History About The Multiple Input And Multiple Output

Published Date: 02 Nov 2017

Abstract

Applying LDPC encoding to Multiple Input Multiple Output (MIMO) antennas Orthogonal frequency Division Multiplexing OFDM combination MIMO-OFDM based on Discrete Wavelet Packet Transform DWPT system with different channel models including fading environment.

A coded Discrete Wavelet Transform DWT Multicarrier CDMA MC-CDMA system has been proposed and to enhanced the bit error rate performance of the traditional MC-CDMA which based on Fast Fourier Transform FFT. A LDPC is used in the proposed system. The computer simulation tests show that the BER of the DWT based MC-CDMA has been improved by ……………. dB compared with FFT based MC-CDMA. The performance at BER=10-5.

The usage of the LDPC DWT MC-CDMA system is a bout ……dB over uncoded DWT MC-CDMA system and about ………..db over the LDPC FFT MC-CDMA system system.

1-Introduction

A new wireless broadband technology known as MIMO-OFDM (multiple input multiple output orthogonal frequency division multiplexing) has obtained great popularity due its capability of high rate transmission and its robustness against multi-path fading and other channel impairments [Kala]. It increase in the diversity gain refers the quality of signal and multiplexing gain refers the transmission capacity since it has an arrangement of multiple antennas at the transition end and reception end results [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 is a combination of OFDM and MIMO techniques which results in 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 [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 work, a parallel concatenated convolutional code PCCC of two convolutional codes are used as a channel coding scheme with the wavelet packet transform WPT based MIMO-OFDM which uses the STBC technique in order to strongly reduce the level of interference and increase spectral efficiency. We provide the performance comparisons of FFT-MIMO-OFDM and WPT- MIMO-OFDM with PCCC code in both cases on three different channel models: AWGN, flat fading and selective fading. The results of simulation 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-Parallel Concatenated Convolutional (TURBO CODE) Encoding

The convolutional turbo coder consists of a parallel concatenation of recursive systematic convolutional RSC encoders separated by a pseudo-random interleaver [Ramasmay 2006, Husam 2010]. The main aim of RSC is to produce more high weight codes even though input contains more number of zeros [Shanmugam 2005]. A natural rate for such a code is 1/3 (one systematic bit and two parity bits for one data bit). The rate can be relatively easily increased by puncturing the parity bits but reducing the rate below 1/3 is more difficult and may involve repetition of some bits [Ramasmay 2006]. The structure of such a Turbo coder is shown in Figure (3a).

One important feature of turbo codes is the iterative decoding which uses a soft-in/soft-out (SISO) like the Max-Log- Maximum A Posteriori (MLMAP) algorithm is a good compromise between performance and complexity [Vogt 1999]. It is very simple and, with the correction operation, also very effective [Robertson 1995]. Compared to the Maximum A Posteriori (MAP)/Log-MAP algorithm no SNR-information is necessary and the critical path within the add-compare-select (ACS) unit is shorter because of the maximum operation without the correction term [Robertson 1997].

Like other methods max-log-APP algorithm calculates approximate log-likelihood ratios LLR's for each input sample as an estimate of which possible information bit was transmitted at each sample time[Robertson 1995].They are calculated according to [Robertson 1995, Robertson 1997, Husam 2010]

where i is the sample time index, m {0, … , Ns-1} is the present state, Ns is the number of encoder states, f(d, m) is the next state given present state m and input bit d {0,1}, is the forward state metric for state m at time i, is the reverse or backward state metric for state m at time i, and is the branch metric at time i given present state m and input bit d{0,1}. More formally, the state and branch metrics are given by [Robertson 1995, Robertson 1997, Husam 2010]

where b(d,m) is the previous state given present state m and previous input bit d{0,1}, xi is the ith systematic sample, yi is the ith parity sample, d is a systematic bit, is the corresponding coded bit given state m and bit d, =1-2d , and . The state metrics provide a measure of the probability that state m is the correct one at time i, while the branch metrics are a measure of the probability that each possible combination of encoder outputs is the correct one given the channel outputs xi and yi.

