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Documentation Help Center. The Kasami Sequence Generator block generates a sequence from the set of Kasami sequences. The Kasami sequences are a set of sequences that have good cross-correlation properties. This block can output sequences that vary in length during simulation. There are two sets of Kasami sequences: the small set and the large set.

The large set contains all the sequences in the small set. Only the small set is optimal in the sense of matching Welch's lower bound for correlation functions. The large set is defined by the following table, in which k and m are the shift parameters for the sequences v and w , respectively. See the reference page for the Gold Sequence Generator block for a description of Gold sequences. However, the Kasami sequences form a larger set than the Gold sequences.

The Generator polynomial parameter specifies the generator polynomial, which determines the connections in the shift register that generates the sequence u. You can specify the Generator polynomial parameter using 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. The Initial states parameter specifies the initial states of the shift register that generates the sequence u. Initial States is a binary scalar or row vector of length equal to the degree of the Generator polynomial.

If you choose a binary scalar, the block expands the scalar to a row vector of length equal to the degree of the Generator polynomial , all of whose entries equal the scalar.

The Sequence index parameter specifies the shifts of the sequences v and w used to generate the output sequence. You can specify the parameter in either of two ways:. To generate sequences from the small set, for n is even, you can specify the Sequence index as an integer m. The range of m is [-1, The following table describes the output sequences corresponding to Sequence index m :. In this case, the output sequence is from the large set.

The range for k is [-2, The following table describes the output sequences corresponding to Sequence index [k m]:. You can shift the starting point of the Kasami 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 Kasami Sequence Generator block.

The way the block resets the internal shift register depends on whether its output signal and the reset signal are sample-based or frame-based. See Reset Behavior for an example. The following table lists some of the polynomials that you can use to generate the Kasami set of sequences. Character vector or binary vector specifying the generator polynomial for the sequence u. Binary scalar or row vector of length equal to the degree of the Generator polynomial , which specifies the initial states of the shift register that generates the sequence u.

Integer or vector specifying the shifts of the sequences v and w used to generate the output sequence. Integer scalar that determines the offset of the Kasami sequence from the initial time. Select this if you want the output sequences to vary in length during simulation. The default selection outputs fixed-length signals. When you select Dialog parameter , the value you enter in the Maximum output size parameter specifies the maximum size of the output.

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 must be less than or equal to the Maximum output size parameter. When you select Inherit from reference port , the block output inherits sample time, maximum size, and current size from the variable-sized signal at the Ref input port. This parameter only appears when you select Output variable-size signals. The default selection is Dialog parameter.

Specify a two-element row vector denoting the maximum output size for the block. The second element of the vector must be 1. For example, [10 1] gives a by-1 maximum sized output signal. 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. Samples per frame, specified as a positive integer indicating the number of samples per frame in one channel of the output data.

When selected, you can specify an input signal that resets the internal shift registers to the original values of the Initial states. The output type of the block can be specified as a boolean or double. By default, the block sets this to double. This model considers Kasami spreading for a combined two-user transmission in a multipath environment.

You can see very good user separation over multiple paths with the gains of combining. This can be attributed to the "good" correlation properties of Kasami sequences, which provide a balance between the ideal cross-correlation properties of orthogonal codes and the ideal auto-correlation properties of PN sequences. To experiment with this model further, try selecting other path delays to see how the performance varies for the same code. Also try different codes with the same delays.

IEEE , Vol. 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 by-1 vector is output every 10 seconds.

This ensures that the equivalent output rate is not dependent on the Samples per frame parameter. To reset the generator sequence, you must first select Reset on nonzero input to add the Rst input. Suppose that the Kasami 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 Kasami Sequence Generator block output for the property values indicated.

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. Existing models automatically update to load the Kasami Sequence Generator block version announced in Source blocks output frames of contiguous time samples but do not use the frame attribute in the Rb Release Notes.

For more information on block forwarding, see Forwarding Tables Simulink. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.

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Toggle Main Navigation. Search Support Support MathWorks. Search MathWorks. Off-Canvas Navigation Menu Toggle. Description The Kasami Sequence Generator block generates a sequence from the set of Kasami sequences. Kasami Sequences There are two sets of Kasami sequences: the small set and the large set. Block Parameters The Generator polynomial parameter specifies the generator polynomial, which determines the connections in the shift register that generates the sequence u.

Polynomials for Generating Kasami Sequences The following table lists some of the polynomials that you can use to generate the Kasami set of sequences. Parameters Generator polynomial Character vector or binary vector specifying the generator polynomial for the sequence u.

Initial states Binary scalar or row vector of length equal to the degree of the Generator polynomial , which specifies the initial states of the shift register that generates the sequence u.

Sequence index Integer or vector specifying the shifts of the sequences v and w used to generate the output sequence. Shift Integer scalar that determines the offset of the Kasami sequence from the initial time.

Output variable-size signals Select this if you want the output sequences to vary in length during simulation. Maximum output size source Specify how the block defines maximum output size for a signal. Example Kasami Spreading with Two Users and Multipath This model considers Kasami spreading for a combined two-user transmission in a multipath environment.

More About expand all Sample Timing The time between output updates is equal to the product of Samples per frame and Sample time. Reset Behavior To reset the generator sequence, you must first select Reset on nonzero input to add the Rst input. Select a Web Site Choose a web site to get translated content where available and see local events and offers. Select web site.

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## On the generalized large set of Kasami sequences

Documentation Help Center. The Kasami Sequence Generator block generates a sequence from the set of Kasami sequences. The Kasami sequences are a set of sequences that have good cross-correlation properties. This block can output sequences that vary in length during simulation. There are two sets of Kasami sequences: the small set and the large set. The large set contains all the sequences in the small set. Only the small set is optimal in the sense of matching Welch's lower bound for correlation functions.

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## comm.KasamiSequence

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up. I'm trying to understand why Gold codes and Kasami codes are used instead of pure m-sequences, in direct-sequence spread-spectrum DSSS communication systems, to prevent interference between multiple transmitters. If I understand correctly, Gold codes are defined as the XOR between two m-sequences with different polynomials of the same degree e. Kasami is also an XOR so I guess it's similar.

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## Kasami code

Documentation Help Center. The KasamiSequence object generates a sequence from the set of Kasami sequences. The Kasami sequences are a set of sequences that have good cross-correlation properties. Define and set up your Kasami sequence object. See Construction. Call step to generate a Kasami sequence according to the properties of comm.

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