Maximum length sequence
A maximum length sequence (MLS) is a type of pseudorandom binary sequence.
They are bit sequences generated using maximal linear feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2m − 1). An MLS is also sometimes called an n-sequence or an m-sequence. MLSs are spectrally flat, with the exception of a near-zero DC term.
These sequences may be represented as coefficients of irreducible polynomials in a polynomial ring over Z/2Z.
Practical applications for MLS include measuring impulse responses (e.g., of room reverberation). They are also used as a basis for deriving pseudo-random sequences in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping spread spectrum transmission systems, and in the efficient design of some fMRI experiments
MLS are generated using maximal linear feedback shift registers. An MLS-generating system with a shift register of length 4 is shown in Fig. 1. It can be expressed using the following recursive relation:
where n is the time index and represents modulo-2 addition.
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