The Multiple Input Multiple Output Mimo Computer Science Essay

Published Date: 02 Nov 2017

Abstract

The Multiple Input Multiple Output MIMO technique improves the capacity of the wireless link when operating in a dense multipath scattering environment through the use of multiple antennas in both transmitter and receiver. Wavelet-based MIMO- Orthogonal frequency Division Multiplexing MIMIO-OFDM system can better combat narrowband interferences and more robust to Intercarrier Interference ICI than traditional FFT filters.

A Low Density Parity Check LDPC coded Discrete Wavelet Packet Transform DWPT-MIMO-OFDM system has been proposed and to improve the bit error rate over that of the traditional OFDM which based on Fast Fourier Transform FFT with different models of channels.

The system uses sum product decoding algorithm. The computer simulation tests which implemented using matlab 2012a, show that the BER of the DWT based MC-CDMA has been improved by ……………. dB compared with FFT based MC-CDMA.

1-Introduction

A new wireless broadband technology known as MIMO-OFDM (multiple input multiple output orthogonal frequency division multiplexing) has gained great popularity for its capability of high rate transmission and its robustness against multi-path fading and other channel impairments [Kala]. The arrangement of multiple antennas at the transition end and reception end results increase in the diversity gain refers the quality of signal and multiplexing gain refers the transmission capacity [Kala]. MIMO systems employ multiple antennas at both the transmitter and receiver. In an MIMO system, N signals are transmitted by N antennas at the same time using the same bandwidth and effective processing at the receiver side based on the M received signals by M different antennas, is able to distinguish the different transmitted signals [Abdul-Latef 2]. MIMO techniques can basically be split into two groups: space time coding (STC) [Alamouti] and space division multiplexing (SDM) [Abdul-Latef, Zelst, Wolniansky]. Space time block coding used in this paper to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of data to improve reliability of data transfer [Kala]. STC increases the performance of the communication system by coding over the different transmitter branches; whereas SDM achieves a higher throughput by transmitting independent data streams on different transmit branches simultaneously and at the same carrier frequency [Zelst]. Since increasing the bit rates is one of the goals, focusing on SDM algorithms is done in this paper [Abdul-Latef].

MIMO-OFDM combines OFDM and MIMO techniques thereby achieving spectral efficiency and increased throughput. MIMO systems do not increase bandwidth in order to increase throughput. They simply exploit the spatial dimension by increasing the number of unique spatial paths between the transmitter and receiver. However, to ensure that the channel matrix is invertible, MIMO systems require an environment rich in multipath [California].

A potential application of the MIMO principle is the next-generation wireless local area network (WLAN). The current WLAN standers IEEE 802.11a [Abdul-Latef, Prasad] are based on orthogonal frequency division multiplexing (OFDM) [Abdul-Latef, Lawerey, Wang].

Normally OFDM is implemented using IFFT and FFT’s in order to multiplex the signals together and decode the signal at the receiver respectively [Khaizuran]. To decrease the BW waste [4] brought by adding cyclic prefix, wavelet based OFDM is employed. Due to use of wavelet transform the transmission power is reduced. The spectral containment of the channels is better since it does not use cyclic prefix. To increase the delay spread of the channel so that it becomes larger than the channel impulse response, the system adds cyclic prefixes (CP) before transmitting the signal. This is done to minimize inter-symbol interference (ISI). However, this is done at the expense of reducing the spectral containment of the channels [Khaizuran].

The spectral containment of the channels is better in WT based OFDM since it does not use cyclic prefix to deal with delay spreads of the channel. This due to the overlapping nature of wavelet properties [Rashmi]. One type of wavelet transform is Discrete Wavelet transforms [Veena]. Due to use of wavelet transform the transmission power is reduced. The wavelet transform is discrete both in time as well as scale as compared to other transforms such as Fourier transform.

The increasing demand of higher rates and robust transmission in modern communication systems, have motivated the search for a suitable error correction schemes allowing high performance and errors near the theoretical limit (Shannon limit) [Ammar].

In this paper FFT-MIMO-OFDM is replaced by LDPC coded DWT-MIMO-OFDM using STBC technique in order to further reduce the level of interference and increase spectral efficiency. We provide the performance comparisons of FFT-MIMO-OFDM DMA and DMWT- MIMO-OFDM on three different channel models: AWGN, flat fading and selective fading. Simulation results show that proposed design achieves much lower bit error rates, increases Signal to Noise power Ratio (SNR), and can be used as an alternative to the conventional MIMO-OFDM.

