A new hybrid ARQ scheme based on blind separation sources over MIMO system in multipaths radio fading channel

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A new Hybrid ARQ scheme based on Blind Separation Sources over MIMO system in multipaths radio fading channel

Conference Paper · January 2010

DOI: 10.1109/ICM.2009.5418633 · Source: IEEE Xplore

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A new Hybrid ARQ Scheme based on Blind Separation Sources over MIMO System in

Multipaths Radio Fading Channel

Moulay Ahmed Faqihi

LRIT, FSR

Universit´e Mohamed V-Agdal Rabat, Maroc

Benayad Nsiri

Facult´e des Science s Universit´e Ain Chok Casablanca, Maroc

Abdellah Adib

LIM, FST Universit´e Hassan II Mohammedia, Maroc

Driss Aboutajdine

LRIT, FSR

Universit´e Mohamed V-Agdal Rabat, Maroc

Samir Saoudi

D´epartement SC Telecom-Bretagne

Brest, France

Email:saoudi@telecom-bretagne.eu

Abstract— In this paper, we propose a new scheme of Hybrid

ARQ ( Automatic Repeat reQuest) strategy, based on Blind Separation Sources over Multi Input Multi Output (MIMO) architecture. In the classical HARQ case, when the received packet is erroneous, the system should send a NACK to ask the transmitter to re-send the same packet. Known that in this case, the receiver could use different copies of the emitted signal to ensure a combination of ARQ, we propose in our approach to transmit different copies of the same packet, but simultaneously over multiple antennas, in order to provide a MIMO system.

This approach makes possible the recovering of the erroneous packets, by using the received copies instead of asking for a retransmission, which is very time- and treatment- consuming.

The temporary diversity is assured by applying the interleaver to each copy of the transmitted packet, as well as the determination of the emitted signal’s copies by using the Blind Separation Sources (BSS) concepts, without prior information about the transmission channel. The simulations show that the proposed scheme provides good results in term of frame error rate.

I.

Wireless data networks provide access to multimedia ap- plications such as video streaming and internet, together with classical applications such as voice. While there is an increasing demand for wireless services, radio resources are often scarce, and therefore a careful and efficient allocation of limited resources is vital. The challenge is that different applications have different quality of service requirements.

In this paper, we propose a novel scheme for HARQ algorithm using Orthogonal Frequency Division Multiplexing MIMO-OFDM system, the investigation is carried out for a blind equalization method based on BSS concepts. OFDM, is considered today to be a reliable choice for high rate transmissions and is now widely adopted and tested in many communication systems. Specifically, OFDM has been chosen for digital audio and video broadcasting (DAB [8], DVB [5]), for high-speed modems over twisted pairs (digital subscriber line: xDSL [11]), and, more recently, for 5-GHz broadband wireless local area networks (HIPERLAN/2, IEEE802.11a and MMAC standards [2]).

OFDM is a promising technique for the next generation of wireless communication systems [3] [9] [6]. The basic idea of

multicarrier transmission is to divide the available bandwidth into a large number of narrow sub-channels, and transmitting all chips in the same time, but in different orthogonal sub- channels. OFDM divides the available bandwidth into N c orthogonal sub-channels which are orthogonal to each other.

To prevent Inter Symbol Interference (ISI) and Inter Block Interference (IBI), a cyclic prefix (CP) (or guard interval) is added to each OFDM symbol, the channel appears to be circular if the CP length is longer than the multipath spread T

. Each sub-channel can be modelled as a time- varying gain plus Additive White Gaussian Noise (AWGN) with variance σ

. Thus, each data symbol modulates a sub- channel frequency over a multipaths Rayleigh Fading Chan- nel. Therefore, the effect of the multipaths channel on each subcarrier can be represented by a single complex multiplier, affecting the amplitude and phase of each subcarrier. Hence, the equalizer at the receiver can be, easily, implemented by a Matrix of complex multiplier, one for each subcarrier. The OFDM modulation and demodulation can be applied by means of the Inverse Fast Fourier Transform (IFFT) at the transmitter and the FFT at the receiver [12]. A Discreet Fourier Transform is used at the transmission so that the transmitted signal at every carrier is multiplied by a gain expressed in frequency domain. The equalization of the received signal consists of eliminating the above mentioned gain.

