Gold Sequence Generator

Generate Gold sequence from set of sequences

Library:
Communications Toolbox / Comm Sources / Sequence Generators

Description

The Gold Sequence Generator block generates a binary sequence with small periodic cross-correlation properties from a bounded set of sequences. For more information on Gold sequences, see Gold Sequences.

This block can output sequences that vary in length during simulation. For more information about variable-size signals, see Variable-Size Signal Basics (Simulink).

Ports

Input

expand all

`oSiz` — Current output size
scalar | two-element row vector

Current output size, specified as a scalar or a two-element row vector. The second element of the vector must be 1.

Example: [10 1] indicates the current output column vector will be of size 10-by-1.

Dependencies

To enable this port select the Output variable-size signals parameter and set Maximum output size source to Dialog parameter.

Data Types: double

`Ref` — Reference input signal
scalar | column vector

Reference input signal, specified as a scalar, column vector.

Dependencies

To enable this port select the Output variable-size signals parameter and set Maximum output size source to Inherit from reference input.

Data Types: double

`Rst` — Reset signal
scalar | column vector

Reset signal, specified in one of these forms.

When the output size is variable specify as a scalar.
Otherwise, specify as a scalar or a 2-D column vector with a length equal to Samples per frame.

The output signal resets for nonzero Rst input values. For more information, see Reset Behavior

Dependencies

To enable this port, select the Reset on nonzero input parameter.

Data Types: double

Output

expand all

`Out` — Output signal
binary column vector

Output signal, returned as a binary column vector. At least one element of the Initial states (1) or Initial states (2) vector must be nonzero in order for the block to generate a nonzero sequence.

Data Types: double

Parameters

expand all

`Preferred polynomial (1)` — First sequence polynomial
`'z^6 + z + 1'` (default) | polynomial character vector | binary row vector | integer row vector

First sequence polynomial, specified in one of these forms.

A polynomial character vector such as 'z^3 + z^2 + 1'.
A binary row vector that represents the coefficients of the generator polynomial in order of descending power. The length of this vector is (N+1), where N is the degree of the generator polynomial. For example, [1 1 0 1] represents the polynomial x³+ z²+ 1.
An integer row vector containing the exponents of z for the nonzero terms in the polynomial in descending order. For example, [3 2 0] represents the polynomial z³+ z²+ 1.

For more information, see Character Representation of Polynomials and Preferred Pairs of Sequences.

`Initial states (1)` — Initial states for first sequence polynomial
`[0 0 0 0 0 1]` (default) | binary vector

Initial states of the shift register for first sequence polynomial of the preferred pair, specified as a binary vector with length equal to the degree of Preferred polynomial (1).

`Preferred polynomial (2)` — Second sequence polynomial
`'z^6 + z^5 + z^2 + z + 1'` (default) | polynomial character vector | binary row vector | integer row vector

Second sequence polynomial, specified in one of these forms.

A polynomial character vector such as 'z^3 + z^2 + 1'.
A binary row vector that represents the coefficients of the generator polynomial in order of descending power. The length of this vector is (N+1), where N is the degree of the generator polynomial. For example, [1 1 0 1] represents the polynomial x³+ z²+ 1.
An integer row vector containing the exponents of z for the nonzero terms in the polynomial in descending order. For example, [3 2 0] represents the polynomial z³+ z²+ 1.

For more information, see Character Representation of Polynomials.

`Initial states (2)` — Initial states for second sequence polynomial
`[0 0 0 0 0 1]` (default) | binary vector

Initial states of the shift register for second sequence polynomial of the preferred pair, specified as a binary vector with length equal to the degree of Preferred polynomial (2).

`Sequence index` — Sequence index
`0` (default) | integer scalar in the range [–2, 2ⁿ–2]

Sequence index of the output sequence from the set of sequences, specified as an integer scalar in the range [–2, 2ⁿ–2]. n is the degree of the preferred polynomials.

`Shift` — Offset of Gold sequence
`0` (default) | integer scalar

Offset of Gold sequence from the initial time, specified as an integer scalar.

`Output variable-size signals` — Output variable-size signals
off (default) | on

Select this parameter to permit variable length output sequences during simulation. When set to off, fixed-length sequences are output. When set to on, variable-length sequences can be output. For information about variable-size signals, see Variable-Size Signal Basics (Simulink).

`Maximum output size source` — Maximum output size source
`Dialog parameter` (default) | `Inherit from reference port`

Maximum output size source, which indicates how the maximum sequence output size is specified.

Dialog parameter configures the block to use the Maximum output size parameter setting as the maximum permitted output sequence length. When you make this selection, the oSiz input port specifies the current size of the output signal and the block output inherits 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 adds the Ref input port and configures the block to inherit the sample time, maximum size, and the current output size from the variable-sized signal at the Ref input port to set the maximum permitted output sequence length.

