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L when
Table 2. Some possible parameters and optimal set sizes
M =4and
N = 6248
L
L
N
Z
L
η
N
Z
L
η
4
6
8
10
12
14
16
18
20
22
1560
1040
780
624
520
446
390
346
312
282
1570
1046
785
628
523
449
392
348
314
285
24
26
28
30
50
100
300
500
1000
1500
260
240
222
208
124
62
20
12
6
4
261
241
224
209
125
62
20
12
6
4
4 2 6248
4 2
6248
Sidel'nikov sequences are well-known as M -ary sequences with good autocorre-
lation property [9]. Thus we can also construct M -ary LCZ sequences using an
M -ary Sidel'nikov sequence by the construction in Section III. Table 2 shows
some possible parameters of quaternary LCZ sequence sets of period 6248 con-
structed from a quaternary Sidel'nikov sequence of period 3124. Note that there
is no construction for the cases such that M
=2or N = 6248 in [8].
Remark: Table 2 tells us that there is a gap between the optimal set size
and the possible set size when the LCZ size Z is very small compared to the
period, since the maximum magnitude of the out-of-phase autocorrelation of a
Sidel'nikov sequence is greater than 1. However, for larger LCZ sizes, we can
get LCZ sequence sets having an optimal set size with respect to the Tang-Fan-
Matsufuji bound as in the case that N =2(2 n
1).
5Con lu on
We proposed a new method to construct M -ary LCZ sequence sets from any M -
ary sequence with good autocorrelation for even M . The proposed design gives
M -ary LCZ sequence sets which are optimal or nearly optimal with respect to
the Tang-Fan-Matsufuji bound. Furthermore, our design is very flexible in the
selection of period, LCZ size, and alphabet size. Therefore, our new design can
be applied to various situations in the QS-CDMA environment.
References
1. De Gaudenzi, R., Elia, C., Viola, R.: Bandlimited quasi-synchronous CDMA: A
novel satellite access technique for mobile and personal communication systems.
IEEE J. Sel. Areas Commun. 10, 328-343 (1992)
2. Gong, G.: Theory and applications of
q -ary interleaved sequences. IEEE Trans.
Inform. Theory 41, 400-411 (1995)
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