Parallel Concatenated Convolutional Encoding

Published Date: 02 Nov 2017

Abstract

Multiple Input Multiple Output (MIMO) is a new technology that uses multiple antennas at both transmitter and receiver in order to improve the reliability and data transfer. In this work, Parallel Concatenated Convolutional Code PCCC is applied to the Multiple Input Multiple Output (MIMO) Orthogonal frequency Division Multiplexing OFDM combination MIMO-OFDM based on Discrete Wavelet Packet Transform DWPT system with different channel models including fading environment.

The MIMO system uses the Almouti Space Time Block Code A-STBC technique with 2 antennas at both transmitter and receiver. The DWPT use the mallat's fast algorithm and turbo code uses the max-log algorithm which an iteration algorithm for decoding process. The simulation tests show that the BER of the PCCC coded DWPT based MIMO-OFDM has been improved by greatly compared with the PCCC coded FFT based MIMO-OFDM.

1-Introduction

The combination of Multiple Input Multiple Output (MIMO) with the OFDM modulation is considered very good solution for the robustness and higher data rates in the next generation wireless LAN. The system in such a case is capable of supporting high bit rates in wireless communication and achieving attractive diversity gain. 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 we can transmit different signals in the same time over different antennas. Using antenna diversity which is very effective in the case of scattering environment, having diversity of receive antennas give us the option to combine, select and switch in order to improve the quality of our received signal[32][44]. 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 paper FFT-MIMO-OFDM is replaced by PCCC coded DWT-MIMO-OFDM using STBC technique in order to further reduce the level of interference and increase spectral efficiency. The performance of both FFT-MIMO-OFDM and DMWT- MIMO-OFDM systems was compared over the AWGN and fading channel models. The results show that the BER greatly reduced by adopting the suggested system.

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 A1, A2, …, AN) 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 Aj[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

Let the data stream at the transmitter is first modulated and STBC coded. 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 modulation is done using 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, consists 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. the knowledge of the scaling filter and wavelet tree depth is sufficient to design the wavelet transform. The scaling filter gand dilatation filter h, and the corresponding reversed filters g(-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]). At the output of the channel, the received signal can be calculated 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 block diagram of the proposed system shown in figure (). This model shows the system of a turbo coded MIMO-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 IFFT or M-array inverse wavelet packet transform (IWPT) for both models discussed here. Figures1 and 2, show the discrete wavelet transform based MCM transceiver operating Mallat’s fast algorithm. In IEEE 802.11n, the IFFT 256 useful modulated bits including the pilots bits with the guard interval we have 64 bits.

The Almouti space time block coding A-STBC is applied to the transmitting data over a couple of antennas for MIMO system with a receiving antennas of 2 also (i.e. N = M = 2). The channels used in the work including the Additive White Gaussian Noise AWGN channel and Rayleigh multipath fading channel. The transmitted data then convoluted with the channel selected in the work

At the receiver side, the received serial data is converted back into parallel data by serial to parallel converter. Then, the FFT or DWPT is used to find the corresponding frequency domain of the parallel data. For the DWPT the length of output data 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. The data comes from the FFT or DWPT used by the A-STBC decoder to reconstruct the original modulated vector. This vector passed through the demodulator and turbo decoder to obtain a copy of the original information.

In the work the, the data encoded with the parallel concatenated convolutional coder PCCC with both the upper and lower coder of a generator polynomial of [1 0 1 1; 1 1 0 1] ) polynomial generators and a constraint length of (4) and MAX-LOG-MAP decoding algorithm which is an iterative decoding algorithm. The performance of the concatenated convolutional code system depends upon the number of iteration of the decoder. Haar wavelet is used in the design of the proposed model with three wavelet level, due its simplicity and better performance. 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). The parameters and system configuration used in the simulation are summarized in Table (1).

Table (1): The parameters and system configuration of the proposed system

Modulation scheme

2,4,16,64 PSK

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

Required BER

10-4

6.Results

The proposed system illustrated in Figure [ ] is the wavelet Packet based MIMO-OFDM system using turbo coding technique. 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 PCCC coded DWPT-MIMO-OFDM system with that of PCCC coded Fast Fourier Transform FFT-MIMO-OFDM 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. the parameters and configurations of the system are listed in Table (1).

6.1.Performance of the Proposed System in AWGN Channel

When the an Additive White Gaussian Noise AWGN channel was used as achannel. The resultant performance curves of the system are shown in Figures [6, 7,8,9 and 10]. These figures illustrate how the variations of BER versus signal to noise ratio (SNR) (Es/Nͦ signal power to the noise power) for PCCC coded data for both FFT based MIMO-OFDM system and DWPT based MIMO-OFDM 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 multipath fading channel was modeled as a transmission channel. the performance of LDPC coded FFT-MIMO-OFDM system and LDPC coded DWT-MIMO-OFDM systems with QAM modulation scheme of M value of 2,4, and16 are shown in figures [11, 12 and 13] respectively. It can be noticed that when M= 16, a BER of 10-3 was achieved at a SNR of 16 dB for DWPT-MIMO-OFDM system and 20.5 dB for FFT-MIMO-OFDM system with a gain of 4,5 dB is obtained by this model.

7.Conclusion:

The use of the parallel concatenated convolutional coded (PCCC) technique in conjunction with the DWPT-MIMO-OFDM system improves the performance of the system over that which uses the PCCC-FFT-MIMO-OFDM system with both types of channels, the AWGN and Rayleigh channels. When the LDPC coded DWPT-MIMO-OFDM system was used with AWGN channel, it can be noted that the BER of 10-3 is about 1 dB better better than LDPC coded FFT-MIMO-OFDM system for BPSK and 6 dB gain over uncoded for QPSK. The gain value depends on the order of modulation. But for the Rayleigh channel, the improvement was , , , and dB for 2, 4, 16,32 and 64 psk modulation respectively for a BER of 10-3.

For low SNR the results contain a little difference from both uncoded data and convolution coded data.For better performance and higher computational complexity, the number of iterations can be increased to 100 as clarified in Fig. 8.