INTRODUCTION
Multicarrier CDMA is wellknown as the name for hybrid transmission techniques based on codedivision multipleaccess (CDMA) and MultiCarrier Modulation (MCM), particularly Orthogonal Frequency Division Multiplexing (OFDM). The hybrid schemes are intended to incorporate the benefits of OFDM, mainly its robustness against frequency selective channel, into CDMA. It can be divided into two groups, i.e. frequency domain spreading and time domain spreading. The spreading on the frequency domain was first introduced by Yee et al. (1993) and named MultiCarrier CDMA (MCCDMA), which is an intuitively very acceptable name. It was also the first published hybrid MCM and CDMA scheme using the name and since then, the commonly used name for the general idea overlaps with the name for the specific frequency domain spreading case. To differentiate the two, this paper uses multicarrier CDMA for the general name of the hybrid schemes and MCCDMA for the specific frequency domain spreading case. As for the time domain spreading method, it was introduced in MultiCarrier DSCDMA (MCDSCDMA) proposed by DaSilva and Sousa (1993) and also in MultiTone CDMA (MTCDMA) by Vandendorpe (1993).
Later on, induced by the uncovering of the limits and capacity of Multiple
Input Multiple Output (MIMO) systems (Foschini and Gans, 1998; Telatar, 1999),
Space Time Coding (STC) came forward as a promising method for broadb and wireless
communication system. STC schemes optimize channel efficiency in radio communication
by effectively utilizing MIMO channel, where coding is performed in the spatial
and temporal domain. It is basically employed in MIMO systems to take the benefits
of the higher channel capacity. In general, variants of STC can be classified
as Space Time Block Codes (STBC) (Alamouti, 1998; Tarokh et al., 1999a,b),
Space Time Trellis Codes (STTC) (Tarokh et al., 1998), Space Time Turbo
Codes (Liu and Fitz, 1999; Firmanto et al., 2002), Layered Space Time
(Foschini, 1996; El Gamal and Hammons, 2001; Golden et al., 1999) and
also concatenated versions of STC with outer channel codes.
In another development, in the area of information theory, Karystinos and Pados (2001, 2003) provided a tight lower bound for total squared correlation (TSC) of a binary signature set. They also established the optimum design of CDMA spreading codes with minimum TSC for almost any number of signatures K and almost any length of signatures L. This opens up possibilities of its application within multicarrier CDMA schemes and more interestingly the combinations of multicarrier CDMA and STC.
PROPOSED SYSTEMS
First, based on the concepts of MCCDMA and minimum TSC spreading codes a pilot aided scheme was designed. In this scheme, the MCCDMA building block employs overloaded minimum TSC spreading codes based on PadosKarystinos design. The term overloaded here means that the system capacity (number of available signatures K) is greater than the processing gain (signatures length L).
Naturally, the original MCCDMA scheme (Yee et al., 1993) employs orthogonal codes such as WalshHadamard codes, in which L = K equals to the number of subchannels M. If the number of subchannels M is maintained to be the same and the WalshHadamard codes changed with the overloaded minimum TSC codes, which is shorter so that L < M, then there will be some subchannels which are not occupied by data. Those unused subchannels can be filled with pilot signals.
Furthermore, by using the concepts of STBC, MCCDMA and minimum TSC spreading codes a second pilot aided scheme was designed. This scheme is a combination of the first scheme mentioned above with 2x2 STBC system (Alamouti, 1998). Studies on the basic forms of STBC combined with MCCDMA can be found in (Auffray and Helard, 2002; Hu and Chew, 2003; Zhou et al., 2002; Deng et al., 2003; Arifianto et al., 2006).
In the overloaded minimum TSC based MCCDMA, for low MultipleAccess Interference (MAI), i.e. low number of operating user K_{o}, it was expected that since the TSC value is maintained at the minimum, then the advantage of having pilot tones outweigh the drawback of having nonorthogonal codes. This is also expected for the second scheme, i.e. STBC MCCDMA with overloaded minimum TSC. Note that low number of operating users is commonly found in wireless Personal Area Network (PAN). For example, in a Bluetooth picocell the maximum number of active slave is only seven.
