Adaptive Switching between SpaceTime and SpaceFrequency Block Coded OFDM Systems in Rayleigh Fading Channel ()
1. Introduction
Future Wireless communication systems have to be designed to integrate high data rates and high quality of service and multimedia wireless communications. This increasing demand has led to the demand for higher network capacity and performance. Multiple antenna architecture on the transmitter and receiver sides, which is called multiple input multiple output (MIMO) is a suitable technique to improve the channel capacity [1].
Two MIMO schemes can be exploited, Space diversity and Spatial Multiplexing. In Space Diversity scheme, SpaceTime Block Coding (STBC) and Maximal Ratio Combining (MRC) can be used to exploit the maximum spatial diversity available in the channel [1].
Space diversity is employed to counter fight fading and it is widely used in wireless systems. The basic idea behind this approach is to transmit more copies of a signal which permits to be more resistant to deep fading: if the receiver is supplied with more than one replica of the signal, transmitted over independent fading channels, the probability that all the copies are in deep fade is greatly reduced. The MIMO diversity gain can be obtained exploiting every domain of the wireless transmission. Typical examples are time diversity and frequency diversity where signals are repeated over time or over different frequencies [2]. For multiple antennas, an effective way of providing diversity is through STBC; usually multiple transmissions are done over the two dimensions of space (antennas) and time (successive time slots), STBC system assume that the channel is constant over time for the whole duration of the STBC block, as the performance is degraded if the channel is varying over successive time slots.
The simplest STBC is the Alamouti code. In its basic version, it employs two antennas at the base station and one antenna at the mobile terminal. The scheme transmits two symbols from two antennas in two successive time slots, thus a total of four symbols per Alamoutiblock are transmitted [3]. Alamouti has been widely adopted because it is simple and requires a low signal processing load at the receiver (i.e. a portable device, being mobile and energylimited). A simple receiver, with a linear combiner and a single antenna, can extract an order of diversity equal to 2 if the assumption of constant channel over two time slots is met. Alamouti code with two transmitting antennas and a single receiving antenna provides a diversity gain of two; if two receiving antennas are used, the diversity gain will be four [3]. No spatial gain is achieved with STBC. Over the recent years, the combination of Multiple Input Multiple Output (MIMO) with Orthogonal Frequency Division Multiplexing (OFDM) has gained significant interest and is considered as one of the most promising techniques for present and future wireless communication systems [4]. MIMOOFDM system is used in many applications like WiMax, WiFi, WLANs. Block Coding is also possible over the two domains of antenna and frequency with SpaceFrequency Block Coding (SFBC) in a Multi Carrier system, such as OFDM. This means that the SFBC coded blocks are transmitted during the same symbol time but from different antennas and over various sub carriers [5].
This paper is focused on the analysis of the performances of SpaceTime and Space Frequency Coded MIMOOFDM with simple two branches transmit diversity scheme over time frequency selective channels. The assumption of constant channel response during the transmission becomes critical in STBCOFDM over time varying channels. Similarly, the channel gain can not be constant for neighboring subcarriers in SFBCOFDM over frequency selective channels. Adaptive switching between STBC and SFBC has been proposed in [6]. It has been found that the adaptive system switching between STBC and SFBC provides remarkable performance improvement. However, the proposed criteria in [6] can not be implemented at the transmitter side without perfect channel state information, channel correlation matrix is needed. Otherwise, this adaptive switching might cause some problems such as feedback delay, sensibility to channel estimation errors, etc.
In this paper, we propose a switching criterion based on normalized maximum Doppler frequency and normalized delay spread. Different from [6], the system needs only to estimate the channel delay spread and the Doppler frequency. Therefore, assumptions can be made at the transmitter side.
This paper is organized as follows. Section 2 presents SpaceTime and Space Frequency Coded MIMOOFDM system model. Section 3 describes time frequency selective channel. The proposed adaptive switching system is introduced in Section 4. The system simulation results are presented in Section 5.
2. MIMOOFDM System Description
2.1. MIMO Alamouti Space Time Block Coding
Alamouti coding is defined by using two transmit antennas using an orthogonal space time coding which is presented in Figure 1.
