Author : Lavish Kansal, Ankush Kansal, Kulbir Singh

International Journal of Scientific & Engineering Research Volume 2, Issue 6, June-2011

ISSN 2229-5518

Download Full Paper : PDF**Abstract -** In this paper, a general Alamouti space time block code structure is proposed for multiple-input multiple-output–orthogonal frequency-division multiplexing (MIMO-OFDM) in WiMAX systems for 2 X NR antenna configurations. The signal detection technology used in this paper for MIMO-OFDM system is Zero-Forcing Equalization (linear detection technique). The analysis of Signal to Noise Ratio (SNR) vs Bit Error Rate (BER) for MIMO in WiMAX system has been done. For this purpose modulation technique QPSK has been considered for different convolution-codes (CC)-rates. Also Reed-Solomon (RS) codes have been implemented along with CC codes. Comparisons between ideal channel, Additive White Gaussian Noise (AWGN) and practical fading channel, Rayleigh channel has been done. Also the comparison is provided on the basis of SNR vs BER graph for different antenna configurations.

**Index Terms: **- WiMAX, OFDM, MIMO, Alamouti Space Time Coding, Zero Forcing Equalisation, BER(Bit Error Rate), FEC

**1. INTRODUCTION**Among the emerging technologies for broadband wireless access, IEEE 802.16e is one of the most promising and attractive candidates. However, it also presents very challenging aspects in terms of radio resource management which intentionally left open to implementers [1]. The IEEE

802.16e air interface standard [2] is based on orthogonal frequency-division multiplexing (OFDM), which has been regarded as an efficient way to combat the inter-symbol interference (ISI) for its excellent performance over frequency selective channels for broadband wireless networks. Multi-Input Multi-Output (MIMO) technology has also been recognized as a key approach for achieving a dramatic increase in the capacity of wireless communication systems [3].

In particular, the use of OFDM technology combined with MIMO is an attractive solution for future

broadband wireless systems that require reliable and high-rate data transmission. The inherent structure of MIMO-OFDM allows the use of dynamic resource allocation of subcarriers, bits, power and antennas which will improve the system performance remarkably.

Currently, Worldwide Interoperability for Microwave Access (WiMAX) has received much attention. It is based on the IEEE 802.16e standard and can be classified into Fixed WiMAX [4] and Mobile WiMAX . October 2007, wireless broadband technology, WiMAX, was formally adopted to be one of the 3G standards by International Telecommunication Union (ITU), which is a milestone in the development of WiMAX. For 802.16e MAC & PHY layers has been defined, but for present work only PHY has been taken into consideration. PHY layer for mobile WiMAX (IEEE-802.16e) has scalable FFT size128-2048 point FFT with OFDMA, Range is from 1.6 to 5 Km. at 5Mbps in 5MHz. channel BW, it supports 100Km/hr speed.

**2. WiMAX MODEL FOR PHYSICAL LAYER**The block diagram for Wi-MAX system (standard: 802.16e) is shown in figure 1 [5]. Now we will take each block one by one in detail and in present paper simulation has been done for each block separately.

Randomization is the first process carried out in layer after the data packet is received from the higher layers each burst in Downlink and Uplink is randomized. It is basically scrambling of data to generate random sequence to improve coding performance.

In Forward Error Correction (FEC) there are number of coding system like RS codes, convolution codes Turbo codes etc. But in the present paper only RS codes and convolution codes has been taken for simulation.

RS codes basically add redundancy to the data .this redundancy improves Blocks error. RS-encoder is based on Galois field computation to add the redundancy bits. Wi-MAX is based on GF (28) that corresponds to as RS (N = 255, K = 239, T =8)

where:

N = Number of Bytes after encoding

K = Data Bytes before encoding

T - Number of bytes that can be corrected

In this coding two polynomials are required namely code generator polynomial g(x)and field generator polynomial p(x) .For Wi-MAX system

Code generator polynomial

G(x)=(x+k^0 )(x+k^1 )(x+k^2 )……..

