see
Sample Timing.
Example: 1
specifies a sample time of 1 second.
Dependencies
To enable this parameter, clear Output variablesize signals.
Data Types: double
Samples per frame
— Samples per frame
1
(default)  positive integer
Samples per frame in one channel of the output signal, specified as a positive integer. For information on the relationship between Sample time and Samples per frame, see Sample Timing.
Dependencies
To enable this parameter, clear Output variablesize signals.
Data Types: double
Reset on nonzero input
— Reset on nonzero input
off (default)  on
Select this parameter to add the Rst
input port. For more
information, see Reset Behavior.
Enable bitpacked outputs
— Enable bitpacked outputs
off (default)  on
Select this parameter to make the Number of packed bits and Interpret bitpacked values as signed parameters available.
When this parameter is selected, the object outputs a column vector of length M, which contains mostsignificantbit (MSB) first integer representations of bit words of length P. M is the number of samples per frame specified in the Samples per frame parameter. P is the size of the bitpacked words specified in the Number of packed bits parameter.
Note
The first bit from the left in the bitpacked word contains the most significant bit for the integer representation.
Number of packed bits
— Number of packed bits
8 (default)  integer in the range [1, 32]
Number of packed bits, specified as an integer in the range [1, 32].
Dependencies
To enable this parameter, select Enable bitpacked outputs.
Data Types: double
Interpret bitpacked values as signed
— Interpret bitpacked values as signed
off (default)  on
Interpret bitpacked values as signed integer data values when selected or unsigned integer data values when cleared. When selected, a 1 in the most significant bit (sign bit) indicates a negative value.
Dependencies
To enable this parameter, select Enable bitpacked outputs.
Output data type
— Output data type
double
(default)  boolean
 Smallest unsigned integer
Output data type, specified as double
,
boolean
, or Smallest unsigned
integer
.
When Enable bitpacked outputs is cleared, the output data type can be specified as a
double
,boolean
, orSmallest unsigned integer
. When the Output data type parameter is set toSmallest unsigned integer
, the output data type is selected based on the settings used in the Hardware Implementation pane of the Configuration Parameters dialog box of the model. IfASIC/FPGA
is selected in the Hardware Implementation pane, the output data typeufix(1)
= ideal minimum onebit size. For all other selections, it is an unsigned integer with the smallest available word length large enough to fit one bit, usually corresponding to the size of a char (for example,uint8
).When Enable bitpacked outputs is selected, the output data type can be specified as
double
orSmallest unsigned integer
. When the Output data type parameter is set toSmallest unsigned integer
, the output data type is selected based on the Interpret bitpacked values as signed and Number of packed bits parameters, and the settings used in the Hardware Implementation pane of the Configuration Parameters dialog box of the model. IfASIC/FPGA
is selected in the Hardware Implementation pane, the output data type is the ideal minimum nbit size, such assfix(n)
orufix(n)
, based on the Interpret bitpacked values as signed parameter. For all other selections, it is a signed or unsigned integer with the smallest available word length large enough to fit n bits.
Model Examples
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

More About
Simple Shift Register Generator
A linearfeedback shift register (LFSR), implemented as a simple shift register generator (SSRG), is used to generate PN sequences. This type of shift register is also known as a Fibonacci implementation. For an example, see Model PN Sequence Generation With Linear Feedback Shift Register.
The Generator Polynomial parameter determines the feedback connections of the shift register. It is a primitive binary polynomial in z, g_{r}z^{r}+g_{r–1}z^{r–1}+g_{r–2}z^{r–2}+...+g_{0}. For the coefficient, g_{k=0 to r}, the coefficient g_{k} is 1 if there is a connection from the kth register to the adder. The leading term, g_{r}, and the constant term, g_{0}, of the Generator Polynomial parameter must be 1 because the polynomial must be primitive. The Initial states parameter specifies the initial values of the registers. For example, the following table indicates two sets of parameter values that correspond to a generator polynomial of p(z) = z^{8} + z^{2} + 1.
Quantity  Example 1  Example 2 

Generator polynomial  g1 = [1 0 0 0 0 0 1 0 1]
 g2 = [8 2 0]

Degree of generator polynomial  8, which is length(g1)1
 8 
Initial states  [1 0 0 0 0 0 1 0]
 [1 0 0 0 0 0 1 0]

At each time step, all r registers in the generator update their values according to the value of the incoming arrow to the shift register. The adders perform addition modulo 2. The output of the LFSR reflects the sum of all connections in the m mask vector.
The Output mask vector (or scalar shift value) parameter, m, determines the shift of the PN sequence starting point. For more information, see Shifting PN Sequence Starting Point.
Shifting PN Sequence Starting Point
To shift the starting point of the PN sequence, specify the Output mask vector (or scalar shift value) parameter as:
An integer representing the length of the shift.
The default Output mask vector (or scalar shift value) setting of 0 corresponds to no shift. As illustrated in the LFSR shift register diagram in Simple Shift Register Generator, there is no shift when the only connection is along the arrow labeled m_{0}.
This table shows the shift that occurs when you set Output mask vector (or scalar shift value) to 0 versus a positive integer d.
T = 0 T = 1 T = 2 ... T = d T = d+1 Shift = 0 x_{0} x_{1} x_{2} ... x_{d} x_{d+1} Shift = d x_{d} x_{d+1} x_{d+2} ... x_{2d} x_{2d+1} A binary vector whose length is equal to the degree of the generator polynomial. The LFSR shift register diagram in Simple Shift Register Generator shows Output mask vector (or scalar shift value) specified as a mask vector, m. The binary vector must have N elements, where N is the degree of the generator polynomial. To calculate the mask vector, use the
shift2mask
function.The binary vector corresponds to a polynomial in z, m_{r–1}z^{r–1} + m_{r–2}z^{r–2} + ... + m_{1}z + m_{0}, of degree at most r–1. The mask vector that correspond to a shift of d is the vector that represents m(z) = z^{d} modulo g(z), where g(z) is the generator polynomial.
For example, if the degree of the generator polynomial is 4, then the mask vector that corresponds to d = 2 is
[0 1 0 0]
, which represents the polynomial m(z) = z^{2}.
Reset Behavior
Before you can reset the generator sequence, you must select the
Reset on nonzero input parameter to enable the
Rst input port. Suppose that the PN Sequence Generator block outputs
[1 0 0 1 1 0 1 1]
when no reset exists. This table shows the effect
on the PN Sequence Generator block output for the parameter values indicated.
Reset Signal  Reset Signal Settings  PN Sequence Generator block  Reset Signal and Output Signal 

