Documentation

# commsrc.pn

Create PN sequence generator object

## Syntax

```h = commsrc.pn h = commsrc.pn(property1,value1,...) ```

## Description

`h = commsrc.pn` creates a default PN sequence generator object h, and is equivalent to the following:

```H = commsrc.pn('GenPoly', [1 0 0 0 0 1 1], ... 'InitialStates', [0 0 0 0 0 1], ... 'CurrentStates', [0 0 0 0 0 1], ... 'Mask', [0 0 0 0 0 1], ... 'NumBitsOut', 1)```

or

```H = commsrc.pn('GenPoly', [1 0 0 0 0 1 1], ... 'InitialStates', [0 0 0 0 0 1], ... 'CurrentStates', [0 0 0 0 0 1], ... 'Shift', 0, ... 'NumBitsOut', 1)```

`h = commsrc.pn(property1,value1,...)` creates a PN sequence generator object, h, with properties you specify as property/value pairs.

## Properties

A PN sequence generator has the properties shown on the following table. All properties are writable except for the ones explicitly noted otherwise.

PropertyDescription
GenPolyGenerator polynomial vector array of bits; must be descending order
InitialStatesVector array (with length of the generator polynomial order) of initial shift register values (in bits)
CurrentStatesVector array (with length of the generator polynomial order) of present shift register values (in bits)
NumBitsOutNumber of bits to output at each `generate` method invocation
`Mask` or `Shift`

A mask vector of binary 0 and 1 values is used to specify which shift register state bits are XORed to produce the resulting output bit value.

Alternatively, a scalar shift value may be used to specify an equivalent shift (either a delay or advance) in the output sequence.

The `'GenPoly'` property values specify the shift register connections. Enter these values as either a binary vector or a vector of exponents of the nonzero terms of the generator polynomial in descending order of powers. For the binary vector representation, the first and last elements of the vector must be 1. For the descending-ordered polynomial representation, the last element of the vector must be 0. For more information and examples, see the LFSR SSRG Details section of this page.

## Methods

A PN sequence generator is equipped with the following methods.

### generate

Generate [NumBitsOut x 1] PN sequence generator values

### reset

Set the `CurrentStates` values to the `InitialStates` values

### getshift

Get the actual or equivalent `Shift` property value

Get the actual or equivalent `Mask` property value

### copy

Make an independent copy of a `commsrc.pn` object

### disp

Display PN sequence generator object properties

## Side Effects of Setting Certain Properties

### Setting the GenPoly Property

Every time this property is set, it will reset the entire object. In addition to changing the polynomial values, `'CurrentStates'`, `'InitialStates'`, and `'Mask'` will be set to their default values (`'NumBitsOut'` will remain the same), and no warnings will be issued.

### Setting the InitialStates Property

Every time this property is set, it will also set `'CurrentStates'` to the new `'InitialStates'` setting.

## LFSR SSRG Details

The `generate` method produces a pseudorandom noise (PN) sequence using a linear feedback shift register (LFSR). The LFSR is implemented using a simple shift register generator (SSRG, or Fibonacci) configuration, as shown below.

All r registers in the generator update their values at each time step according to the value of the incoming arrow to the shift register. The adders perform addition modulo 2. The shift register is described by the `'GenPoly'` property (generator polynomial), which is a primitive binary polynomial in z, grzr+gr-1zr-1+gr-2zr-2+...+g0. The coefficient gk is 1 if there is a connection from the kth register, as labeled in the preceding diagram, to the adder. The leading term gr and the constant term g0 of the `'GenPoly'` property must be 1 because the polynomial must be primitive.

You can specify the Generator polynomial parameter using either of these formats:

• A vector that lists the coefficients of the polynomial in descending order of powers. The first and last entries must be 1. Note that the length of this vector is one more than the degree of the generator polynomial.

• A vector containing the exponents of z for the nonzero terms of the polynomial in descending order of powers. The last entry must be `0`.

For example, `[1 0 0 0 0 0 1 0 1]` and ```[8 2 0]``` represent the same polynomial, p(z) = z8 + z2 + 1.

The Initial states parameter is a vector specifying the initial values of the registers. The Initial states parameter must satisfy these criteria:

• All elements of the Initial states vector must be binary numbers.

• The length of the Initial states vector must equal the degree of the generator polynomial.

### Note

At least one element of the Initial states vector must be nonzero in order for the block to generate a nonzero sequence. That is, the initial state of at least one of the registers must be nonzero.

For example, the following table indicates two sets of parameter values that correspond to a generator polynomial of p(z) = z8 + z2 + 1.

QuantityExample 1Example 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]`

Output mask vector (or scalar shift value) shifts the starting point of the output sequence. With the default setting for this parameter, the only connection is along the arrow labeled m0, which corresponds to a shift of 0. The parameter is described in greater detail below.

You can shift the starting point of the PN sequence with Output mask vector (or scalar shift value). You can specify the parameter in either of two ways:

• An integer representing the length of the shift

• A binary vector, called the mask vector, whose length is equal to the degree of the generator polynomial

The difference between the block's output when you set Output mask vector (or scalar shift value) to 0, versus a positive integer d, is shown in the following table.

T = 0 T = 1 T = 2 ... T = d T = d+1
Shift = 0 x0 x1 x2 ... xd xd+1
Shift = d xd xd+1 xd+2 ... x2d x2d+1

Alternatively, you can set Output mask vector (or scalar shift value) to a binary vector, corresponding to a polynomial in z, mr-1zr-1 + mr-2zr-2 + ... + m1z + m0, of degree at most r-1. The mask vector corresponding to a shift of d is the vector that represents m(z) = zd 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 corresponding to d = 2 is ```[0 1 0 0]```, which represents the polynomial m(z) = z2. The preceding schematic diagram shows how Output mask vector (or scalar shift value) is implemented when you specify it as a mask vector. The default setting for Output mask vector (or scalar shift value) is `0`. You can calculate the mask vector using the Communications Toolbox™ function `shift2mask`.

### Sequences of Maximum Length

If you want to generate a sequence of the maximum possible length for a fixed degree, r, of the generator polynomial, you can set Generator polynomial to a value from the following table. See Proakis, John G., Digital Communications, Third edition, New York, McGraw Hill, 1995 for more information about the shift-register configurations that these polynomials represent.

rGenerator PolynomialrGenerator Polynomial
2 `[2 1 0]` 21 `[21 19 0]`
3 `[3 2 0]` 22 `[22 21 0]`
4 `[4 3 0]` 23 `[23 18 0]`
5 `[5 3 0]` 24 `[24 23 22 17 0]`
6 `[6 5 0]` 25 `[25 22 0]`
7 `[7 6 0]` 26 `[26 25 24 20 0]`
8 `[8 6 5 4 0]` 27 `[27 26 25 22 0]`
9 `[9 5 0]` 28 `[28 25 0]`
10 `[10 7 0]` 29 `[29 27 0]`
11 `[11 9 0]` 30 `[30 29 28 7 0]`
12 `[12 11 8 6 0]` 31 `[31 28 0]`
13 `[13 12 10 9 0]` 32 `[32 31 30 10 0]`
14 `[14 13 8 4 0]` 33 `[33 20 0]`
15 `[15 14 0]` 34 `[34 15 14 1 0]`
16 `[16 15 13 4 0]` 35 `[35 2 0]`
17 `[17 14 0]` 36 `[36 11 0]`
18 `[18 11 0]` 37 [37 12 10 2 0]
19 `[19 18 17 14 0]` 38 [38 6 5 1 0]
20 `[20 17 0]` 39 [39 8 0]
40 `[40 5 4 3 0]` 47 [47 14 0]
41 `[41 3 0]` 48 [48 28 27 1 0]
42 `[42 23 22 1 0]` 49 [49 9 0]
43 `[43 6 4 3 0]` 50 [50 4 3 2 0]
44 `[44 6 5 2 0]` 51 [51 6 3 1 0]
45 `[45 4 3 1 0]` 52 [52 3 0]
46 `[46 21 10 1 0]` 53 [53 6 2 1 0]

## Examples

collapse all

Set up a PN sequence generator. Define the polynomial in binary vector format or exponential vector format.

This figure defines a PN sequence generator with a generator polynomial $p\left(z\right)={z}^{6}+z+1$.

Define this PN sequence generator as follows:

```h1 = commsrc.pn('GenPoly', [1 0 0 0 0 1 1], 'Mask', [1 1 0 1 0 1]); h2 = commsrc.pn('GenPoly', [1 0 0 0 0 1 1], 'Shift', 22); mask2shift ([1 0 0 0 0 1 1],[1 1 0 1 0 1])```
```ans = 22 ```

Alternatively, you can input `GenPoly` as the exponents of z for the nonzero terms of the polynomial in descending order of powers:

`h = commsrc.pn('GenPoly', [6 1 0], 'Mask', [1 1 0 1 0 1])`
```h = GenPoly: [1 0 0 0 0 1 1] InitialStates: [0 0 0 0 0 1] CurrentStates: [0 0 0 0 0 1] Mask: [1 1 0 1 0 1] NumBitsOut: 1 ```

Typically `commsrc.pn` is used to output pseudorandom data streams.

Construct a PN object.

`h = commsrc.pn('Shift',0);`

Output 10 PN bits.

```set(h,'NumBitsOut',10); generate(h)```
```ans = 10×1 1 0 0 0 0 0 1 0 0 0 ```

Output 10 more PN bits.

`generate(h)`
```ans = 10×1 0 1 1 0 0 0 1 0 1 0 ```

Reset the object to the initial shift register state values.

`reset(h);`

Output 4 PN bits.

```set(h,'NumBitsOut',4); generate(h)```
```ans = 4×1 1 0 0 0 ```

When a `commsrc.pn` object is copied, its states are also copied. Subsequent outputs from the copied object are likely to be different from the initial outputs from the original object.

Construct a PN object and output a sequence from it.

```h = commsrc.pn('Shift', 0); set(h, 'NumBitsOut', 5); generate(h)```
```ans = 5×1 1 0 0 0 0 ```

Make a copy of `h`. Generate a sequence from the copied object. Because the copy was made after the state of `h` changed, the initial sequence generated by `g` is different from the initial sequence generated from `h`.

```g=copy(h); generate(g)```
```ans = 5×1 0 1 0 0 0 ```

But if `g` is reset, it generates the same sequence that `h` generated.

```reset(g); generate(g)```
```ans = 5×1 1 0 0 0 0 ```