WO2010030104A2

WO2010030104A2 - Method for detecting and decoding a signal in multi-antenna system of transmitting/receiving

Info

Publication number: WO2010030104A2
Application number: PCT/KR2009/005079
Authority: WO
Inventors: Alexander Victorovich Chernysh; Mikhail Vladimirovich Golikov; Sergey Anatolievich Goreinov; Jong-Ho Lee; Joo-Hyun Lee; Alexey Olegovich Melnikov; Andrey Leonidovich Rog; Sung-Soo Hwang
Original assignee: Samsung Electronics Co., Ltd.
Priority date: 2008-09-09
Filing date: 2009-09-08
Publication date: 2010-03-18
Also published as: WO2010030104A3; RU2008136226A

Abstract

Method for detecting and decoding a radio signal in a wireless multi-antenna system of transmitting/receiving (MIMO) using Orthogonal Frequency Division Multiplexing (OFDM) and adaptive modulation where the procedure of the ordered type of modulation of a layer is included calculating a probability of an error symbol detection based on modulation type, and determining a layer ordering with a minimum error probability among the calculated probability.

Description

METHOD FOR DETECTING AND DECODING A SIGNAL IN

MULTI-ANTENNA SYSTEM OF TRANSMITTING/RECEIVING

BACKGROUND OF THE INVENTION

1. Field Of The Invention

The invention relates to telecommunications, in particular, to wireless multi-antenna systems of transmitting/receiving (MIMO - Multiple Input Multiple Output), which is based on methods of decoding and applies the technique of the ordered consecutive cancellation of interference component (OSIC).

2. Description Of The Related Art

A Multiple-Input Multiple-Output (MIMO) communication system transmits and receives data using multiple transmit antennas and multiple receive antennas. A MIMO channel formed by Nt transmit antennas and Nr receive antennas is divided into a plurality of independent spatial subchannels. Because the MIMO system employs multiple transmit/receive antennas, it outperforms a Single-Input Single-Output (SISO) antenna system in terms of channel capacity. Conventionally, the MIMO system undergoes frequency selective fading that causes Inter- Symbol Interference (ISI). The ISI causes each symbol within a received signal to distort other successive symbols. This distortion degrades the detection accuracy of a received symbol, and it is an important noise factor affecting a system designed to operate in a high Signal-to-Noise Ratio (SNR) environment. To remove the ISI, a stage at the receiving end has to perform an equalization process for a received signal. This equalization requires high processing complexity.

On the other hand, Vertical Bell Labs Layered Space-Time (V-BLAST) architecture, which is one of space division multiplexing schemes, offers an excellent tradeoff between performance and complexity. The V-BLAST scheme uses both linear and non-linear detection techniques. In other words, the V-BLAST scheme suppresses interference from a received signal before detection and removes interference using a detected signal.

When an Orthogonal Frequency Division Multiplexing (OFDM) scheme is used, an equalization process for the received signal is possible at low complexity. An OFDM system divides a system frequency band into a plurality of subchannels, modulates data of the subchannels, and transmits the modulated data. The subchannels undergo different frequency-selective fading according to transmission paths between transmit and receive antennas. The ISI incurred due to this fading phenomenon can be effectively removed by prefixing each OFDM symbol with a cyclic prefix. Therefore, when the OFDM scheme is applied to the MIMO system, the ISI is not considered for all practical purposes.

For this reason, it is expected that the MIMO-OFDM system based on a detection algorithm of the V-BLAST detection scheme will be selected as a next-generation mobile communication system. However, the conventional V-BLAST detection scheme is based on the consecutive cancellation of interference and demonstrates good performance parameters while maintaining an acceptable calculation complexity. However the conventional OSIC method can not be used for adaptive modulation and coding (AMC). In this kind of system the ordering procedure has to take into account a difference between the layers in order to provide better performance.

SUMMARY OF THE INVENTION

Accordingly, the present invention has been designed to solve the above and other problems occurring in the prior art.

The present invention is provided a method for detecting and decoding a signal that can improve the reliability of a received signal by detecting the signal.