…… (x+ k^(2T-1) ) (1)

Field generator polynomial

P(x)=x^8+x^4+x^3+x^2+1 (2)

Convolutional codes are commonly specified by three parameters n, k, m. Where n is the number of output bits, k is the number of input bits and m is the number of memory registers. Encoder for a convolutional code accepts k-bit blocks of information sequence and produces an encoded sequence (codeword) of n-bit blocks. However, each encoded block depends not only on the corresponding k-bit message block at the same time unit, but also on M previous blocks. Hence, the encoder has a memory length of m. Encoder operates on the incoming message sequence continuously in a serial manner.

The quantity k/n called the code rate, is a measure of code’s efficiency. Other important parameter of convolutional code is the constraint length of the code and is defined by L= k*(m− 1) The constraint length L represents the number of bits in the encoder memory that affect the generation of the n output bits. The error correction capacity is related with this value. The number of bits’ combinations in the registers is called the states of the code and are defined by number of states Ns = 2L, where L is the constraint length of the code.

Interleaving aims to distribute transmitted bits in time or frequency or both to achieve desirable bit error distribution after demodulation. What constitutes a desirable error distribution depends on the used FEC code. What kind of interleaving pattern is needed depends on the channel characteristics. If the system operates in purely AWGN environment, no interleaving is needed, because the error distribution cannot be changed by relocating the bits.

Communication channels are divided into fast and slow fading channels. A channel is fast fading if the impulse response changes approximately at the symbol rate of the communication system, whereas a slow fading channel stays unchanged for several symbols.

Modulation and channel coding are fundamental components of a digital communication system. Modulation is the process of mapping the digital information to analog form so it can be transmitted over the channel. Consequently every digital communication system has a modulator that performs this task. Closely related to modulation is the inverse process, called demodulation, done by the receiver to recover the transmitted digital information. The design of optimal demodulators is called detection theory. Different coherent mapping used are BPSK, QPSK and M-QAM .However there is trade-off between, different Mapping tech and spectral efficiency. In present paper all mappings are used for simulation purpose.

Pilot insertion is used for channel estimation & synchronization purpose.

An inverse Fourier transform converts the frequency domain data input to time domain representing OFDM Subcarrier. IFFT is useful for OFDM because it generates samples of a waveform with frequency component satisfying orthogonality condition. It also removes the need of oscillator. A general N-to-N point linear transformation requires N2 multiplications and additions. This would be true of the DFT and IDFT if each output symbol were calculated separately.

However, by calculating the outputs simultaneously and taking advantage of the cyclic properties of the multipliers e±j2πkn/N Fast Fourier Transform (FFT) techniques reduce the number of computations to the order of N log N. The FFT is most efficient when N is a power of two. Several variations of the FFT exist, with different ordering of the inputs and outputs, and different use of temporary memory.

One way to prevent IS1 is to create a cyclically extended guard interval, where each OFDM symbol is preceded by a periodic extension of the signal itself. Considering the discrete time implementation of the Multi Carrier system, sampling the transmitted Multi Carrier signal at a rate equal to the data rate one obtains a frame structure composed of the IDFT of the data symbols and of a cyclic prefix and where the OFDM frame will contain Ntotal = L + N samples. Here L is the number of samples copied from the end of N sample IDFT frame and glued at the start of each IDFT frame.

At the receiver, removing the guard interval becomes equivalent to removing the cyclic prefix, while the effect of the channel transforms into the periodic convolution of the discrete time channel with the IDFT of the data symbols. Performing a DFT on the received samples after the cyclic prefix is discarded, the periodic convolution is transformed into multiplication, as it was the case for the analog Multi Carrier receiver.1/2 or 1/4 or1/8 or 1/16 or 1/32 times of data symbol is added at beginning of the OFDM.

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