Performance evaluation of space-time-frequency spreading for MIMO OFDM-CDMA systems
© Dahman and Shayan; licensee Springer. 2011
Received: 12 February 2011
Accepted: 23 December 2011
Published: 23 December 2011
In this article, we propose a multiple-input-multiple-output, orthogonal frequency division multiplexing, code-division multiple-access (MIMO OFDM-CDMA) scheme. The main objective is to provide extra flexibility in user multiplexing and data rate adaptation, that offer higher system throughput and better diversity gains. This is done by spreading on all the signal domains; i.e, space-time frequency spreading is employed to transmit users' signals. The flexibility to spread on all three domains allows us to independently spread users' data, to maintain increased system throughput and to have higher diversity gains. We derive new accurate approximations for the probability of symbol error and signal-to-interference noise ratio (SINR) for zero forcing (ZF) receiver. This study and simulation results show that MIMO OFDM-CDMA is capable of achieving diversity gains significantly larger than that of the conventional 2-D CDMA OFDM and MIMO MC CDMA schemes.
Modern broadband wireless systems must support multimedia services of a wide range of data rates with reasonable complexity, flexible multi-rate adaptation, and efficient multi-user multiplexing and detection. Broadband access has been evolving through the years, starting from 3G and High-Speed Downlink Packet Access (HSDPA) to Evolved High Speed Packet Access (HSPA+)  and Long Term Evolution (LTE). These are examples of next generation systems that provide higher performance data transmission, and improve end-user experience for web access, file download/upload, voice over IP and streaming services. HSPA+ and LTE are based on shared-channel transmission, so the key features for an efficient communication system are to maximize throughput, improve coverage, decrease latency and enhance user experience by sharing channel resources between users, providing flexible link adaptation, better coverage, increased throughput and easy multi-user multiplexing.
An efficient technique to be used in next generation wireless systems is OFDM-CDMA. OFDM is the main air interface for LTE system, and on the other hand, CDMA is the air interface for HSPA+, so by combining both we can implement a system that benefits from both interfaces and is backward compatible to 3G and 4G systems. Various OFDM-CDMA schemes have been proposed and can be mainly categorized into two groups according to code spreading direction [2–5]. One is to spread the original data stream in the frequency domain; and the other is to spread in the time domain.
The key issue in designing an efficient system is to combine the benefits of both spreading in time and frequency domains to develop a scheme that has the potential of maximizing the achievable diversity in a multi-rate, multiple-access environment. In , it has been proposed a novel joint time-frequency 2-dimensional (2D) spreading method for OFDM-CDMA systems, which can offer not only time diversity, but also frequency diversity at the receiver efficiently. Each user will be allocated with one orthogonal code and spread its information data over the frequency and time domain uniformly. In this study, it was not mentioned how this approach will perform in a MIMO environment, specially in a downlink transmission. On the other hand, in , it was proposed a technique, called space-time spreading (STS), that improves the downlink performance, however they do not consider the multi-user interference problem at all. It was assumed that orthogonality between users can somehow be achieved, but in this article, this is a condition that is not trivially realized. Also, in , multicarrier direct-sequence code-division multiple-access (MC DS-CDMA) using STS was proposed. This scheme shows good BER performance with small number of users and however, the performance of the system with larger MUI was not discussed. Recently, in , they adopted Hanzo's scheme , which shows a better result for larger number of users, but both transmitter and receiver designs are complicated.
In this article, we propose an open-loop MIMO OFDM-CDMA system using space, time, and frequency (STF) spreading . The main goal is to achieve higher diversity gains and increased throughput by independently spreading data in STF with reasonable complexity. In addition, the system allows flexible data rates and efficient user multiplexing which are required for next generation wireless communications systems. An important advantage of using STF-domain spreading in MIMO OFDM-CDMA is that the maximum number of users supported is linearly proportional to the product of the S-domain, T-domain and the F-domain spreading factors. Therefore, the MIMO OFDM-CDMA system using STF-domain spreading is capable of supporting a significantly higher number of users than other schemes using solely T-domain spreading. We will show through this article, that STF-domain spreading has significant throughput gains compared to conventional schemes. Furthermore, spreading on all the signal domains provides extra flexibility in user multiplexing and scheduling. In addition, it offers better diversity/multiplexing trade-off. The performance of MIMO OFDM-CDMA scheme using STF-domain spreading is investigated with zero-forcing (ZF) receiver. It is also shown that larger diversity gains can be achieved for a given number of users compared to other schemes. Moreover, higher number of users are able to share same channel resources, thus providing higher data rates than conventional techniques used in current HSPA+/LTE systems.
2. System model
In this section, joint space-time-frequency spreading is proposed for the downlink of an open-loop multi-user system employing single-user MIMO (SU-MIMO) system based on OFDM¬CDMA system.
A. MIMO-OFDM channel model
where the N r × N t complex-valued random matrix represents the l th tap. The channel is assumed to be Rayleigh fading, i.e., the elements of the matrices are independent circularly symmetric complex Gaussian random variables with zero mean and variance , i.e., . Furthermore, channel taps are assumed to be mutually independent, i.e., , the path gains are determined by the power delay profile of the channel.
where with denoting the data symbol received from the j th antenna on the q th subcarrier, n q is complex-valued additive white Gaussian noise satisfying . The data symbols are taken from a finite complex alphabet and having unit average energy (E s = 1).