The present invention is provided a method for detecting and decoding a radio signal in a wireless multi-antenna system of transmitting/receiving (MIMO) using Orthogonal Frequency Division Multiplexing (OFDM) and adaptive modulation including the steps of receiving a signal by a pickup antennas; detecting symbols from the received signal; analyzing error symbols from the detected symbols; and recovering original data transmitted from the detected symbols, wherein step of the detecting symbols from the received signal further comprising; calculating a probability of an error symbol detection based on modulation type; and determining a layer ordering with a minimum error probability among the calculated probability.

Also, the present invention is provided a method for detecting and decoding a signal in wireless multi-antenna system of transmitting/receiving (MIMO) based on Orthogonal Frequency Multiplexing (OFDM) and adaptive modulation, comprising the steps of: receiving a signal by multiple pickup antennas; detecting symbols from the received signal; analyzing error symbolsing from the detected symbols; and recovering original data from the detected symbols, wherein step of the detecting symbols from the received signal further comprising; calculating mean square errors of error symbols based on modulation type; and determining a layer ordering with a minimum mean square error among the calculated mean square error.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a graphic of frequency of occurrence of erroneous bits (more often mentioned as BER - Bit Error Rate)

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in detail herein below with reference to the accompanying drawings.

Various approaches are known in this subject, which are supposed to overcome the number of problems described, to certain degree, in publications [1] - [5]. In particular, the currently widely used approach, known as MIMO V-BLAST (Vertical Bell Laboratories Layered Space Time), has demonstrated very high spectral efficiency [I].

The technical solution most similar to the claimed invention, is described in the published patent application KR N°2005-23795 (Publication info: KR20060102050-2006-09-27, see esp@cenet database - Worldwide) [2], and deals with the method comprising the procedure of decoding OSIC for MIMO-OFDM systems, (here OFDM means Orthogonal Frequency Division Multiplexing), and estimating probability of the soft output bit (soft output). This algorithm has also been described in [3]. At this, for consecutive detecting a symbol it was proposed to use a new equalization matrix based on MMSE (MMSE - Minimum Mean Square Error).

where

H - channel matrix dimension MxN,

H₁ - matrix, consisting of columns, corresponding to Tx streams, which have not been detected and excluded at the previous stages,

H,_, - matrix, consisting of columns, corresponding to the excluded streams,

* - complex (Ηermitian) conjugation

Q_e - covariance matrix of solution errors (detecting), computed by formula

a = — "- - ratio of the noise energy to the signal energy, where σ_n ²,σ] - cr noise variance and mean signal power value.

The elements of decision errors covariance matrix E[e_me^*|x_m,χJ corresponding to the conditional expectation value, indicate that errors e_m and e_n occur due to inaccurate decisions associated with x_m ≠ x_m and x_n ≠ x_n . Diagonal elements E[|eJ|² χJ of the decision error covariance matrix Q_e indicate a mean square error value of the detected symbol. It is assumed that non-diagonal elements E[e_me_π' x_m,x_n] have no correlation between errors, so form ≠ n , they are the same as E[e_m xj E[e^* xj .

The expectation value of the decision error E[e_m x_m] and the expectation value of the square of the decision error E[|e_mf *J is calculated on the basis of the decision error probability P_e , which, in turn, is determined by the hard decision x_m and noise variance σ_w ² , corresponding to that decision.

The noise variance for layer m, which is calculated at step i, is determined by formula:

j≠m (3) where g_m - is the column of matrix G , corresponding to decision with minimum covariance value at step i.

In the prototype the decision error probability is determined on the basis of the error probability P₇ between two neighboring points in the constellation of the OFDM symbol with the minimal distance d :

'■--it) ⁽⁴⁾ where

and σ² corresponds to the noise variation in an in-phase or quadrature direction. This criterion is not accurate as it does not consider the whole set of points in the constellation.

The ordering in the OSIC is performed on the basis of the estimated minimal variance of the decision error.

Although the assumption about uncorrelated decision errors in Q_e looks controversial as well as assumption about Gauss distribution of decision error probability, the simulation results show that the described algorithm is superior over the conventional OSIC.

However, the method does not provide for proper ordering in the procedure of the successive interference cancellation in case of transmitted layers having different modulation, like it happens in AMC mode, because for ordering it considers only the decision error variance (or decision noise), but does not consider different distances between the points of constellation, which happens in AMC mode.

The problem to be solved by the claimed invention consists in development of an improved detection method in a MIMO system, which could offer more accurate layer ordering based on the difference of their modulation, and also higher accuracy of OSIC algorithm while reducing the calculation complexity.