It means that the first antenna transmit s_{0} and respectively, simultaneously the second antenna transmit s_{1} and.
Figure 1. Space Time Alamouti coding [3].
If we assume that the channel is invariant between the first and second time of transmission, it results that the received signal can be expressed as:
(1)
(2)
Equations (1) and (2) show the output r of the receiver at time t and t + T, w_{0} and w_{1} are complex random variables representing receiver noise. H_{0} and H_{1} are the channel coefficients.
The main advantage using this coding is that we can recover the signal using a simple linear operation without amplifying the noise [3]:
(3)
(4)
Equations (3) and (4) give the symbol’s estimation by the Alamouti combining scheme. The combiner is shown in Figure 1 and the two combined signals and are sented to the maximum likelihood detector.
2.2. Combining MIMO with OFDM
As well as known, the OFDM is a promising technology, which transforms a frequency selective channel into flat fading sub channels. In this paragraph we will present how the OFDM is used with MIMO systems.
2.2.1. Alamouti STBCOFDM Scheme
Let us consider that we have a transmission sequence. In normal transmission, we will be sending s_{1} in the first time slot, s_{2} in the second time slot, s_{3} and so on. However, Alamouti suggested that we group the symbols into groups of two. In the first time slot, we send s_{1} and s_{2} from the first and second antenna. In second time slot we send and from the first and second antenna. In the third time slot send s_{3} and s_{4} from the first and second antenna and so on.
According to Alamouti Space time code applied for the OFDM system, we have the signals transmitted at times t and t + T from antennas 1 and 2 respectively given by:
Antenna 1:
Antenna 2:
Where S_{0} and S_{1} are the outputs for pathways 1 and 2 respectively of the space time encoder, are the signal symbols, 2N is representing the total symbol number and N is equal to the number of subcarriers.
The encoded data are passed through a serial to parallel block where data are regrouped according to the subcarrier and time as shown in Table 1.
The MIMOOFDM system model based on STBC is shown in Figure 2 [7].
We suppose that the channel is invariant, by assuming the received signal can be expressed as:
(5)
where
Table 1. STBCOFDM scheme for two antennas.
Figure 2. Block diagram of a two transmit and one receive antennas MIMOOFDM system In Space Time Alamouti coding.
R(n, k) is the received symbols in subcarrier k. S_{0} and S_{1} are the transmitted symbols, W the Gaussian noise, n refers to the nth OFDM block.
According to (3) and (4) the combined signals and sent to the maximum likelihood detector are given by:
(6)
(7)
where, represent the symbol number and k refers to the k^{th} subcarrier,.
The receiver need to estimate the channel H_{0} and H_{1} in order to use the Maximum Likelihood Decision Rule to produce and.
2.2.2. Alamouti SFBCOFDM Scheme
The main idea behind the use of SFBC in OFDM is that the channel frequency response of adjacent subcarriers remains almost constant in such a system. The spacetime block code STBC has been applied to frequency selective channels by using OFDM, which transforms a frequency selective channel into flat fading sub channels. The use of OFDM offers the opportunity for coding in the frequency domain in the form of spacefrequency block codes SFBC [8].
The use of frequency diversity SFBC has an impact on spectral efficiency but this problem can be overcome by an increase of modulation order.
For 2 transmitter antennas, for each OFDM symbol, adjacent subcarriers k and k + 1 are used in spacefrequency code. The n^{th} OFDM symbol vector,, is coded into two vectors and by spacefrequency block encoder. S_{1}(n) is transmitted from the first antenna while S_{2}(n) is transmitted simultaneously from the second antenna. The symbol assignment of the 1^{st} OFDM symbol vector is shown in Figure 3.
According to the symbol assignment given in Figure 3, the receiver output for subcarriers k and k + 1 for adjacent subcarriers can be written as
(8)
(9)
By assuming that adjacent subchannels in the OFDM spectrum have the same channel transfer functions [7], we have and, in this case Equations (8) and (9) are similar to (1) and (2) and maximum diversity is achieved [3].