The Max-Log-APP algorithm is sub-optimum due to the approximations involved. However, most of the performance loss associated with this sub optimality can be recovered by applying a simple scale factor correction to the output of the constituent decoder. The so-called extrinsic information may be approximated as [Robertson 1995, Robertson 1997, Husam 2010]

where n{1,2} denotes one of the constituent decoders, represents the set of LLRs produced by the max-log-MAP decoder, represents the set of input LLRs, and sf is an appropriate scale factor. The turbo concatenated decoder architecture is shown in Figure (3b).

3-MIMO-OFDM

MIMO-OFDM for the systems in IEEE 802.11n is what distinguishes this WLAN among the others from the same family of IEEE 802.11 and it is considered a very good improvement. MIMO system considers more robustness and offers higher gain in comparison to the single antenna case, and also in MIMO system one can transmit different signals in the same time over different antennas [Ammar 32][44].

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 WPT and WPT 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-IMO-OFDM 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 is the received signal, and W 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:-

6.Results

The proposed system illustrated in Figure [ ] is the wavelet Packet based MC-CDMA system. An 20 Mbps was transmitted over the system. The modulation schemes are the MPSK with M=2, 4, 16,and 64. The work implied performance comparision of the proposed DWT-MC-CDMA system with that of Fast Fourier Transform FFT MC-CDMA system.

A simulation of the two systems has been made using MATLAB version 2012a. The BER performance of the two systems will also be studied in different channel models which are Additive White Gaussian Noise AWGN and multipath fading channel, with a bandwidth of 5 MHz and Walsh-Hadamard (code 20) has been used with 32 bits

The system uses LDPC code. The LDPC specifications used are irregular [16384] Matrix of rate ½. The decoding algorithm is Sum-Product Decoding Algorithm,which is the soft decision type of message passing. The performance of the LDPC decoding depends upon the number of iteration of the decoder.

6.1.Performance of the Proposed System in AWGN Channel

When the channel was modeled as an Additive White Gaussian Noise AWGN channel. The performance of the system was shown in Figures [6, 7,8,9 and 10]. These figures show the variations of BER versus signal to noise ratio (SNR) (Es/Nͦ signal power to the noise power) for LDPC coded data for both FFT MC-CDMA system and DWPT MC-CDMA system with QAM modulation scheme of M value of 2,4, 16,and 64 respectively. It can be noticed that when M = 64, at SNR of 22 dB the BER is 10-3 DWPT MC-CDMA system, while BER is 10-3 at 26 dB for FFT MC-CDMA system with a gain of 4 dB is obtained by the proposed model.

6.2.Performance of the Proposed System in Multipath Fading Channel

Here, the channel was modeled as a multipath fading channel. Figures [11, 12 and 13] show the performance of LDPC coded FFT MC-CDMA system and LDPC coded DWT MC-CDMA systems with QAM modulation scheme of M value of 2,4, and16 respectively. When M= 16, the BER at 10-3 was achieved at a SNR of 16 dB for DWPT-MC-CDMA system and 20.5 dB for FFT MC-CDMA system with a gain of 4,5 dB is obtained by this model.

7.Conclusion:

The results show that LDPC coded DWPT MC-CDMA gives better results for different channel models including the AWGN and Rayleigh channels over LDPC coded FFT MC-CDMA.

For AWGN channel with LDPC coded DWPT MC-CDMA system, the BER of 10-3 is about 1 dB better than and 2 dB better than LDPC coded FFT MC-CDMA system for BPSK and 6 dB gain over uncoded for QPSK . The gain increases as the order of modulation increase showing superiority for higher data rates. For low SNR the results contain a little difference from both uncoded data and convolution coded data.

For Rayleigh channel, at a BER of 10-3, the performance of the LDPC coded MC-CDMA system is better than that with LDPC coded FFT MC-CDMA system by about 2 and 3 dB for bpsk and 4psk modulation schemes respectively. It’s better by 4.5dB than convolutional coding for 16psk. The number of iterations was set to 10 which represents a low computational complexity comparable to covolutional decoder. For better performance and higher computational complexity, the number of iterations can be increased to 100 as clarified in Fig. 8.