The technical result is achieved due to application of any of two variants of the claimed method of detecting and decoding a signal in a wireless multi-antenna system of transmitting/receiving (MIMO) using Orthogonal Frequency Division Multiplexing (OFDM) and adaptive modulation, which method, according to Variant I, comprises the steps of: receiving a signal by pickup antennas; analyzing errors, occurring at symbol detection, and detecting a symbol from the received signal; recovering original data transmitted from the detected symbol, wherein symbols are detected successively layer-by- layer using Ordered Successive Interference Cancellation (OSIC) method, wherein each symbol is detected by means of a MMSE-based equalization matrix (where MMSE is abbreviation of Minimum Mean Square Error)

where H - is matrix, consisting of columns, corresponding to Tx streams, which have not been detected and excluded at previous stages; ■" _/_i - matrix, consisting of columns, corresponding to excluded streams; * - complex (Ηermitian) conjugation; - detection error, arising because of wrong a = detecting of a symbol; Q. ^e - covariance matrix of detection errors e . - ratio of noise energy to energy of signal, and I - identity matrix, differing that type of modulation of a layer is considered in procedure of ordered consecutive cancellation of interference component (OSIC), for this purpose the probability k of wrong detection of symbol is estimated for each layer ^A , at that the estimation of error of decision (noise of MMSE decision) and the type of modulation are taken into consideration, then the layer ^m with minimal m = arg (min {ErrPA) probability of an error of detection ^ ' is chosen for decoding; elements ^^e< l ^x<] and ^l ^e/ U K] of matrix *^^β are calculated, and Log Likelihood Ratio (LLR) is calculated for generation of soft decision based on the equalized value ^{t ~ t} P _an(j dispersion of its complex noise w " " , using the formulas:

M,

E[e_t \ x_t] = ∑ P₁ W s₁ - S_,

where: ^k is one of the points of constellation of symbol OFDM, which is chosen as hard decision due to its minimal Euclidian distance to the decision X₁ and which should be eliminated from the decision, and corresponding column should be eliminated from the matrix H in accordance with OSIC procedure, P₁ - probability of symbol detection error, which is calculated in accordance with equations:

The method in Variant II includes the steps of: receiving a signal through multiple pickup antennas; analyzing errors arising during symbol detection, and detecting a symbol from the received signal; recovering original data transmitted from the detected symbol, wherein the symbols are detected step by step layer by layer using Ordered Successive Interference Cancellation (OSIC) method, and each symbol is detected using

MMSE-based equalization matrix

, where H₁ - is matrix consisting of columns, corresponding to Tx streams, which have not been detected and excluded (eliminated) at the previous stages;

-" _/-_l - matrix, consisting of columns corresponding to the excluded (eliminated) streams;

* - complex conjugation; - detection error, arising because of wrong

detecting of a symbol; Q ^e - covariance matrix of detection errors e ; ^{a =} ^ - ratio of noise energy to energy of signal, and I - identity matrix, differing in that the type of modulation of a layer is taken into consideration in the procedure of ordered consecutive cancellation of interference component (OSIC), for this puφose the error square ^k , which errors is the result of the wrong detection of symbol, is estimated for each layer ^ , at that the estimation of the decision error, i.e. noise of MMSE decision, and the type of modulation are taken into consideration, then the layer ^m with minimal average square of detection error m = arg(mm{MSE_k}) v *^{■ ;} ' is chosen for decoding; elements ^E[^e>

are calculated, and Log Likelihood Ratio (LLR) is calculated for generation of a soft decision based on the equalized value ' ' ^ and the dispersion of its complex noise σ = σ^Δ

, using the formulas:

i=\,i≠k

S_k where is one of the points of constellation of symbol OFDM, which is chosen as a hard decision due to its minimal Euclidian distance to decision x_t and which should be eliminated from decision, and corresponding column should be eliminated from matrix H in accordance with the OSIC procedure, P₁ - probability of erroneous detection, which is calculated in accordance with equations:

The detailed description of the proposed improvements is presented below accompanied by the graphic materials.

Fig. 1 shows the graphic of frequency of occurrence of erroneous bits (more often mentioned as BER - Bit Error Rate), showing an overall performance of system 3x3 MIMO-OFDM with decoder Viterbi.

