xvi List of Figures
6.3 Chip-synchronous, soft-limiting error probabilities of the synchronous
multilevel carrier-hopping prime codes for L = w = {10,15, 20}, N =
p = 89, k = 1, and n = {1, 2}.......................................................................263
6.4 Chip-synchronous, soft-limiting error probabilities of the synchronous
trilevel carrier-hopping prime codes, optimized as a function of K,for
L = w = {8,12}, N = p = {23,31}, k = 1, and n = 2. ................................264
6.5 Gaussian error probabilities of the CIK Walsh-based synchronou s and
Barker-based asynchronous prime-permuted codes for various p and N.....270
7.1 Some double-length carrier-hopping prime codewords with 4 wave-
lengths and lengths {5, 25},basedonp
1
= p
2
= 5, and t
1
= 2, where
dark squares indicate the wavelength-time locations of pulses. ...................276
7.2 A complete periodic cross-correlation process of a long address code-
word of length N
2
= rN
1
and r + 1consecutiveOOKtransmissionsofa
short interfering codeword of length N
1
.......................................................277
7.3 Chip-synchronous, hard-limiting error probabilities of the triple-weight,
triple-length carrier-hopping prime codes (using lower-order wave-
lengths) versus K
3,2
and K
3,3
,wherew
1
= 9, w
2
= 11, w
3
= 13, N
1
= 17,
N
2
= 323, and N
3
= 7429, and K
1,1
= K
1,2
= K
1,3
= K
2,1
= K
2,2
= K
2,3
=
K
3,1
= 3.........................................................................................................2 8 4
7.4 Chip-synchronous, hard-limiting error probabilities of the triple-weight,
triple-length carrier-hopping prime codes (using lower-order wave-
lengths) versus K
2,1
and K
2,2
,wherew
1
= 9, w
2
= 11, w
3
= 13, N
1
= 17,
N
2
= 323, and N
3
= 7429, and K
1,1
= K
1,2
= K
1,3
= K
2,1
= K
2,2
= K
2,3
=
K
3,1
= 3.........................................................................................................2 8 5
7.5 Chip-synchronous, soft-limiting error probabilities of the single-weight,
double-length expanded carrier-hopping prime codes versus K
1,2
for
w
1
= 5, p
$
= 7, t
1
= 11, N
1
= 23, and N
2
= 529..........................................290
7.6 Chip-synchronous, soft-limiting error probabilities of the single-weight,
double-length expanded carrier-hopping prime codes versus K
1,1
for
w
1
= 5, p
$
= 7, t
1
= 11, N
1
= 23, and N
2
= 529..........................................291
7.7 Chip-synchronous, soft-limiting error probabilities of the single-weight,
triple-length expanded carrier-hopping prime codes versus K
1,2
and K
1,3
for w
1
= 7, p
$
= 3, t
1
= 6, t
2
= 3, N
1
= 13, N
2
= 169, N
3
= 2197, and
K
1,1
= 5.........................................................................................................2 9 2
7.8 Chip-synchronous, hard-limiting error probabilities of the double-length
quadratic-congruence carrier-hopping prime codes versus K
2
for t
1
= 11,
L = w = 7, N
1
= 31, and N
2
= 1147.............................................................296
7.9 Chip-synchronous, hard-limiting error probabilities of the double-length
quadratic-congruence carrier-hopping prime codes versus K
1
for t
1
= 11,
L = w = 7, N
1
= 31, and N
2
= 1147.............................................................297
7.10 Chip-synchronous, hard-limiting error probabilitiesofthedouble-length
quadratic-congruence carrier-hopping prime codes in OOK and multi-
code keying versus K
1
for t
1
= 11, L = w = 7, N
1
= 31, N
2
= 1147, and
K
2
= 15. ........................................................................................................ 301
List of Figures xvii
7.11 Chip-synchronous, hard-limiting error probabilitiesofthedouble-length
quadratic-congruence carrier-hopping prime codes in OOK and multi-
code keying versus K
2
for t
1
= 11, L = w = 7, N
1
= 31, N
2
= 1147, and
K
1
= 5. ..........................................................................................................3 0 2
7.12 Chip-synchronous, hard-limiting error probabilitiesofthedouble-length
quadratic-congruence carrier-hopping prime codes in multicode keying
versus K
1
and K
2
for t
1
= 20, L = w = 12, N
1
= p
1
= 41, N
2
= p
1
p
2
=
1763, and m
1
= m
2
= 5.................................................................................303
7.13 Chip-synchronous, soft-limiting error probabilitiesofthesingle-weight,
double-length prime-permuted codes versus K
1,2
for t
1
= 1, t
2
= 3, L =
p = w = 5, N
1
= 61, and N
2
= 671...............................................................309
7.14 Chip-synchronous, soft-limiting error probabilitiesofthesingle-weight,
double-length prime-permuted codes versus K
1,1
for t
1
= 1, t
2
= 3, L =
p = w = 5, N
1
= 61, and N
2
= 671...............................................................310
7.15 Same-bit-power, chip-synchronous, hard-limiting error probabilities of
the double-weight carrier-hopping prime codes versus K
1
for L = w
1
,
N = 49, w
1
= 5, w
2
= 3, c = 2, and K
2
= {5,10,20}..................................315
7.16 Same-bit-power, chip-synchronous, hard-limiting error probabilities of
the double-weight carrier-hopping prime codes versus K
2
for L = w
1
,
N = 121, w
1
= {5,7}, w
2
= 3, c = {2,3},andK
1
= 20. .............................317
7.17 Same-bit-power, chip-synchronous, hard-limiting error probabilities of
the light-weight codewords in the 1-D double-weight OOCs versus w
2
for N = 307, w
1
= 15, and K
1
= K
2
= 12..................................................... 318
7.18 Chip-synchronous, soft-limiting error probabilitiesofthedouble-length
OOCs in Construction 2 versus K
2
for t = 10, p
1
= 5, w = 5, N
1
= 201,
and N
2
= 1005. .............................................................................................328
7.19 Chip-synchronous, soft-limiting error probabilitiesofthedouble-length
OOCs in Construction 2 versus K
1
for t = 10, p
1
= 5, w = 5, N
1
= 201,
and N
2
= 1005. .............................................................................................329
8.1 Concatenated prime codeword U
1,0
over GF(3) with y = 2. ........................334
8.2 Chip-synchronous, soft- and hard-limiting error probabilities of the 3-
DconcatenatedprimecodesinOOKwithN = p
2
, L = w = {17,21},
M = 5, and p = {7, 11}................................................................................3 3 8
8.3 Two multicarrier prime codewords over GF(3) with y = 2. .........................339
8.4 Chip-synchronous, soft- and hard-limiting error probabilities of the 3-D
multicarrier prime codes in OOK with L = Ip
2
, w = Ip, I = {1, 2},and
N = p = {7,11}............................................................................................342
8.5 Chip-synchronous, hard-limiting bit error probabilities of the 3-D con-
catenated prime codes of L = Ip
2
= 121, w = Ip= 11, and N = p = 11
in OOK and 2
m
-ary shifted-code keying for I = 1andm = {1,2, 3,4}.......343
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