No reset 



Scalar reset signal 



Vector reset signal 


For the noreset case, the block outputs the sequence without resetting it.
For the scalar and vector reset signal cases, the block inputs the reset signal [0
0 0 1 0 0 0 0]
to the Rst port. Because the fourth bit of
the reset signal is a 1
and Sample time is
1
, the block resets the sequence output at the fourth bit.
For variablesized outputs, the block supports only scalar reset signal inputs.
Sequences of Maximum Length
To generate a maximum length sequence for a generator polynomial that has the degree r, set Generator polynomial to a value from the following table. The maximum sequence length is 2^{r} – 1.
r  Generator Polynomial  r  Generator Polynomial  r  Generator Polynomial  r  Generator Polynomial 

2  [2 1 0]
 15  [15 14 0]
 28  [28 25 0]
 41  [41 3 0]

3  [3 2 0]
 16  [16 15 13 4 0]
 29  [29 27 0]
 42  [42 23 22 1 0]

4  [4 3 0]
 17  [17 14 0]
 30  [30 29 28 7 0]
 43  [43 6 4 3 0]

5  [5 3 0]
 18  [18 11 0]
 31  [31 28 0]
 44  [44 6 5 2 0]

6  [6 5 0]
 19  [19 18 17 14 0]
 32  [32 31 30 10 0]
 45  [45 4 3 1 0]

7  [7 6 0]
 20  [20 17 0]
 33  [33 20 0]
 46  [46 21 10 1 0]

8  [8 6 5 4 0]
 21  [21 19 0]
 34  [34 15 14 1 0]
 47  [47 14 0] 
9  [9 5 0]
 22  [22 21 0]
 35  [35 2 0]
 48  [48 28 27 1 0] 
10  [10 7 0]
 23  [23 18 0]
 36  [36 11 0]
 49  [49 9 0] 
11  [11 9 0]
 24  [24 23 22 17 0]
 37  [37 12 10 2 0]  50  [50 4 3 2 0] 
12  [12 11 8 6 0]
 25  [25 22 0]
 38  [38 6 5 1 0]  51  [51 6 3 1 0] 
13  [13 12 10 9 0]
 26  [26 25 24 20 0]
 39  [39 8 0]  52  [52 3 0] 
14  [14 13 8 4 0]
 27  [27 26 25 22 0]
 40  [40 5 4 3 0]
 53  [53 6 2 1 0] 
For more information about the shiftregister configurations that these polynomials represent, see Digital Communications by John Proakis.[1].
Sample Timing
The time between output updates is equal to the product of the
Samples per frame and Sample time parameter
values. For example, if Sample time and Samples per
frame each equal 1
, the block outputs a sample every
second. If you increase Samples per frame to 10, then the block outputs
a 10by1 vector every 10 seconds. This ensures that the equivalent output rate is not
dependent on the Samples per frame parameter.
Compatibility Considerations
Existing models automatically update this block to current version
Behavior changed in R2020a
Starting in R2020a, Simulink^{®} no longer allows you to use the PN Sequence Generator block version available before R2015b.
Existing models automatically update to load the PN Sequence Generator block version announced in Source blocks output frames of contiguous time samples but do not use the frame attribute in the R2015b Release Notes. For more information on block forwarding, see Maintain Compatibility of Library Blocks Using Forwarding Tables (Simulink).
References
[1] Proakis, John G. Digital Communications. 3rd ed. New York: McGraw Hill, 1995.
[2] Lee, J. S., and L. E. Miller. CDMA Systems Engineering Handbook. Boston and London. Artech House, 1998.
[3] Golomb, S.W. Shift Register Sequences. Laguna Hills. Aegean Park Press, 1967.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has a single, default HDL architecture.
ConstrainedOutputPipeline  Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is

InputPipeline  Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

OutputPipeline  Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

You can select
Input port
as the Output mask source on the block. In this case, theMask
input signal must be a vector of data typeufix1
.If you select Reset on nonzero input, the input to the
Rst
port must have data typeBoolean
.Outputs of type
double
are not supported for HDL code generation. All other output types (including bitpacked outputs) are supported.You cannot generate HDL for this block inside a Resettable Synchronous Subsystem (HDL Coder).
You cannot generate HDL for this block inside a Triggered Subsystem if the Use trigger signal as clock option is selected. See Using Triggered Subsystems for HDL Code Generation (HDL Coder).
See Also
Blocks
Objects
Topics
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