When the channel bandwidth is limited, the overloaded
CDMA may be needed. Most of the research in the overloaded
case is related to code design and multiaccess interference
(MAI) cancelation to lower the probability of error. Examples
of these types of research are pseudorandom spreading (PN)
[6], [7], OCDMA/OCDMA (O/O) [8], [9], multiple-OCDMA
(MO) [10], PN/OCDMA (PN/O) [11] signature sets, serial
and parallel interference cancelation (SIC and PIC) [12]–[16].
The papers that discuss double orthogonal codes for increasing
capacity [17], [18] are actually non-binary complex codes
(equivalent to phases for MC-OFDM) and are not really fair
for comparison.
The codes with minimum total squared correlation (TSC)3
[20]–[22] maximize the channel capacity of a CDMA system
when the input distribution is Gaussian [23]. But for binary
input signals, the WBE codes do not necessarily maximize
the channel capacity. Moreover, if the WBE codes are binary
(BWBE), the optimality is no longer true. Another problem
with WBE codes is that its ML implementation is impractical4.
In our comparisons of our codes with WBE, we use iterative
decoding methods with soft thresholding for WBE codes.

[6] S. Verdu and S. Shamai, “Spectral efficiency of CDMA with random
spreading,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 622–640, Mar.
1999.
[7] A. J. Grant and P. D. Alexander, “Random sequence multi-sets for
synchronous code-division multiple-access channels,” IEEE Trans. Inf.
Theory, vol. 44, no. 7, pp. 2832–2836, Nov. 1998.
[8] F. Vanhaverbeke, M. Moeneclaey, and H. Sari, “DS-CDMA with two
sets of orthogonal spreading sequences and iterative detection,” IEEE
Commun. Lett., vol. 4, no. 9, pp. 289–291, Sep. 2000.
[9] H. Sari, F. Vanhaverbeke, and M. Moeneclaey, “Multiple access using
two sets of orthogonal signal waveforms,” IEEE Commun. Lett., vol. 4,
no. 1, pp. 4–6, Jan. 2000.
[10] F. Vanhaverbeke, M. Moeneclaey, and H. Sari, “Increasing CDMA
capacity using multiple orthogonal spreading sequence sets and successive
interference cancelation,” in Proc. IEEE Int. Conf. Commun.
(ICC’02), New York, Apr.–May 2002, vol. 3, pp. 1516–1520.
[11] H. Sari, F.Vanhaverbeke, and M. Moeneclaey, “Extending the capacity
of multiple access channels,” IEEE Commun. Mag., vol. 38, no. 1, pp.
74–82, Jan. 2000.
[12] M. Kobayashi, J. Boutros, and G. Caire, “Successive interference cancelation
with SISO decoding and EM channel estimation,” IEEE J. Sel.
Areas Commun., vol. 19, no. 8, pp. 1450–1460, Aug. 2001.
[13] D. Guo, L. K. Rasmussen, S. Sun, and T. J. Lim, “A matrix-algebraic
approach to linear parallel interference cancelation in CDMA,” IEEE
Trans. Commun., vol. 48, no. 1, pp. 152–161, Jan. 2000.
[14] G. Xue, J. Weng, T. Le-Ngoc, and S. Tahar, “Adaptive multistage
parallel interference cancelation for CDMA,” IEEE J. Sel. Areas
Commun., vol. 17, no. 10, pp. 1815–1827, Oct. 1999.
[15] X.Wang and H. V. Poor, “Iterative (turbo) soft interference cancelation
and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47, no.
7, pp. 1046–1061, Jul. 1999.
[16] M. C. Reed, C. B. Schlegel, P. D. Alexander, and J. A. Asenstorfer,
“Iterative multiuser detection for CDMA with FEC: Near-single-user
performance,” IEEE Trans. Commun., vol. 46, no. 12, pp. 1693–1699,
Dec. 1998.
[17] B. Natarajan, C. R. Nassar, S. Shattil, M. Michelini, and Z. Wu, “High
performance MC-CDMA via carrier interferometry codes,” IEEE
Trans. Veh. Technol., vol. 50, no. 6, pp. 1344–1353, Nov. 2001.
[18] M. Akhavan-Bahabdi and M. Shiva, “Double orthogonal codes for increasing
capacity in MC-CDMA systems,” Wireless Opt. Commun.
Netw., pp. 468–471, Mar. 2005, WOCN 2005.
[19] J. L. Massey and T. Mittelholzer, , R. Capocelli, A. De Santis, and
U. Vaccaro, Eds., “Welch’s bound and sequence sets for code-division
multiple-access systems,” in Sequences II, Methods in Communication,
Security, and Computer Sciences. New York: Springer-Verlag, 1993.
[20] L.Welch, “Lower bound on the maximum cross correlation of signals,”
IEEE Trans. Inf. Theory, vol. 20, no. 3, pp. 397–399, May 1974.
[21] G. N. Karystinos and D. A. Pados, “Minimum total-squared-correlation
design of DS-CDMA binary signature sets,” in Proc. IEEE Global
Telecommun. Conf. (GLOBECOM’01), San Antonio, TX, Nov. 2001,
vol. 2, pp. 801–805.
[22] G. N. Karystinos and D. A. Pados, “New bounds on the total squared
correlation and optimum design of DS-CDMA binary signature sets,”
IEEE Trans. Commun., vol. 51, no. 1, pp. 48–51, Jan. 2003.