MINIMUM TOTAL SQUARED CORRELATION OVERVIEW
Total Squared Correlation: Following descriptions by Karystinos and Pados (2001, 2003), the Total Squared Correlation (TSC) measures the crosscorrelation properties of a signature set by taking the sum of the squared magnitudes of all inner products of the signatures. Suppose that S is a set of signatures (complex for generality), or spreading codes (typically binary), c_{i}, with chip length of L, allowing up to K users as follows:
where and I = 1,2,...,K then the TSC of set S is defined by:
where the superscript ^{H} denotes the hermitian operator.
Minimum TSC: The lower bound of TSC is defined by Welch (1974) as
Although this classical Welch bound is tight for realvalued signatures, the bound is loose for binary signatures whose number is not a multiple of four. Hence, such binary signatures meeting Welch bound do not automatically mean that the binary signatures achieve the minimum TSC value.
The PadosKarystinos bound is tight for binary signature sets with almost any number of signatures K and almost any length of signatures L. Any binary signatures or spreading codes meeting the bound have the minimum TSC value.
The summary chart of PadosKarystinos bound for both underloaded and overloaded CDMA system is shown in Fig. 1. The design procedure for obtaining binary signature sets meeting the minimum TSC can be found in (Karystinos and Pados, 2001, 2003).

Fig. 1: 
PadosKarystinos
bound for underloaded and overloaded CDMA spreading codes 
SYSTEM MODEL
MCCDMA Block Review: The diagram of the frequency domain spreading MCCDMA transmitter is shown in Fig. 2. Here, the direct sequence CDMA spreading is still being used. Orthogonal frequency division multiplexing (OFDM), equipped with Cyclic Prefix Insertion (CPI), is performed after the spreading. The serial to parallel operation in the OFDM module operates at the chip level, which implies that each symbol is transmitted on all of the subchannels, giving frequency diversity. The number of subchannels M is actually represented by the size of the IFFT block.
Theoretically, in the frequency domain spreading there is no offset between the sequences. Hence, it is clear that orthogonal codes are the finest codes for MCCDMA. Moreover, the chip length of WalshHadamard codes L, where L, L/12 or L/20 must be a power of 2, fits well with the size of the IFFT block, which is typically a power of 2.
For the MCCDMA receiver as shown in Fig. 3, after Cyclic Prefix Removal (CPR) and the FFT block, the combiner employs weighting vector w. The simplest case where the weighting vector only consists of ‘1’ is known as Equal Gain Combining (EGC). If the weighting vector element values are the squared amplitudes of the received signal in the subchannels then the combiner is called Maximum Ratio Combining (MRC). It is under assumption that the higher amplitude has the better SNR, hence given more weight.
Pilot Aided MCCDMA Using Overloaded Minimum TSC: In an OFDM based system,
pilot symbols can be inserted at certain interval at the transmitter so that
the received pilot signals can be used for channel estimation at the receiver.

Fig. 2: 
MCCDMA
transmitter 
There are two types of OFDM pilot arrangement, namely combtype pilot and blocktype
pilot (Coleri et al., 2002; Hsieh and Wei, 1998).
In combtype pilot signaling, some of the subcarriers are always reserved
and designated for the purpose of pilot signaling. The combtype pilot symbols
are inserted at fixed frequency interval. Blocktype pilot signaling works by
assigning all subcarriers only in a specific period for pilot signaling. The
blocktype pilot symbols are inserted at fixed time interval.
In our overloaded minimum TSC based MCCDMA, the chip length is less than the IFFT block size, so that some subchannels will be unused for data transmission. Thus, it is clear that the pilot to be applied is the combtype pilot arrangement. The characteristics of the pilot subchannels can be estimated by Least Square (LS), Minimum Mean Square Error (MMSE) or Least Mean Square (LMS), while characteristics of the data subchannels can be made available by using interpolation methods (Coleri et al., 2002; Hsieh and Wei, 1998).
Pilot Aided STBC MCCDMA Using Overloaded Minimum TSC: The model of STBC MCCDMA is presented in Fig. 4. Here, the input to the Alamouti scheme encoder (Alamouti, 1998), of the kth user, is two consecutive symbols represented as
and the encoder output matrix is
For the orthogonality, the inner product of the output sequences is 0 and the output matrix G satisfies
The first row of the output matrix belongs to the first transmitter Tx_{1}, while the second row belongs to the second transmitter Tx_{2}. The first column of the matrix occupies one time slot and the second column occupies the next time slot.