Dependencies

To enable this parameter, select Output variable-size signals.

`Maximum output size` — Maximum output size
`[10 1]` (default) | two-element row vector

Maximum output size, specified as a two-element row vector that denotes the maximum output size for the block. The second element of the vector must be 1.

Example: [10 1] gives a 10-by-1 maximum sized output signal.

Dependencies

To enable this parameter select Output variable-size signals and set Maximum output size source to Dialog parameter.

Data Types: double

`Sample time` — Output sample time
`1` (default)

Output sample time, specified as -1 or a positive scalar that represents the time between each sample of the output signal. If Sample time is set to -1, the sample time is inherited from downstream. For information on the relationship between Sample time and Samples per frame, see Sample Timing.

Dependencies

To enable this parameter do not select Output variable-size signals.

`Samples per frame` — Samples per frame
`1` (default) | positive integer

Samples per frame, specified as a positive integer indicating the number of samples per frame in one channel of the output data. For information on the relationship between Sample time and Samples per frame, see Sample Timing.

Dependencies

To enable this parameter do not select Output variable-size signals.

`Reset on nonzero input` — Reset output signal
`off` (default) | `on`

Select this parameter to enable the Rst port. When a nonzero value is input at the Rst port, the internal shift registers are reset to the original values of the Initial states (1) and Initial states (2) parameters.

`Output data type` — Output data type
`double` (default) | `boolean` | `Smallest unsigned integer`

Output data type, specified as boolean, double, or Smallest unsigned integer.

When set to Smallest unsigned integer, the output data type is selected based on the settings used in the Hardware Implementation Pane (Simulink) of the Configuration Parameters dialog box of the model. If ASIC/FPGA is selected in the Hardware Implementation pane, the output data type is the ideal minimum one-bit size (ufix(1)). 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 (uint8).

Model Examples

Generate Gold Code Sequence

Generate the same Gold code sequences using two PN Sequence Generator blocks or one Gold Sequence Generator block.

Gold Sequence Generator Reset Behavior

The Gold Sequence Generator output behavior for reset related parameter settings.

WCDMA End-to-End Physical Layer

Part of the frequency division duplex (FDD) downlink physical layer of the third generation wireless communication system known as wideband code division multiple access (WCDMA).

Generate GPS Coarse Acquisition Codes

How to configure the Gold Sequence Generator block to generate coarse acquisition (C/A) codes as presented in [ 1 ] and uses a discrete block model representation of the same configuration for validating the code generated. GPS uses C/A codes to facilitate acquisition and tracking of transmission signals.

Block Characteristics

Data Types	`Boolean` \| `double` \| `fixed point`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`

More About

expand all

Sample Timing

The time between output updates is equal to the product of Samples per frame and Sample time. For example, if Sample time and Samples per frame equal one, the block outputs a sample every second. If Samples per frame is increased to 10, then a 10-by-1 vector is output every 10 seconds. This ensures that the equivalent output rate is not dependent on the Samples per frame parameter.

Gold Sequences

The characteristic cross-correlation properties of Gold sequences make them useful when multiple devices are broadcasting in the same frequency range. The Gold sequences are defined using a specified pair of sequences u and v, of period N = 2ⁿ – 1, called a preferred pair, as defined in Preferred Pairs of Sequences. The set G(u, v) of Gold sequences is defined by

$G (u, v) = {u, v, u \oplus v, u \oplus T v, u \oplus T^{2} v, ..., u \oplus T^{N - 1} v}$

where T represents the operator that shifts vectors cyclically to the left by one place, and $\oplus$ represents addition modulo 2. Note that G(u,v) contains N + 2 sequences of period N. The Gold Sequence Generator block outputs one Gold sequence according to the configured parameters and inputs.

Gold sequences have the property that the cross-correlation between any two, or between shifted versions of them, takes on one of three values: –t(n), –1, or t(n) – 2, where

$t (n) = {\begin{array}{l} 1 + 2^{(n + 1) / 2} & n even \\ 1 + 2^{(n + 2) / 2} & n odd \end{array}$

The Gold Sequence Generator block uses two PN Sequence Generator blocks to generate the preferred pair of sequences, and then XORs these sequences to produce the output sequence, as shown in the following diagram.

You can specify the preferred pair by the Preferred polynomial (1) and Preferred polynomial (2) parameters in the dialog for the Gold Sequence Generator block. These polynomials, both of which must have degree n, describe the shift registers that the PN Sequence Generator blocks use to generate their output. For more details on how these sequences are generated, see the reference page for the PN Sequence Generator block. You can specify the preferred polynomials using these formats:

A polynomial character vector that includes the number 1, for example, 'z^4 + z + 1'.
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, the polynomial z⁵ + z² + 1 can be represented by the character vector 'z^5 + z^2 + 1', the vector [5 2 0], and the vector [1 0 0 1 0 1].

