The Space-Time CODEC for MIMO-OFDM

The Space-Time codes are exploited to extract the relations between different antennas; one of the famous S-T code schemes is Alamouti scheme [12]. In this these, the Alamouti scheme is the only method we use to extract the multi-antenna equations.

In Alamouti scheme, the antennas are design as 2 transmitters and M receiver, which is 2M diversity. The encoding and transmission sequence for the two-branch transmit diversity scheme is shown in table2.

Antenna0 Antenna1

Time t (n-th symbol) S0 S1

Time t+T (n+1-th symbol) -S1* S0*

Table 2 The Encoding and Transmission Sequence for the Two-Branch Transmit Diversity Scheme

In Table2, S0 and S1 are denoted as the n-th transmitted symbol by antenna0 and antenna1 respectively, and * is the complex conjugate notation. In Fig. 3.2 is the channel model with 2*M diversity.

Fig. 3.2 The 2*M MIMO Channel Model Denote that

2

2 1

The channel of Tx antenna0 and Rx antenna The channel of Tx antenna1 and Rx antenna

i The noise of Tx antenna0 and Rx antenna at time t+T (the second symbol)

i

The received signal at time t (the first symbol) of Rx antenna The received signal at time t+T (the second symbol) of Rx antenna

i

With the MIMO channel model, the received signal can expressed as follow

,1 2 0 2 1 1 ,1 Exploiting eq. 3.1, the channel information is accessible if the transmitted signal is known, which is as follow

( )

In Alamouti scheme, the CIR is assumed not changed during time t to time t+T, which

means the first and the second symbol suffer the same channel effects. Because the pilot information is inserted in frequency domain, the Alamouti encoder and decoder are implemented in frequency domain. Fig. 3.3 is the block diagram of MIMO-OFDM with Alamouti scheme in detail.

Fig. 3.3 The Block Diagram of MIMO-OFDM with Alamouti Scheme

3.4 How to Apply 1

and 2

Moments in MIMO

With this MIMO-OFDM architecture, the complicated relationships of multi-antenna are solved by Alamouti CODEC and Alamouti equalizer blocks. After passing through Alamouti Decoder, each output stream can be regarded as a SISO-OFDM system. Therefore, all the channel estimation methods based on comb-type pilot interpolation in SISO-OFDM system are adaptable in MIMO-OFDM system without changing the algorithms. Since each output stream of Alamouti decoder represents each Tx-Rx path, the CFR information on pilot subcarrier is able to calculate the 1^st and 2^nd moments just as Chapter2 does.

Chapter 4

Simulation Results

4.1 Some Simulation Result of the Moment Estimators

The first series simulation results are the improvements of the 1^st and 2^nd moment estimator with factors x and y added. There are three types of power delay profiles (PDP) in this simulation, which are step function, exponential function, and normal function.

Denote that the total powers of them are equal. In Fig. 4.1, there are three types of PDPs.

Fig. 4.1 Three Types of PDPs

In the simulation, the channel length N is 1000, pilot subcarrier number is 333, and all

PDP has the same power, which is equal to one. In Fig. 4.2 and Fig. 4.3, the x-axis of uniform distribution is the width of step function PDP, the x-axis of exponential distribution is the decay parameter alpha, where

2 alpha alpha

The x-axis of normal distribution is the mean value mu, mu=1:200 p=50, and the x-axis of normal distribution1 is the variance value p, p=1:200 mu=50.

The normal distribution is

( )²

2

mu 2

normalizer 2 p2 l

The y-axis in Fig. 4.2 and Fig. 4.3 are the normalized MSE of the estimators in db, which are

⎟ respectively.

Fig. 4.2 The Normalized MSE of m1 Estimator

Fig. 4.3 The Normalized MSE of m2 Estimator

In Fig 4.2, the Normal Distribution1, the blue line with factor x get raised after mu

>160. The reason is when aliasing occurred, the estimated m1 is negative, which is wrong.

However, the x factor is negative too, and that is the reason the blue line get raised when mu>160. With respect to the summation paths of 1^st moment, we can see that when PDP is shorter than N/(4*F_S), the m1 estimator is reliable. In the simulation N/(4*F_S) = 83. And with respect to summation path of 2^nd moment, the estimator is reliable when PDP is shorter than N/(3*F_S), which is 111 in this simulation.

In Fig. 4.4 and Fig. 4.5 are the simulations of MSE of m1 and m2 respectively, which

Fig. 4.4 The m1 Estimator MSE of Theoretical Value and Monte Carlo Method

4.2 Some Simulation Results of the MIMO-OFDM with the Interpolation methods

MIMO-OFDM system parameters used in the simulations are illustrated in Table 3.

Since the aim is to observe channel estimation performance, it assumed to be perfect synchronization in the simulations. Moreover, the guard interval is assumed to be longer than the maximum delay spread of the channel.

Table 3 Simulation Parameters

Parameters Specifications

FFT Size 1024

Pilot Ratio 1/11

Guard Interval 64

Antenna 2*2 Signal Constellation QPSK

Channel Model Rayleigh fading Channel Length 20

Power Delay Profile Exponential

The simulation shows the BER of different interpolation methods used in MIMO-OFDM in different SNR. The simulation result is shown in Fig.4.6. The X-axis represent SNR in db, and the noise is added after the signal convolution to CIR, and the noise power is expressed as

SNR10 _ _

noise power = 10

_

FFT length CP length FFT length

− × + .

Fig. 4.6 BER Performance versus SNR for the Equalizer Based On Alamouti with Comb-Type Pilot Arrangements

Chapter 5 Conclusion

There are two contributions achieved in this thesis. First, a comb-type pilot aided channel estimation method (MA-LPIFD) is proposed. Second, the architecture of MIMO-OFDM that is able to apply to MA-LPIFD is designed. From the simulation result, we can see that the BER performance is better than traditional LPI, and the costs are N_P+3 multiplications and 2*N_P additions to access filter design indexes.

Denote that NP is the number of pilot subcarrier.

Besides the contributions, there are still some future works and some survey I haven’t completed. First, in chapter2, if the centroid (first moment) of CIR can be replaced by the center of CIR, the center of the filter can be designed more precisely, and the performance of BER must be improved. I think the key point is to figure out the relations between time domain and frequency of the center of CIR. Second, at the first place, the Cramér-Rao Lower Bound (CRLB) of this MA-LPIFD method is my index to evaluate how good (or how bad) this estimator is. However, with some mathematical problems, for example, it is difficult to combine ^{[ ]}

[ ]

these two equations. The analysis of CRLB of

this estimator is ceased. Third, in Chapter3, the drawback of this Alamouti-based MIMO-OFDM architecture is that it is assumed the CIR is unchanged in the period of two connecting symbols, and if the CIR changes faster than two symbol time, this architecture will be failed. I think there will be some architecture that can fix this

problem. Forth, in Chapter4, in the simulation, there are some improvement spaces in the usage of the 1^st and 2^nd moments. The filter design is not the topic of this thesis, but it is important when it comes to BER performance evaluation. If the moments can be used better, the filter will have better performance in filtering out the noise, and estimate the CFR more precisely.

References

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[5] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,”Wireless Personal Communication, vol. 6, no. 3, pp. 311–335, Mar. 1998.

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[9] Günter, “Channel Estimation in Two Dimensional for OFDM Systems with Multiple Transmit Antennas,” GLOBECOM, pp. 211-215, 2003.

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Luleå Tekniska Universitet, 1996, pp. 1–58.

[11] The Reserved Resource

[12] S. M. Alamouti, “A simple transmit diversity technique for wireless communication,”

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