Symbols in each row are processed by MCCDMA block in each transmitter. In the process, first the symbols are spread by using an Lchip signature. After that, the data streams enter a serial to parallel converter which operates on chip level, dividing one symbol such that each chip of one symbol occupies one subchannel. Afterwards, inverse FFT of size M is applied to the parallel subchannels consisting of data and inserted pilot subchannels.
Let k be the kth user, j be the jth transmitter and n be the nth time slot,
then the output of the IFFT operation on each transmitter and time slot for
the kth user is
where is
the spreading codes for the kth user, function f_{P} is considered
as the operation for inserting the pilot subchannels into (ML) unoccupied
subchannels, while is
the vector output of the IFFT block. Note that for a synchronous downlink system,
the combined output from all users is
Next to that, parallel to serial operation is employed on the output of the IFFT, followed by CPI to provide the guard interval for inter symbol interference protection. The output signal of that step is ready to be transmitted using the RF components and antennas.
Consider that the system has i as the ith receiver, m as the mth subchannel, ç_{i,n} as the noise at the ith receiver in the nth time slot and h_{ij,n} is the impulse response of the channel between the jth receiver and the ith transmitter in the nth time slot, then the received signal can be described as
At the receiver, after the receiving antennas and RF components, the received signal in each receiver is processed first by guard interval remover, then serial to parallel operation, followed by FFT. The output of the FFT operation for the pilot subchannel is
where P_{jn} is the pilot signal transmitted by the jth transmitter
at the nth time slot, while subscript m_{P} into represents the mth
subchannel being occupied by the pilot.

Fig. 4: 
STBC
MCCDMA diagram 
P_{jn} is set such that in
a time slot its value is 1 for one transmitter and 0 for the other transmitters. The assignment of 1 should also be rotated from one transmitter to another
as the time slot changes. Hence, for the 2 transmitter STBC MCCDMA, (10) can
be converted
The channel is considered to be unvarying across two consecutive symbol durations.
Hence, (11) and (12) may be simplified further by using .
The channel estimation methods mentioned in the previous subsection, namely LS, MMSE and LMS can be applied to the pilot subchannel output so that H_{ij,mp }can be estimated. Based on the estimation result, H_{ij,m} representing the complete channel response can be approximated by using the interpolation methods.
As for the FFT output for the data subchannel the expression is
where subscript m_{l} denotes the mth subchannel only and only if that subchannel is being occupied by the lth chip. The signal in the data subchannels can be expressed as
The matrix based STBC MCCDMA decoder block in this model consists of weighting variables given by
where
is the lth chip of the spreading codes of the user of interest (single user).
In the vector notation, it is written as
On the assumption that ,
consequently
also hold. By using (14) and (16), as well as holding that assumption, the decision
statistics for the 2x2 STBC MCCDMA for the first symbol and the second symbol
can be written as
If all values of w_{l} are 1 then (17) and (18) will maintain the classical definition of EGC in MCCDMA. Where as to maintain the one for MRC, .
SIMULATIONS
The simulated schemes were pilotaided minimum TSC based MCCDMA and STBC MCCDMA with combtype pilot arrangement, original WalshHadamard based MCCDMA without pilot and STBC MCCDMA using blocktype pilot arrangement. All have implementations using the EGC and MRC combining. For fair comparison, all the systems were given equal IFFT block size of 32. Each of them used the same cyclic prefix guard interval of 12.5%. All were fed by r andom BPSK data symbols of 10 Mbps.
For the STBC MCCDMA, all schemes were subjected to identical uncorrelated 2x2 MIMO channel model. Each MIMO entries is simulated by the 3tap model of JTC 94 Indoor Channel ModelResidential A (Pahlavan and Levesque, 1995) as shown in Table 1. Each tap undergoes rayleigh fading with the assumption of maximum users velocity 1.5 m/s and 17 GHz carrier frequency, which creates maximum Doppler frequency of 85Hz. The same channel model was also implemented for the MCCDMA schemes, which are single input single output (SISO) in nature with single channel entry.