(10)
(11)
3. Time Frequency Selective Channel
In the design and implementation of a transmitter/receiver for wireless communications, it is very important to understand the wireless radio channel. The channel is characterized by two important parameters: the delay spread τ_{max} and the maximum Doppler frequency f_{d}_{max}. Channels with long delay spread τ_{max} and high Doppler frequency f_{d}, exhibit a lower coherence bandwidth and a lower coherence time, corresponding to timefrequency selective channel as it is indicated in Figure 4. In other words, the frequency selectivity of the channel depends on the delay spread τ_{max}, and time selectivity depends on the Doppler frequency [8].
3.1. Channel Model
In the analogue domain, the multipath channel is described by the following complexvalued impulse response [9]:
where α_{l} is the complex gain of the l^{th} path, τ_{l} is the propagation delay for the l^{th} path. In digital transmission systems, symbols are often transmitted in regular time interval Ts, called the sampling period. This period is often small in comparison with the maximum delay time τ_{max}.
The discrete multipath model is regarded as a reference for most of the contemporary wideband terrestrial wireless systems under a reasonable approximation of constant
Figure 3. Symbol assignment for subcarriers in SFBC.
Figure 4. Time frequency selective channel.
number of multipath components L and slow variation of the delay values τ_{l}(t). The multipath channel is then modeled as
α_{l}(t) depends on Doppler frequency f_{d} which is caused by the velocity v_{m} of the receiver.
, is the azimuth of arrival of the radio wave, f is the carrier frequency, and c is the speed of the impacting radio wave.
3.2. Time Selectivity in Mobile Radio Channel
The channel time selectivity is due to the movement of the transmitter and/or the receiver. The frequency changes due to the Doppler effect depends on the relative motion between the source and receiver and on the speed of propagation of the wave.
The Doppler effect is characterized by two parameters:
The coherence duration T_{c} and the Doppler spread B_{d}.
• Coherence time T_{c} is a statistical measure of the time duration over which the channel impulse response is essentially invariant.
• The Doppler spread B_{d} given by
The Doppler spread B_{d}, and the coherence time T_{c}, are reciprocally related (within a multiplicative constant) [8].
A channel is referred to as fast fading channel if
where T is the time duration of an OFDM symbol.
The below Figure (Figure 5) shows simulation results obtained with Rayleigh fading model for different Dop
Figure 5. Rayleigh fading channel for varying mobile velocities.
pler frequency at varying mobile velocity ranging 80, 40 and 10 km/hour.
It can be observed from Figure 5 that the mobile velocity affect channel time selectivity.
3.3. Frequency Selectivity in Mobile Radio Channel
New applications such as wireless local area networks (LANs) require very high data rate transmissions. These applications are usually used in indoor environments. The result of radio signal multipath propagation in real environment is signal spread in time and it leads to the frequency selectivity of the channel.
Indoor fading channels are usually frequency selective for data rates over several Mbps.
Coherence bandwidth B_{c} is a statistical measure of the range of frequencies over which the channel can be considered “flat”.
We define severely frequency selective channel when coherence bandwidth is smaller than a pair of subcarrier bandwidth, Δf < B_{c} < 2Δf, where Bc denote the coherence bandwidth and Δf the subcarrier spacing in the OFDM spectrum.
In relation to severely frequencyselective channel, we define moderately frequencyselective channel when B_{c} > 2Δf, and in that case we can easily say that neighboring subcarriers have identical channel frequency response.
For the Rayleigh fading model, the relation between the coherence bandwidth and delay spread was stated [8]

 A channel is said to exhibit frequency nonselective or flat fading if B < B_{c}, this inequality can be expressed as T_{s} > τ_{max}, where B is the signal bandwidth (B = 1/T_{s}), T_{s} is the sampling time. In this case, all the received multipath components of a symbol arrive within the symbol time duration.
 A channel is said to exhibit frequency selective fading if B > B_{c}, this inequality can be expressed as T_{s} < τ_{max}.
This condition occurs when the received multipath components of a symbol extend beyond the symbol’s time duration.