2-LDPC Coding

The advantages and the performance of LDPC codes make it one of the best options among other correcting codes, in which these codes are capable of the fulfillment of these requirements and have been proposed for the next generation wireless standards. Now these codes are widely applied in the current wireless networks, such as WiFi (IEEE 802.11n), WiMAX (IEEE802.16e) and DVB-S2 standards. Also they are an important option for forward error correction in fourth generation (4G) wireless communication systems[Ammar] .

LDPC codes are linear block codes specified by a very sparse (containing mostly 0’s and only a small number of 1’s) random parity-check matrix, but are not systematic. The parity-check matrix of an LDPC is an M × N matrix A , where M is the number of parity bits, and N is the transmitted block length (N = K + M , with K as the source block length). The matrix A is specified by a fixed column weight j and a fixed row weight k = j N /M (in the MacKay’s and Neal’s codes k is as uniform as possible [MacKay 1999, Aqiel 2011, Husam 2012], and code rate R = K /N. LDPC codes can be decoded using probability propagation algorithm known as the sum-product or belief propagation algorithm [Kschischang 2001, Husam 2012], which is represented by a factor graph [Tanner Graph, Husam 2012] that contains two types of nodes: the "bit nodes" corresponding to a column of the parity-check matrix, which also corresponds to a bit in codeword and the "check nodes" corresponding to a row of the parity-check matrix, which represents a parity-check equation.

2-1-SUM-PRODUCT DECODING ALGORITHM

The decoding problem is to find the most probable vector x such that Ax mod 2 = 0 , with the likelihood of x given by xnΠnfn, where fn0 = 1 − fn1 and f1n = 1/(1 + exp(−2yn / σ2 )) for AWGN channel or f1n = (yn / σ2 ) exp[−y2n / 2σ2 ] for Rayleigh channel, and yn, σ2 represent the received bit and noise variance, respectively. We denote the set of bits, n , that participate in check m as N (m) ≡ {n : Amn = 1}, where Amn represents the element of the mth row and nth column in the parity-check matrix. Similarly, we define the set of checks m in which bit n participates as M(n ) ≡ {m : Amn = 1}. We denote a set N (m) with bit n excluded as N (m) \ n. The algorithm has two alternating parts, in which quantities qmn and rmn associated with each non-zero element in the matrix A are iteratively update. The quantity x qmn is meant to be the probability that bit n of x is x, given the information obtained via checks other than check m. The quantity rmn is meant to be the probability of check m being satisfied if bit n of is x considered fixed at x and the other bits have a separable distribution given by the probabilities {qmn' : n ' ∈ N (m) \ n }. The aposteriori probabilities for a bit are calculated by gathering all the extrinsic information from the check nodes that connect to it, which can be obtained by the iterative sum-product procedure described in details in [Luis 2006, Aqiel 2011, Husam 2012].

3-MIMO-OFDM

The general transceiver structure of MIMO-OFDM is presented in Fig. 1. The system consists of N transmit antennas and M receive antennas. The transmit antennas transmit independent data (say X1, X2, …, XN) simultaneously and in the same frequency band. A MIMO decoder uses M ≥ N antennas at the receiver side. The received MIMO-OFDM symbol of the n:th subcarrier and the m:th OFDM symbol of the i:th receive antenna after FFT can be written as [Helka]

where Xj[n,m] is the transmitted data symbol on n:th carrier and m:th OFDM symbol, Wi[n,m] is the additive noise contributions. and Hi,j[n,m] is the channel coefficient in the frequency domain between the j:th transmit antenna and the i:th receive antenna. The channel matrix H is an NxM matix corresponding to the n:th subcarrier and m:th OFDM

symbol.

The received data symbols of all antennas can be found as in below:

Where

are the Nx1 and Mx1 vectors of the transmitted and received data symbols. The transmitted data symbols can be obtained by solving equation (8) which is called MIMO-OFDM equalization.

This equalization works well in case of small noise and no ISI or ICI.

Wavelet Packet Transform and Wavelet Packet Based MIMO-OFDM system

Wavelet packets transform has been first introduced for data compression due to it functions are localized in both time and frequency domains [Haitham]. Let the data stream at the transmitter is first modulated. Here the modulation schemes adopted may be the BPSK, QPSK, and M-QAM. The modulated output symbols are defined as be X = (x[1], x[2], …., x[N]). This stream is converted into parallel sequences Sk and then modulated with M-array inverse wavelet packet transform (IWPT). Figures (1) shows the wavelet packet based MCM transmitter operating Mallat’s fast algorithm [Giovanni, Haleh].