All the pilotaided minimum TSC based schemes employed the overloaded minimum
TSC spreading codes with L = 18 and K = 32 generated according to (Karystinos
and Pados, 2003). Hence, out of the M = 32 subchannels, 14 of them were not
being utilized for data transmission. Then, those 14 subchannels, that were
arranged to be located evenly within the 32 subchannels, were filled by the
combtype pilot symbols. The pilot subchannels characteristics were estimated
by LS method.
Table 1: 
JTC
94 Indoor Channel ModelResidential A 


Fig. 5: 
BER
vs Number of Operating Users for MCCDMA using EGC, MRC and pilotaided
minimum TSC (E_{b}/N_{0} =15 dB) 

Fig. 6: 
BER
vs Number of Operating Users for STBC MC CDMA using the blocktype pilot
WalshHadamard (WH) and using the combtype pilotaided minimum TSC (E_{b}/N_{0}
=15 dB) 
Then, the channel characteristics available from the pilot signaling system
were exploited to interpolate the channel transfer function in all subchannels.
Here, the interpolation mechanism worked by means of linear interpolation method.
The LS method and linear interpolation were selected for their relatively low
complexity and fast processing time. As for the WalshHadamard based schemes
system, L = K = 32 equaling the size of the IFFT block M = 32 were being used.
The simulation result in terms of BER vs. number of operating users K_{o} is shown in Fig. 5 and Fig. 6 for MCCDMA and STBC MCCDMA respectively. Obviously, as the number of operating users K_{o} increases, MAI increases as well, instigating BER to become worse. In Fig. 5, it can be observed that although the overloaded Minimum TSC codes are not orthogonal, for low number of users (less than seven users) the MCCDMA system under test outperformed EGC and MRC based MCCDMA. Here, the benefit of having minimum TSC property and channel information is indeed more than the drawbacks of having shorter and non orthogonal codes. Here, the EGC and MRC based MCCDMA does not make use of channel information.
Similarly, in Fig. 6, it is shown that the combtype pilot aided STBC MCCDMA with nonorthogonal overloaded Minimum TSC codes outperformed the WalshHadamard based STBC MCCDMA with blocktype pilot for both cases EGC and MRC frequency combining, for lower number of operating users. The proposed system performed better than the original one when it was less than eight users when both utilized MRC and less than seven users for EGC. Overall, less than seven users should be maintained for the system of interest to outperform the original one. In this case, the benefit of having the minimum TSC property and continuously having updated channel information is indeed more than the drawbacks of having shorter and non orthogonal codes. Note that the WalshHadamard based STBC MCCDMA schemes here take the benefits of the availability of channel information required in the STBC processing.
For the larger number of operating users, the systems under test performed worse than the benchmark system, i.e the WalshHadamard based systems. For the same number of operating users the overloaded minimum TSC schemes have higher level of MAI compared to that of the benchmark system. Higher level of MAI is the consequence of using shorter codes (L = 18 compared to L = 32). Not only that, they are also having more burdens from the non zero cross correlation property of the overloaded minimum TSC.
For the MCCDMA scheme of interest, for the larger number of operating users, this higher level of MAI is negatively affecting it more than the positive effect of using the channel information given by the pilot signaling. Similarly for the STBC MCCDMA with overloaded minimum TSC codes, for the larger number of operating users, this higher level of MAI is negatively affecting the system of interest more than the positive effect of having the continuously updated channel information given by the combtype pilot signaling.
It is also noted that when the systems of interest, both pilot aided MCCDMA and STBC MCCDMA with overloaded minimum TSC codes, are “operationally overloaded”, i.e. when the number of operating users K_{o} > L, the performance begins to deteriorate faster.
CONCLUSIONS
This work has shown that for a low number of users, for the same size of IFFT block and the same system capacity, STBC MCCDMA with overloaded minimum TSC spreading codes combined with a very simple and low complexity linearly interpolated combtype pilot and LS channel estimation performed better than STBC MCCDMA with WalshHadamard orthogonal codes using blocktype arrangement. For MCCDMA, the pilot aided system with overloaded minimum TSC codes is also found to be superior compared to the original WalshHadamard based MCCDMA for low number of users, i.e. less than seven users. These results make the schemes of interest attractive for Wireless PAN where the typical number of operating users is low.