The following table provides a short list of preferred pairs.

n	N	Preferred Polynomial (1)	Preferred Polynomial (2)
5	31	`[5 2 0]`	`[5 4 3 2 0]`
6	63	`[6 1 0]`	`[6 5 2 1 0]`
7	127	`[7 3 0]`	`[7 3 2 1 0]`
9	511	`[9 4 0]`	`[9 6 4 3 0]`
10	1023	`[10 3 0]`	`[10 8 3 2 0]`
11	2047	`[11 2 0]`	`[11 8 5 2 0]`

The Initial states (1) and Initial states (2) parameters are vectors specifying the initial values of the registers corresponding to Preferred polynomial (1) and Preferred polynomial (2), respectively. These parameters must satisfy these criteria:

All elements of the Initial states (1) and Initial states (2) vectors must be binary numbers.
The length of the Initial states (1) vector must equal the degree of the Preferred polynomial (1), and the length of the Initial states (2) vector must equal the degree of the Preferred polynomial (2).
Note
At least one element of the initial states vectors ( Initial states (1) or Initial states (2)) must be nonzero in order for the block to generate a nonzero sequence. Specifically, the initial state of at least one of the registers must be nonzero.

The Sequence index parameter specifies which Gold sequence in the set G(u, v) is output. The range of Sequence index is [–2, –1, 0, 1, 2, ..., 2ⁿ–2], where n is the degree of the generator polynomials specified by the Preferred polynomial (1) and Preferred polynomial (2) parameters. This table shows the correspondence between Sequence index and the output sequence.

Sequence Index	Output Sequence
–2	u
–1	v
0	$u \oplus v$
1	$u \oplus T v$
2	$u \oplus T^{2} v$
...	...
2 ⁿ –2	$u \oplus T^{2^{n} - 2} v$

T represents the operator that shifts vectors cyclically to the left by one place, and $\oplus$ represents addition modulo 2.

You can shift the starting point of the Gold sequence with the Shift parameter, which is an integer representing the length of the shift.

You can use an external signal to reset the values of the internal shift register to the initial state by selecting Reset on nonzero input. This creates an input port for the external signal in the Gold Sequence Generator block. The way the block resets the internal shift register depends on whether its output signal and the reset signal are scalar or vector. For more information, see Reset Behavior.

Reset Behavior

To reset the generator sequence, you must first select Reset on nonzero input to add the Rst input. Suppose that the Gold Sequence Generator block outputs [1 0 0 1 1 0 1 1] when there is no reset. The following table shows the effect on the Gold Sequence Generator block output for the property values indicated.

Reset Signal Properties

Gold Sequence Generator block

	Reset Signal Properties	Gold Sequence Generator block
No reset	Sample time = `1` Samples per frame = `1` Rst = `[0 0 0 0 0 0 0 0]`	Sample time = `1` Samples per frame = `1` Out = `[1 0 0 1 1 0 1 1]`
Scalar reset signal	Sample time = `1` Samples per frame = `1` Rst = `[0 0 0 1 0 0 0 0]`	Sample time = `1` Samples per frame = `1`
Vector reset signal	Sample time = `1` Samples per frame = `8` Rst = `[0 0 0 1 0 0 0 0]`	Sample time = `1` Samples per frame = `8`

Reset Signal

Output Signal

No reset

Sample time = 1

Samples per frame = 1

Rst = [0 0 0 0 0 0 0 0]

Sample time = 1

Samples per frame = 1

Out = [1 0 0 1 1 0 1 1]

Scalar reset signal

Sample time = 1

Samples per frame = 1

Rst = [0 0 0 1 0 0 0 0]

Sample time = 1

Samples per frame = 1

Vector reset signal

Sample time = 1

Samples per frame = 8

Rst = [0 0 0 1 0 0 0 0]

Sample time = 1

Samples per frame = 8

For the no reset case, the sequence is output without being reset. For the scalar and vector reset signal cases, the reset signal [0 0 0 1 0 0 0 0] is input to the Rst port. The sequence output is reset at the fourth bit, because the fourth bit of the reset signal is a 1 and the Sample time is 1.

For variable-sized outputs, the block only supports scalar reset signal inputs.

The Gold Sequence Generator Reset Behavior example demonstrates the reset behavior in a Simulink^® model.

Preferred Pairs of Sequences

The requirements for a pair of sequences u, v of period N = 2ⁿ–1 to be a preferred pair are as follows:

n is not divisible by 4
v = u[q], where
- q is odd
- q = 2^k+1 or q = 2^2k–2^k+1
- v is obtained by sampling every qth symbol of u
$\gcd (n, k) = {\begin{matrix} 1 & n \equiv 1 \mod 2 \\ 2 & n \equiv 2 \mod 4 \end{matrix}$

Compatibility Considerations

expand all

Existing models automatically update this block to current version

Behavior changed in R2020a

Starting in R2020a, Simulink no longer allows you to use the Gold Sequence Generator block version available before R2015b.