B. MIMO OFDM-CDMA system
Now, we will describe in details the Joint STF spreading block shown in Figure 1b, where the signal is first spread in space, followed by time spreading and then time-frequency mapping is applied to ensure signal independency when transmitted and hence maximizing achievable diversity  on the receiver side.
1) Spatial spreading
where M is the number of users in the system, and is orthogonal code with size N t for user k.
2) Time Spreading
where is the transmitted signal for user k from antenna i at time n.
3) Time-Frequency mapping
The assignment for each OFDM subcarrier is calculated from the fact that the IFFT matrix for our OFDM transmitted data for symbol 1 is with size N c × N f , where F H ⊂ FFT matrix with size N f . F matrix in this paper is a WIDE matrix N c × N f where the rows are picked from an FFT matrix and complex transposed (Hermitian). For this matrix to satisfy the orthogonality condition and to maintain independence, those rows needs to be picked as every N f /N c column, so then and ONLY then, each column and row are orthogonal. The max rank cannot be more than N c . The frequency spacing or jump introduced, made it possible to achieve the max rank, where each row and column is orthogonal within the rank. In order to achieve independent fading for each signal and hence maximizing frequency diversity, we need to have F H F = I. F H F = I is only possible if F H is constructed from every N f /N c columns of the FFT matrix, . Therefore, if K1 = 1, then K2 = N f /N c ,..., and .
A. Received signal of SU-MIMO system
Here, stands for the K n -th column of the (N f × N f ) FFT matrix, L is the cyclic shift on each antenna where L > L' (L' is the channel length), and h i,j is the impulse response from the i-th transmit antenna to the j-th receive antenna. Here, cyclic shifting in time has transformed the effective channel response j-th receive antenna to as shown in Equation (6) instead of the addition of all channel responses. This will maximize the number of degrees of freedom from 1 to N t .
In our scheme, we assumed that all users transmit on same time and frequency slots. As shown in Figure 1, we have the ability to achieve flexible scheduling in both time and frequency. This will contribute in more flexible system design for next-generation wireless systems as compared to other schemes.
B. Achievable Diversity in SU-MIMO
Since the maximum achievable degrees of freedom for the transmitter is equal to N t L', diversity can be found as d = min(N c , N t L') . For this reason, in order to achieve maximum spatial diversity, we need to choose time spreading length N c ≥ N t L'.
C. Receiver Design
where k stands for user index and K n is the K-th subcarrier at time n (n = 1, 2,..., N c ).
where , and M is the number of users.
D. Performance Evaluation for Zero Forcing Receiver
where, x k (MAI) are assumed to be mutually independent, therefore input symbols are assumed Gaussian with unit variance. The expectation is taken over the user symbols x k , k = 1,..., M and noise k.
where and are chi-squared random variables, as Equation (21) shows that is gaussian random variable ~ CN(0, 1)
where F a,b is F-distribution random variable (ratio between two chi-squared random variables) where a = N t N c and b = M - 1 degrees of freedom, and χ2 is chi-squared random variable with N t N c degrees of freedom. It is clear that when interference is small enough, the most dominant part will be the χ2 which agrees with Raleigh fading channel where no MUI exists. When the MUI dominates channel noise, Equation (27) can be approximated as Γ = F a,b
4. Simulation results
Computer simulations were carried out to investigate the performance gain of the proposed open-loop MIMO OFDM-CDMA system with joint space-frequency-time spreading. The channel is a multipath channel modelled as a finite tapped delay line with L = 4 Rayleigh fading paths. Walsh-Hadamard (WH) codes are utilized for both space and time spreading. Different codes are assigned to different users. The OFDM super-frame contains 16 OFDM symbols, which is equal to the length of the time spreading code N c = 16, where each OFDM symbol has 128 subcarriers. The channel estimation is assumed to be perfect, quadrature phase-shift keying (QPSK) constellation is used. We assume a MIMO channel with N t = 4 transmit antennas and N r = 1, 2, 4 receive antennas. It is assumed that the mean power of each interfering user is equal to the mean power of the desired signal. The maximum number of users allowed by the system is N c (min(N t , N r )).
In this paper, we have proposed an open-loop MIMO OFDM-CDMA scheme using space-time-frequency spreading (STFS), in the presence of frequency-selective Rayleigh-fading channel. The BER and BLER performance of the OFDM-CDMA system using STFS has been evaluated taking into consideration diversity/multiplexing trade-off over frequency-selective Rayleigh-fading channels.
We showed that our proposed system gives the advantage of maintaining maximum achievable spatial diversity on the receiver side in the case of slow frequency-selective Rayleigh-fading channels. Also, by appropriately selecting the system parameters N t , and N c , the OFDM-CDMA system using STFS is rendered capable of achieving higher number of users than other schemes. System throughput has increased as our proposed system was capable of achieving higher SINR than other schemes at similar SNRs. Higher diversity gains than other systems were shown, when number of receive antennas are reduced to one, as our system was able to maximize the number of degrees of freedom, by exploiting the spatial dimension of the channel. Our system showed great improvements, in system performance and throughput compared to other systems without sacrificing complexity.
Upper bound for P e
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