The transmitted signal Y, is composed of successive K symbols, as the sum of M amplitude modulated waveforms by φk as:

where Y = (y[1], y[2], …., y[n],…, y[N]), is the transmitted signal. SK = (sο [k], s1 [k],….Sm [k], …, SN [k]), is the output of serial to parallel converter ,and φk,

is the waveforms matrix in which φm[n] represent the WPT-MIMO-OFMM basis function that are mutually Orthogonal [jamine] to reduce the symbol errors [Haleh] .

In the wavelet packet scheme, one limits his analysis to subcarrier waveforms defined through a set of FIR filters, and implemented by Mallat’s fast algorithm [halleh, Mallat] with less complexity for wireless communication.

The Mallat algorithm implemented by quadrature mirror filter pair (QMF) that consists of the scaling filter gand dilatation filter h, and knowledge of the scaling filter and wavelet tree depth is sufficient to design the wavelet transform. The scaling filter g and dilatation filter h, and the corresponding reversed filtersg(-n) and h(-n), are used to form a wavelet packet tree. These filters satisfy following conditions [Hongbing, Kenneth, Haitham, Giovanni, Haleh aqiel]:

where M is the length of the filters.

The carrier waveforms are obtained by iteratively filtering the signal into high and low frequency components. The waveforms φm[m] are derived by J successive iterations as the following recursive equations:

Where j is the iteration index, , and m the waveform index . Y is the transmitted signal through the channel H, with L multi-paths, H = (h[0], h[1], …,h[l], …, h[L-1]) and received signal at the output of the channel can be written as:

where R = (r[1], r[2], …,r[n], …, r[N]), is the received signal, and W=(w[1], w[2], …, w[n], …, w[N]) is additive white Gaussian noise (AWGN).

6- Proposed System

The proposed system block diagram shown in figure (). This model shows the system of OFDM based on FFT transform and WPT transform systems. At the transmitter the incoming data stream is first encoded using the turbo encoder. Then it is modulated using QAM modulation scheme with M = 2,4, 8, and 64. The modulated data is converted to parallel sequences and then modulated with M-array inverse wavelet packet transform (IWPT). Figures1 and 2, show the discrete wavelet transform based MCM transceiver operating Mallat’s fast algorithm.

As in the FFT-OFDM system model, the input serial data stream is converted into parallel word size required for transmission. The data to be transmitted on each carrier is modulated into a MPSK format. An Inverse Wavelet Packet Transform (IWPT) is used to find the corresponding time domain waveform. The IWPT requires two groups of data input, the first part is called approximation and the second group called details (the length of approximation part equal to the length of details part). In the proposed system the input parallel BPSK data represents approximation part, while zeros are inserted as a details part. The length of output signal from the IWPT stage is equal to double the length of parallel BPSK data. This output data is converted to serial vector, then this vector is convoluted with the channel selected in the work.

At the receiver side, the serial data is converted into parallel data by serial to parallel converter. Then, the WPT is used to find the corresponding frequency domain of the parallel data. The length of data out is 2NC. The first half of 2NC output data from WPT stage represents the received signal, and the second half represents details, not used for detection. Single tap frequency domain equalizer is used to overcome channel distortion. Each transmitted subcarrier is then evaluated and converted back into the data word by demodulating the received symbol. Then, the data is decoded to reconstruct the original data.

Therefore, Haar wavelet is used in the design of the proposed model, due its simplicity and better performance.

The parameters and system configuration used in the simulation are summarized as follows:-

Modulation scheme

BPSK

Number of subcarrier of FFT

256 subcarriers

Wavelet level

three

Type of wavelet transform

Haar wavelet

OFDM symbol duration

64*10-6 sec

Required bandwidth

5 MHz

Model of simulated channel

Jacks Model

Number of path

6 paths

Pilot Carriers

8

Doppler frequency

50 Hz

Types of spreading code used

Walsh Hadamrd

code

Processing gain (Walsh code)

32

Required BER

10-4

When the number of subcarriers is equal to 128, the number of IDWT points is equal to 256 (128 approximation and 128 details). At the receiver, the length of data out from the DWT is equal to 256 (the first 128 subcarriers represent the received data, while the second 128 subcarriers represent the details).