Existing models automatically update to load the Gold 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 Forwarding Tables (Simulink).

References

[1] Proakis, John G. Digital Communications 3rd ed. New York: McGraw Hill, 1995.

[2] Gold, R. “Maximal Recursive Sequences with 3-Valued Recursive Cross-Correlation Functions (Corresp.).” IEEE Transactions on Information Theory 14, no. 1 (January 1968): 154–56. https://doi.org/10.1109/TIT.1968.1054106.

[3] Gold, R. “Optimal Binary Sequences for Spread Spectrum Multiplexing (Corresp.).” IEEE Transactions on Information Theory 13, no. 4 (October 1967): 619–21. https://doi.org/10.1109/TIT.1967.1054048.

[4] Sarwate, D.V., and M.B. Pursley, "Crosscorrelation Properties of Pseudorandom and Related Sequences," Proc. IEEE , Vol. 68, No. 5, May, 1980, pp. 583-619.

[5] Dixon, Robert C. Spread Spectrum Systems: With Commercial Applications. 3rd ed. New York: Wiley, 1994.

Documentation

Gold Sequence Generator

Description

Ports

Input

oSiz — Current output size scalar | two-element row vector

Dependencies

Ref — Reference input signal scalar | column vector

Dependencies

Rst — Reset signal scalar | column vector

Dependencies

Output

Out — Output signal binary column vector

Parameters

Preferred polynomial (1) — First sequence polynomial 'z^6 + z + 1' (default) | polynomial character vector | binary row vector | integer row vector

Initial states (1) — Initial states for first sequence polynomial [0 0 0 0 0 1] (default) | binary vector

Preferred polynomial (2) — Second sequence polynomial 'z^6 + z^5 + z^2 + z + 1' (default) | polynomial character vector | binary row vector | integer row vector

Initial states (2) — Initial states for second sequence polynomial [0 0 0 0 0 1] (default) | binary vector

Sequence index — Sequence index 0 (default) | integer scalar in the range [–2, 2n–2]

Shift — Offset of Gold sequence 0 (default) | integer scalar

Output variable-size signals — Output variable-size signals off (default) | on

Maximum output size source — Maximum output size source Dialog parameter (default) | Inherit from reference port

Dependencies

Maximum output size — Maximum output size [10 1] (default) | two-element row vector

Dependencies

Sample time — Output sample time 1 (default)

Dependencies

Samples per frame — Samples per frame 1 (default) | positive integer

Dependencies

Reset on nonzero input — Reset output signal off (default) | on

Output data type — Output data type double (default) | boolean | Smallest unsigned integer

Model Examples

Generate Gold Code Sequence

Gold Sequence Generator Reset Behavior

WCDMA End-to-End Physical Layer

Generate GPS Coarse Acquisition Codes

Block Characteristics

More About

Sample Timing

Gold Sequences

Reset Behavior

Preferred Pairs of Sequences

Compatibility Considerations

Existing models automatically update this block to current version

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

See Also

Blocks

Objects

Communications Toolbox Documentation

Support

`oSiz` — Current output size
scalar | two-element row vector

`Ref` — Reference input signal
scalar | column vector

`Rst` — Reset signal
scalar | column vector

`Out` — Output signal
binary column vector

`Preferred polynomial (1)` — First sequence polynomial
`'z^6 + z + 1'` (default) | polynomial character vector | binary row vector | integer row vector

`Initial states (1)` — Initial states for first sequence polynomial
`[0 0 0 0 0 1]` (default) | binary vector

`Preferred polynomial (2)` — Second sequence polynomial
`'z^6 + z^5 + z^2 + z + 1'` (default) | polynomial character vector | binary row vector | integer row vector

`Initial states (2)` — Initial states for second sequence polynomial
`[0 0 0 0 0 1]` (default) | binary vector

`Sequence index` — Sequence index
`0` (default) | integer scalar in the range [–2, 2ⁿ–2]

`Shift` — Offset of Gold sequence
`0` (default) | integer scalar

`Output variable-size signals` — Output variable-size signals
off (default) | on

`Maximum output size source` — Maximum output size source
`Dialog parameter` (default) | `Inherit from reference port`

`Maximum output size` — Maximum output size
`[10 1]` (default) | two-element row vector

`Sample time` — Output sample time
`1` (default)

`Samples per frame` — Samples per frame
`1` (default) | positive integer

`Reset on nonzero input` — Reset output signal
`off` (default) | `on`

`Output data type` — Output data type
`double` (default) | `boolean` | `Smallest unsigned integer`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.