Frequency of occurrence of erroneous bits depends on the ratio signal/noise. Three transmitting Tx antennas transmitted signals, using modulation modes (from 1-st to 3-rd): 16-QAM, 64-QAM, QPSK. Channel model corresponds to COST 207 RA-IO model described in [4].

On Fig. 1 the line with triangular markers corresponds to prototype [2], the line with cross markers corresponds to the first of the claimed methods, and the line with circle markers corresponds to the second of the claimed methods (see explanation details below). The graphic illustrates enhanced system performance due to implementation of the claimed new solution, and both new methods demonstrate rather similar performance.

The claimed variants of the method are carried out as follows.

Using the approach described in [2] the decision for the layer i is calculated, using the equation

X = _£,H x, + g,ϊlj,__ι + gn

= g,^h,^x, + ∑ £,^hΛ + &H. A, + 8,ⁿ (⁶)

= βx_t + w where index / corresponds to the strongest layer among layers i...N.

In the prototype, the strongest layer is defined as a layer, having the lowest decision noise, which is determined by the largest diagonal value in matrix GH . This method is correct in case of the same modulation on all transmitted layers. However in case of different modulation, as we have in AMC mode, another method should be applied.

In the current invention two variants of the new method of layer ordering are offered for solution of the problem. Distinction between these variants consists in that they are based on the analysis of different criteria of a choice of the optimum order of exception of layers, however both variants take into account the types of modulation which can be different in different transmitting layers.

First method calculates the probability of error symbol detection for each layer, and determines the strongest layer with the smallest error probability. In case of QAM (Quadrature Amplitude Modulation) modulation with equal probability of symbol transmission within a particular constellation, this probability is a function of the constellation type and the decision noise. For different QAM-modulations this probability is defined as:

ErrP_BPSK = (7)

ErrPr QAM-16 (9)

In the last equations βis Gauss probability function defined by (5), σ_v- complex noise amplitude. Note, that equations (7)-(10) refer to the equalized signal, while for each constellation the mean signal energy has different values, it is 1 for BPSK, 2 for QPSK, 10 for QAM-16, and 42 for QAM-64.

The second "method calculates the mean square error resulting from incorrect symbol detection, for each layer and determines the strongest layer with the smallest noise due to incorrect symbol detection.

MSE_BPSK

Note, that in both variants the probability of detection error or the mean square error, resulting from incorrect detection, can be easily computed for higher modulation levels using the same approach.

In (6) w represents noise consisting of 3 parts: interference from not eliminated layers, detection errors generated at the previous steps and pure noise. Because we assumed that all these parts are independent, we can calculate its variance in the same way as in formula (3).

After scaling for the purpose of receiving an unbiased decision x_ι = Ε_l /β = x_l + v (16) we get hard decision estimation for X₁ = s_k e M_s(mm(\\ x_t -s_k ||) based on minimum Euclidian distance between Jc, and the particular constellation point S₁ , and the unbiased complex noise variance σ²

.

Based on decision for x, and its variance estimation σ] we can calculate LLR for soft decision of the output bit:

and also determine the noise components K I ^X<J _an(j Ul ^e, Il I *J caused by incorrect decision choice.

For E[e, \ x_t] and E[\\ e, ||²| x,] calculation we offer the following procedure different from that of the prototype [2]: for each constellation point S₁ , an exponent part of the conditional probability density is determined:

for each constellation point ^S/ , where ' ^{~ 1} -^M " ' ^{≠ k} , which i is different from strict decision s_k , the decision error probability is calculated

where M. - the number of points in the constellation, based on calculated probability • the noise components caused by decision errors , is calculated

M,

FFe I x I - V P IU - ? Il i=\,ι≠k

£[lk ll²l *,] = ∑ P, \\ s, -s_k ι=\,ι≠k (20)

X = S where ^k - a strict decision based on minimum Euclidian distance between Jc, and s.

It is easy to see that LLR value in formula (17) and decision errors estimation in (20) depend only on two parameters: MMSE decision Jc, and its noise variance σ_v ². Thus the values for LLR, E[e_t \ x_t] and E[|| e, \\²\ χ,] can be stored in three dimension (3D) table (one dimension is added because Jc, is a complex value). Such approach allows to avoid complex calculations in (17) - (20), but the additional memory resource is required.