In this paper, we propose a novel scheme for HARQ algo- rithm using MIMO-OFDM system. In the classic case of the algorithm Hybrid ARQ, when the received packet is erroneous, the receiver sends a NACK to the transmitter requesting re- transmission of the same packet. In our approach, we propose to apply independent N

interleavers to the same packet and transmit, simultaneously, different interleaved copies into N

antennas transmitters. This approach has two major objectives,

the first is to exploit the virtual MIMO transmission performed

by the various copies of the signal, the second is to combine

erroneous packet through different copies, received locally, at

the receiver without sending a NACK to the transmitter for

resending the same packet according to the ARQ algorithm,

the approach is highly desirable for the worst possible channel

conditions in order to be able to exploit all copies issued on the various antennas. The investigation is carried out for a blind equalization method based on BSS concepts. The fact of applying the IDFT (Inverse Discret Fourier Transform), in transmission, guarantees that at each carrier we have an instantaneous mixture, which allows recovering the transmitted signals using frequency techniques of BSS. It is worth to mention that the system mixture is completely unknown at the receiver.

The rest of this paper is organized as follow: In Section 2, a brief description of Blind Separation systems is presented. In Section 3, system model for MIMO-OFDM is described and discussed. In Section 4, we illustrate our proposition by means of some computer experiments. Finally, Section 5 is dedicated to draw remarks and conclusion.

II.

Actually, Blind identification, equalization and separation are dedicated to situations related to the processing of data resulting from the reception of several sources signals lead to difficult analysis, and constitute the most up-to-date methods in signal processing. In recent decade, BSS became [1] [7]

one of the executing new topics in advanced statistics and signal processing and it applies to major fields such as data transmission, audio identification, seismology and even within the medical framework.

Blind identification methods depend on the nature of the criterion to measure the statistical mutual independence be- tween the output signals. For example, in presence of a known distribution noise, the evaluation of input signals can be performed according to a Maximum Likelihood or a Maximum a Posteriori procedure. If this is not the case, contrast criteria are devoted to this kind of situation [1] [10]. In this paper, we use the following standard notations. The vectors and matrices are denoted by bold small and capital letters, respectively, e.g. a vector s and matrix A. The i

element of vector s is denoted by s

and the ij

element of a matrix A by A

. The superscript T denotes the transpose of a matrix or vector.

Time is denoted by t and the complex conjugate is denoted by the superscript (∗).

s(t)

- H

G

S

x(t)

-

-

Fig. 1. General system of separation

Consider the basic (BSS) model, as shown in Figure 1:

x(t) = H.s(t) + n(t) (1) in which the source vector s(t) = [s

(t), . . . , s

(t)]

of N

independent components, the noise vector n(t) =

Fig. 3. Basic MIMO system

[n

(t), . . . , n

(t)]

and the output vector x(t) = [x

(t), . . . , x

(t)]

received by an array of N

≥ N

sensors. The mixing matrix H is assumed to be full column rank, which ensures “space” diversity. The objective is to exploit the assumed mutual independence of the sources to blindly recover the source vector s(t), only from realizations of the output vector x(t), up to a scale factors and permutation ambiguities. This operation consists of finding a matrix S such as the signals y(t) = S . x(t) are copies of the inputs s(t). The global separation matrix is read G = SH.

III.

The proposed system is based on MIMO architecture, and it consists of N t transmitted signals. As it is shown in Figure 2, we consider one data transmitted signal, each binary data is transmitted with a period T

, and all data are equiprobable. The data symbol is convolutionally encoded with a code rate R

= K/N , where K is the input sequence of the turbo-encoder, and N is the length of the soft encoded bit b

and passed through a bit-Mapper for BPSK modulation, the result signal is applied to N

interleavers blocs simultaneously to generate N

signals, one signal per antenna, we consider independent interleavers so that all signals are i.i.d (Independent and identically- distributed), each output signal is Serial to parallel converted, then, applied to N

points IDFT for OFDM modulation, it is important to indicate that all interleaved signals are obtained from the same input data symbol and the interleaved signals are applied to the same frequencies modulators, the scheme can be viewed as a virtually MIMO-OFDM system as that it is shown in Figure 2. The main goal is to propose a new scheme for Hybrid ARQ system based on retransmission packet. In this paper, we exploit MIMO system so that each antenna corresponds to one retransmitted packet of the same input data signal, then we exploit the bloc interleaver for time diversity of the various copies of the signal.

While OFDM system is considered, data are transmitted in blocks, the signal, transmitted at the i

antenna, is expressed as :

s

= [s

(pN

+ 1), . . . , s

(pN

+ N

)], (2) where p is the block index. Each block is of length N

and corresponds to the total number of subcarriers.