4. Proposed Adaptive Switching Technique
4.1. The TimeFrequency Correlation
The basic idea of adaptive switching is to choose the appropriate transmission mode at the given channel condition. In [6], the correlation for the same subcarrier between adjacent blocks, , and the correlation between adjacent subcarriers for the same block, , are compared to choose an appropriate transmission mode. In [10], the theoretical value of and over Rayleigh fading channels are represented as
where, G is the number of guard samples, N number of OFDM subcarriers and T is the duration of an OFDM block. J_{0}[ ] is Bessel function of order zero.
The correlation coefficients and between subcarriers along time and frequency respectively is needed to decide the switching mode (STBC or SFBC).
4.2. Dynamic Allocation of STBC and SFBC in an OFDM System
The proposed adaptive switching system is illustrated in Figure 6.
The transmitter or receiver calculates and. Then it decides where the correlation is higher. The system needs only to estimate the channel delay spread and the Doppler frequency. Therefore, assumption can be made in the transmitter side.
Notice that, for a Rayleigh fading channel, depends only on. depends on and.
5. Simulation Results
In this section, we verify the theory by simulation and we test the performance of the proposed adaptive switching technique. The channel model is Rayleigh with parameters shown in Table 2.
We assume a perfect channel estimation since the aim of our simulation is to study the performance under different channel conditions by varying channel delay spread and Doppler frequency.
5.1. The Comparison between STBCOFDM and SFBCOFDM
The performance of OFDM STBC and SFBC schemes are evaluated depending on the BER versus the signaltonoise ratio (SNR) in E_{b}/N_{0}.
Two types of channels slow fading and fast fading channel are examined. The performance comparison between STBC and SFBC in OFDM system over slow fading channel (f_{d} = 20 Hz) is shown in Figure 7, the performance of the two systems STBC and SFBCOFDM in fast fading channel (f_{d} = 100 Hz) are shown in Figure 8, and the performance of STBC and SFBCOFDM in slow fading (f_{d} = 20 Hz) over frequency selective channel is shown in Figure 9.
Figure 7. Performance of STBC and SFBCOFDM for (f_{d} = 20 Hz).
Figure 8. Performance of STBC and SFBCOFDM for (f_{d} = 100 Hz).
Figure 9. Performance of STBC and SFBCOFDM over severely frequency selective channel.
In Figure 7, it can be observed, that SFBC OFDM achieves similar performance as STBCOFDM in slow fading channel. It can be observed that SFBCOFDM performs better in fast varying channel (Figure 8).
In Figure 9 it is seen that in the frequency selective channel the performance of SFBC is lost. The raison is that in this case the condition B_{c} > 2Δf is not fulfilled as well as the past.
5.2. The Adaptive Switching under Rayleigh Fading Channel
Comparing the values and from Figure 10, we note that the correlation coefficient can be lower in the time or frequency domain, depending on the terminal velocity and delay spread.
Figure 10 shows the correlation and in terms of. We notice that the time correlation is strong (>) under slow time varying channels such as and . Under these conditions STBC performs better than SFBC.
In rapid time varying channels such as and, the frequency correlation can be higher. However, frequency correlation, , is governed by the two parameters: and.
Therefore, the performance of STBCOFDM is only related to the channel time selectivity. Indeed, the performance of SFBCOFDM is governed by both channel time and frequency selectivity.
The performance of the proposed adaptive switching system is illustrated in Figure 11. We note that the bit error rate of the adaptive scheme remains below the STBCOFDM and SFBCOFDM, as expected. Figure 11 shows that adaptive switching scheme performs better than STBC and SFBC over time frequency selective
Figure 10. Time and Frequency correlation in terms of f_{d}∙T.
Figure 11. Performance of adaptive switching over time varying channel.
channels.
6. Conclusions
A combination of STBC in MIMO system with OFDM over time frequency selective channels has been presented. STBCOFDM system is very tolerant to slow time varying environments where the channel time variation is slow but when the channel variation is increased due to the mobility of users, the system performs poorly. In this paper, it is found that SFBC has the same performance as STBC in slow fading channels, thus, SFBC improve the system performance better than STBC over high mobility environments. However, SFBC performs poorly in severely frequency selective channels.
Based on the proposed adaptive switching technique, we showed that adaptive switching between STBC and SFBC provides performance improvement over time frequency selective channels.