The proposed algorithm, as amended, allows to improve the accuracy of decision error estimation occurring because of incorrect symbol detection, which leads to better system performance. The last statement is illustrated by BΕR function on Fig. 1.

Another change concerns optimization of matrix G calculation, which should be done step by step for each layer.

Following the simplification, proposed in prototype [2], we neglect the off-diagonal elements Q_e . Then the matrix D = — Q, ^υi is diagonal. In any

case, D is positive definite. We shall rewrite the formula (1) as follows:

w

here This matrix can be efficiently updated from layer to layer. Indeed, assume Ψ = H'H + i.e.

the same matrix from the previous layer, be already computed. Then Ψ is a rank-one modification of Ψ _p , because the same is true for their inverses (see [5]), namely \-l

Ψ = (ψ_p-^ι +(ad_ι_;² -a)e_l__ie_ι_;j

The last formula, known as formula Sherman- Woodbury-Morrison, means that each column of Ψ can be computed as corresponding column of Ψ_p plus

(/- 1 )th column of Ψ_p scaled by a simple function of two entries of Ψ_p . In other words, update of Ψ elements can be done using small number of arithmetic operations independent of M and N, per one entry. Conventional computation using formula (1) directly corresponds to M operations per one entry of Ψ .

In formula (22) we had used the following notation: d_t__x and ψ_p ,_, ,_, are

(/- 1 )st diagonal elements of D and Ψ_p , respectively. M- vector with all zero components, except (i-l)th component equal to 1, is denoted by e,_, .

For example, in 2x2 case, the following computation formulas for calculation of G for the second layer of OSIC are used. Define:

Ψ = Φ-¹ = {H^*H ₊ OI_N )-\ ₍₂₃₎ at that this matrix anyway is computed for the first (previous) layer. Then:

.(24)

Here y/_{12 >}<Pw - elements of matrixes Ψ and Φ , G₂ corresponds to symbol determined on the second step.

In 2x2 case, this saves half of the scalar multiplications compared with the conventional inversion used in (1) according to prototype.

The proposed algorithm looks simple enough from the point of view of its calculation complexity, thus it can be implemented in future MIMO-OFDM systems.

References:

[I]. RW. Wolniansky, GJ. Foschini, GD. Golden, and R. A. Valenzuela, "V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel," in URSI International Symposium on Signals, Systems and Electronics, pp. 295-300, September [2]. "Method for Detecting and Decoding Signal in a MIMO Communication System», KR Patent application No. 2005-23795, filing date - March 22, 2005.

[3]. 'New Approach for coded layered space-time OFDM systems", Heunchul Lee, Inkyu Lee, 2005, ICC 2005 IEEE International Conference on Communications, Volume 1, 16-20 May 2005 Pages 608-612 Vol. 1.

[4]. Channel Models for Fixed Wireless Applications, IEEE 802.16.3c-01/29r4, 2001-07-17.

[5]. R. Horn, C. Johnson "Matrix Analysis", Cambridge University Press, 1985.

Claims

WHAT IS CLAIMED IS:

1. A method for detecting and decoding a radio signal in a wireless multi-antenna system of transmitting/receiving (MIMO) using Orthogonal Frequency Division Multiplexing (OFDM) and adaptive modulation, comprising the steps of: receiving a signal by a pickup antennas; detecting symbols from the received signal; analyzing error symbols from the detected symbols; and recovering original data transmitted from the detected symbols, wherein step of the detecting symbols from the received signal further comprising; calculating a probability of an error symbol detection based on modulation type; and determining a layer ordering with a minimum error probability among the calculated probability.

2. The method of claim 1, wherein the symbols are detected successively layer-by-layer using Ordered Successive Interference Cancellation (OSIC) method, wherein each symbol is detected using Minimum Mean Square Error (MMSE)-based equalization matrix

where H₁ - is matrix consisting of the columns corresponding to Tx streams, which have not been detected and eliminated at the previous stages; ** i-ι - matrix consisting of columns corresponding to the eliminated streams; * - complex conjugation; - detection error resulting from the wrong detecting a = of a symbo 1l;. Z ²^-'e^e - co variance matrix of detection errors ° ; ^σ' - ratio of noise energy to signal energy, and I - identity matrix, characterized in that the type of modulation of a layer is taken into consideration in the procedure of ordered consecutive cancellation of interference component (OSIC), for which purpose the probability * of wrong detection of symbol is estimated for each layer ^ , and the estimation of error of decision (noise of MMSE decision) and the type of modulation are taken into consideration, thereafter the layer ^m with minimal probability of an error of m = arg (min {ErrP_k }) detection ^v ' is chosen for decoding; the elements