Considering the MIMO case, as shown in Figure 3, the

transmitter and the receiver are formed by N

and N

antennas

respectively, the system is considered sub-determinated ( N

≥

N

). So, we can build blocks of received signals for each

Fig. 2. Proposed System Model

subcarrier k , k = 1, . . . , N

, and r(k) can be interpreted as an instantaneous mixture of the transmitted signals in the frequency domain, and it can be expressed, for all received antennas, as :

r(k) = [r

(pN

+ k), r

(pN

+ k), . . . , r

(pN

+ k)]

,

= H(k)s(k) + n(k), (3)

with,

H(k) =

⎛

⎜ ⎜

⎜ ⎝

h

(k) . . . h

(k) h

(k) . . . h

(k)

.. . . .. .. . h

(k) . . . h

(k)

⎞

⎟ ⎟

⎟ ⎠ (4)

where h

(k) is the k

DFT coefficient of the channel transmission between the transmitter antenna i and the receiver one j . s(k) is the transmitted signal from all antennas in subcarrier k and it can be given by :

s(k) = [s

(pN

+ k), . . . , s

(pN

+ k)]

, (5) and

n(k) = [n

(pN

+ k), . . . , n

(pN

+ k)]

, (6) is an AWGN with zero mean and covariance matrix I σ

.

It is worth mentioning, here, that a particular grouping must be done for all N

receiver antenna signals to recognize the system model as a BSS problem, see Figure 4.

We consider a blind equalization method by using BSS model, so, we exploit only the sequences training to find an estimate of mixture matrix G(k), for each subcarrier k , so that :

˜ s(k) = G

(k)r(k) (7)

= M(k)s(k) + G

(k)n(k), (8) with,

M(k) = G

(k)H(k), (9) Where G(k) is a N

×N

matrix that groups the coefficients of the same subcarrier k related to different transmitter antennas.

The first stage of our system (see Figure 2) consists of

Fig. 4. Blind seperation model

separating the instantaneous mixture in one single frequency bin, noted by r .

Indeed, the essence of our contribution is to highlight one of the many positive aspects of the novel scheme for HARQ algorithm using MIMO-OFDM system; namely to extract emitted signal’s copies by using the BSS concepts.

Powerful algorithms are now at hand to deal with many concrete BSS applications. So, we will investigate the system performance using a low complexity BSS method JADE (Joint Approximated Diagonalization of Eigen-matrices) [4] relying on the maximization of a contrast criterion based on fourth order cumulants. Therefore, we can suppose that each output at the frequency bin r , corresponds to a single source at that same frequency bin multiplied by a certain gain introduced by the algorithm.

It is known that BSS is only possible up to some scaling and

permutation [1]. To compensate this kind of indeterminacies,

we proposed a post-processing solution to overcome the prob-

lem of ordering and scaling of the estimated transmitted sig-

nals using CDMA (Code Division Multiple Access) concepts.

Fig. 5. MIMO-OFDM interleaved system using BSS Model

Indeed, we assign to each antenna transmitted block a unique code sequence (or pilot sequence) of Walsh-Hadamard matrix which is known at the receiver and we find the real order by multiplying the received sequence code with its transpose.

IV.

The simulations are realized by Monte-Carlo runs (see Fig- ure 5), we consider BPSK data modulated, MIMO system is performed for N

= 3, and N

= 3, the number of subcarriers for OFDM modulations is 64, so we have 64 mixture matrices, convolutional coding is used with code rate equals to 1/2, the number of turbo decoding iterations is fixed at 5. The threshold of BLER (Block Error Rate) for that the packet is considered received correctly is = 10

, the performances are carried out for number of retransmissions nharq = 1, 2 and 3. For a good blind estimation of data symbol, we consider 500 blocks for each transmitted signal antenna, for that, we build the estimated signal, at the receiver, according to BSS concepts, for each subcarrier k. We consider Rayleigh model for multipaths radio fading channel implemented by Jake’s model [13] with 6 paths. In the simulations, we change the number of considered copies of transmitted packet, denoted nharq.

In the Figure 5, we illustrate the performances of BLER versus Signal to Noise Ratio in db , and they are shown for nharq = 1, 2 and 3. If an error is detected for one received copy, a negative acknowledgment (NACK) is generated to exploit next copy at the next received antenna, so that it corresponded to nharq = 2, and so on. The different copies are combined at the decoder in order to better exploit the diversity of the channel and to increase the probability of successful decoding based on both hard and soft decision. For nharq = 1, we exploit just one copy of transmitted packet, we remark, that in this case, BLER = 2.10

for SN R = 8.5db . In the case of nharq = 2, we combine two copies of the same packet, we can, easily, remark that we gain 2db for the same simulations conditions. Indeed, nharq = 3 corresponds to combining three

copies of transmitted packet, then, for the same BLER value, we can gain 3.5db, this is very important in order to combine more copies of the same transmitted packet at the receiver to increase the probability of successful received.

V.

In this paper, we proposed a new method for blind equal- ization based on BSS technique, this method was carried out for MIMO-OFDM system in multipaths radio fading channel.

This method outperforms the classical JADE algorithm by applying some contrast functions to improve performances of blind separation methods. We also proposed a new method to overcome the disordering of estimated signals at the received based on CDMA concepts. The simulations show, clearly, that the proposed method improves a good result in term of bloc error probability versus SNR in db and it can start other researches for blind equalization systems.

R

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