In [16], a simple SLM method based on time-domain sequence

cyclic shift and combination of antennas is proposed.

(3)

Cyclic shift of the initial phase sequence [mathematical expression not reproducible] represents cyclically shifted S by [d.sub.pn].

Substitution,

cyclic shift, and transpose phases are functioned as confusion and diffusion.

Input: The original speech signal I and chaotic series matrices B and C Output: The column and row shuffled speech block T (1) Generate the column and row shift matrices by sorting [x.sub.k] and [y.sub.k] chaotic sequence (2) for i = 1 to N do (3) if mod([b.sub.i], 2) = 0 then

Cyclic shift the speech segment in column i of I to down with the step size of b.sub.i]; (4) else

Cyclic shift the speech segment in column i of I to up with the step size of [b.sub.i]; (5) end if (6) end for (7) Denote the column shifted speech block as T.

In the scheme presented in [11], time domain cyclic-SLM with delayed correlation (DC) is applied to reduce a PAPR and to estimate the amount of a

cyclic shift at the receiver without SI transmission.

Closure property of the family of context-free languages under the

cyclic shift operation.

Thus there exists an m-tuple ([l.sub.1], [l.sub.2], * * * , [l.sub.m]) such that cyclic array shift of the error ([e.sub.1](x), * * * , [e.sub.m](x)) through ([l.sub.1], [l.sub.2], * * * , [l.sub.m]) positions (or equivalently,

cyclic shift of error [e.sub.i](x) through li positions (1 [less than or equal to] i [less than or equal to] m) in classical sense) has all its nonzero components confined to first r columns of e (Note that we are identifying e(x) [left and right arrow] e under the map [theta]).

In the proposed scheme, there is a trade-off between the type And pattern of dummy sequence and the iteration time for the

cyclic shift. Therefore, consideration of these elements is an important aspect of PAPR reduction performance and suitable system complexity.

The algorithm to generate S-CHS is divided into three parts: construction of Cayley table, reflection, and

cyclic shift and catenation.

The phase code ofINS MCPC pulse train is the P4 code

cyclic shift. Figure 4 shows the ambiguity function of INS MCPC based on P4 code.

We note that a slight modification of Rubinstein's construction (Example 2.15) gives a Boolean function, invariant under the

cyclic shift of the variables, which still shows the quadratic gap between sensitivity and block sensitivity.

In other words, when the

cyclic shift distance between two users is larger than the maximum delay spread of a multi-path fading channel L, there will be no MAI between them at all.