E\^β, \ x,] _an(j £[lk ll | x,] of matrix ^^e are calculated, and Log Likelihood Ratio (LLR) is calculated to generate a soft decision based on the equalized value

2 2 'H ^Λ"²

' ' ^ and the dispersion of its complex noise " ^w "^{7^} " , using the formulas:

c where: is one of the points of constellation of symbol OFDM, which is chosen as a hard decision due to its minimal Euclidian distance to the decision X₁ and which should be eliminated from the decision, and the corresponding column should be eliminated from the matrix H in accordance with the OSIC procedure, P₁ - probability of symbol detection error, which is calculated in accordance with equations:

3. The method of claim 1, wherein the symbol is detected, using simplified MMSE matrix:

G = H^H₁H^* +aI_My v-l

4. The method of claim 1, wherein off-diagonal elements of matrix G are defined to be zero.

5. The method of claim 1, wherein the symbol is detected using matrix:

received by method of zero forcing.

6. The method of claim 4, wherein the successive calculation of the equalization matrix G is done for each layer using the optimization technique, namely: a part of G is updated using the formula of inverse additive modification of rank-one, namely Sherman- Woodbury-Morrison formula:

7. A method for detecting and decoding a signal in wireless multi-antenna system of transmitting/receiving (MIMO) based on Orthogonal Frequency Multiplexing (OFDM) and adaptive modulation, comprising the steps of: receiving a signal by multiple pickup antennas; detecting symbols from the received signal; analyzing error symbols from the detected symbols; and recovering original data from the detected symbols, wherein step of the detecting symbols from the received signal; calculating mean square errors of error symbols based on modulation type; and determining a layer ordering with a minimum mean square error among the calculated mean square error.

8. The method of claim 7, wherein the symbols are detected step-by-step and layer-by-layer using Ordered Successive Interference Cancellation (OSIC) method, and each symbol is detected using MMSE-based equalization matrix

, where H - is matrix consisting of columns, corresponding to Tx streams, which have not been detected and eliminated at the previous stages; -" M - matrix consisting of columns corresponding to the eliminated streams; * - complex conjugation; - detection error arising because of wrong detection of a symbol; Q ^e -

covariance matrix of detection errors ; ^σ- - ratio of noise energy to signal energy, and I - identity matrix, c h aracter i ze d i n th at the type of modulation of a layer is taken into consideration in the procedure of ordered consecutive cancellation of interference component (OSIC), for which purpose the error square ^k , which errors is the result of wrong detection of a symbol, is estimated for each layer ^ , and the estimation of error of decision, i.e. noise of MMSE decision, and the type of modulation are taken into consideration, then the layer ^m with minimal average square of detection error

and

£[lk Il I *,] of matrix *^^β are calculated, and Log Likelihood Ratio (LLR) is calculated for generation of a soft decision based on the equalized value

.2 2

' ' P and the dispersion of its complex noise " ^{w l|y}~ " , using the formulas:

Il²I I ^Λ xt i J = Z V-I p ' i Iil v / - v A iIiI² i=\,i≠k

S, where is one of the points of constellation of symbol OFDM, which is chosen as a hard decision due to its minimal Euclidian distance to the decision X₁ and which should be eliminated from the decision, and the corresponding column should be eliminated from the matrix H in accordance with the OSIC procedure, P₁ - probability of erroneous detection, which is calculated in accordance with equations:

9. The method of claim 8, wherein symbol is detected using the simplified

MMSE matrix: ^G = ^H< (^H>^H< ^{+ aI}" >^"' .

10. The method of claim 8, wherein the symbol is detected using matrix: N-I

received by method of zero forcing.

11. The method of claim 10, wherein the off-diagonal elements of matrix G are defined to be zero.

12. The method of claim 11, wherein the successive calculation of the equalization matrix G is done for each layer using the optimization technique, namely: a part of G is updated is updated using the formula of the inverse additive modification of rank-one, namely Sherman- Woodbury-Morrison formula: