KR101295131B1 - A time domain equalizing apparatus and method using the omp algorithm in ofdm systems - Google Patents

Abstract

Disclosed are a time domain equalization apparatus and method using an OMP algorithm in an OFDM system. According to the present invention, a pilot symbol included in a received orthogonal frequency division multiplexing (OFDM) signal is used to estimate a channel experienced by a received signal in a time domain through an orthogonal matching pursuit (OPM) algorithm and equalize the received signal. do. According to the present invention, by estimating the time varying channel from the pilot symbols included in the OFDM signal received through the OMP algorithm and equalizing the received signal, the channel estimation complexity is reduced, the influence of noise is reduced, The number of filters to be reduced can be reduced, and the accuracy of channel estimation can be improved to improve the bit error rate (BER) characteristic.

Description

A time domain equalizing apparatus and method using the OMP algorithm in OFDM systems

The present invention relates to an apparatus and method for time domain equalization using an OMP algorithm in an OFDM system, and more particularly, orthogonal matching using a pilot symbol included in a received orthogonal frequency division multiplexing (OFDM) signal. The present invention relates to an apparatus and method for estimating a channel experienced by a received signal in a time domain and equalizing the received signal through a pursuit algorithm.

Orthogonal frequency division multiplexing (OFDM) system transmits data by using a plurality of subcarriers, and the interval of subcarriers is narrowed to half of the symbol bandwidth, and the data symbols are loaded for each subcarrier and frequency It has the advantage of high efficiency and high speed transmission. In addition, by inserting a guard interval to maintain the orthogonality of the symbol by transmitting several symbols in one symbol block at this time, a strong advantage in multipath fading by inserting a guard interval longer than the maximum delay of the channel. There is this.

Next-generation mobile communication services using OFDM include long term evolution (LTE) and wires access in vehicular environments (WAVE). These services provide a wide coverage and high-bandwidth environment. In consideration of this, the symbol length is also getting longer for frequency efficiency. Due to these characteristics, the time-varying characteristics of the OFDM channel become stronger. Due to the influence of the time-varying channel, orthogonality is not maintained between OFDM subcarriers, resulting in inter channel interference (ICI) affecting adjacent subcarriers.

In such an environment, it is difficult to obtain good performance by a simple channel equalization method such as a frequency domain single tap equalizer by the zero forcing (ZF) method. Therefore, we use a time domain equalization method that can achieve higher channel resolution. One of the time-domain equalization methods is the LS (least squares) method, but this method has a problem in that the channel estimation error due to noise increases as the length of the channel increases.

KR 10-2005-0046209 (Samsung Electronics Co., Ltd., et al. 5) 2005. 5. 18. Patent Document 1 is a method of estimating time-varying channels in an orthogonal frequency division multiplexed transmission antenna system. The contents of equalization in the time domain are disclosed. KR 10-2010-0080667 (Seoul National University Industry-University Cooperation Group) 2010. 7. 12. Patent Document 2 is an apparatus and method for order channel estimation using grouping MS in Orthogonal Frequency Division Multiplexing based wireless communication system. The content equalization in the time domain by the least square method is disclosed.

SUMMARY OF THE INVENTION The present invention provides a time domain equalization using an OMP algorithm in an OFDM system that estimates a time varying channel and equalizes a received signal using a pilot symbol included in an OFDM signal received through an OMP algorithm. An apparatus and method are provided.

In the OFDM system according to the present invention for achieving the above technical problem, a time domain equalizer using an OMP algorithm receives an OFDM signal transmitted from an external device and separates a pilot symbol from the received OFDM signal. A signal receiving unit; And

A support, which is an index indicating a non-zero element position in a sparse channel vector, is selected and added to a support set, and a measurement matrix of a preset pilot symbol and the support set are provided. By estimating the original sparse time varying channel from the pilot symbols acquired through the signal receiver through the selection of the support, adding the support, and performing channel estimation repeatedly, the sparse time varying channel is obtained. And a channel estimator for estimating, and obtaining an inverse function of the estimated sparse time-varying channel to equalize the received OFDM signal.

According to an aspect of the present invention, there is provided a time domain equalization method using an OMP algorithm, the method including: receiving an OFDM signal transmitted from an external device; Separating pilot symbols from the received OFDM signal; Selecting a support that is an index indicating the position of a nonzero element in a sparse channel vector; Adding the selected support to a support set; Estimating a one sparse time-varying channel from a pilot matrix obtained from a measurement matrix of a preset pilot symbol and the OFDM signal received through the support set; Estimating a sparse time-varying channel by repeatedly performing the support selection step, the support addition step, and the channel estimation step; And equalizing the received OFDM signal by obtaining an inverse function of the estimated sparse time-varying channel.

According to an apparatus and method for time domain equalization using an OMP algorithm in an OFDM system according to the present invention, by estimating a time varying channel from a pilot symbol included in an OFDM signal received through an OMP algorithm and equalizing a received signal, The channel estimation complexity can be reduced, the effect of noise can be reduced, the number of filters required can be reduced, and the accuracy of channel estimation can be improved to improve the bit error rate (BER) characteristic.

1 is a block diagram illustrating a time domain equalizer according to a preferred embodiment of the present invention;
2 is a flowchart illustrating a time domain equalization method according to a preferred embodiment of the present invention, and
3 to 8 are graphs for explaining the performance of the channel estimation technique according to an embodiment of the present invention.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the time domain equalizer and method (hereinafter referred to as "time domain equalizer and method") using the OMP algorithm in the OFDM system according to the present invention.

1 is a block diagram illustrating a time domain equalizer according to a preferred embodiment of the present invention.

Referring to FIG. 1, the time domain equalization apparatus 100 receives an orthogonal frequency division multiplexing (OFDM) signal from the outside and estimates a channel experienced by the received signal from a pilot symbol of the received OFDM signal. Equalize the received signal. To this end, the time domain equalizer 100 includes a signal receiver 110 and a channel estimator 130.

Here, the channel experienced by the OFDM signal is a multipath fading channel, which has channel coefficient values in the entire frequency band in the frequency domain, but most of them are 0 in the time domain, and some have multipath. A sparse channel with coefficients only at delay.

The signal receiver 110 receives an OFDM signal transmitted from an external device (not shown). The signal receiver 110 separates a pilot symbol from the received signal to estimate the channel. For example, when the received signal is Fourier transformed in a base band, the received signal is converted into a plurality of symbols, and only a predetermined symbol may be selected to separate only a pilot symbol signal. .

The channel estimator 130 estimates a channel from the pilot symbol signal obtained through the signal receiver 110 using an orthogonal matching pursuit (OMP) algorithm and equalizes the received signal. Here, the channel estimator 130 repeatedly performs a support selection process, a support set update process, and a channel estimation process to estimate a sparse time varying channel. The channel estimator 130 obtains an inverse function of the estimated time varying channel and equalizes the received signal.

In more detail, the channel estimator 130 multiplies a residual matrix by a measuring matrix of a preset pilot symbol to support an index of a column having a largest correlation. support). Here, the row of the preset measuring matrix refers to the length of the channel vector. In addition, support refers to an index indicating a position of a non-zero element in a sparse channel vector. The residual refers to a result obtained by subtracting an estimated one sparse time varying channel from a pilot symbol acquired through the signal receiver 110. The channel estimator 130 adds the selected support to the support set. The channel estimator 130 estimates a one sparse time varying channel from a pilot symbol obtained through the signal receiver 110 through a measurement matrix and a support set. . The channel estimator 130 repeatedly performs such an operation and estimates a one sparse time varying channel from a pilot symbol acquired through the signal receiver 110.

Hereinafter, an OFDM system model and an OMP algorithm used in a time domain equalization process according to a preferred embodiment of the present invention will be described in detail.

1. OFDM System Model

개의 협대역 직교 부반송파로 분할하고, 각 부반송파에 정보를 실어서 동시에 전송하는 방식이다. OFDM 송신 신호는

번째 심벌 블록

를

-포인트 IFFT(inverse fast fourier transform)하여 전송한다. 여기서,

는

이다. 전송 신호는 인덱스

를 삭제한 형태로 다음의 [수학식 1]과 같이 나타낼 수 있다.OFDM transmission scheme reduces the overall bandwidth

It is divided into two narrowband orthogonal subcarriers, and the information is loaded on each subcarrier and transmitted simultaneously. OFDM transmission signal

First symbol block

To

-Transmit by inverse fast fourier transform (IFFT). here,

The

to be. Transmit signal index

In a deleted form as shown in Equation 1 below.

는

번째 심벌 블록의

번째 시간 영역 신호로 부반송파

개의 합으로 나타낼 수 있다. 또한, 전송 신호

는 파일럿 신호

와 데이터 신호

의 합으로 나타낼 수 있다.

는

번째 부반송파의 주파수 영역 신호로 파일럿이나 데이터가 들어간다. 그리고,

는 파일럿 신호의 위치를 나타내고,

는 데이터 신호의 위치를 나타낸다.Transmission signal

The

Of the first symbol block

Subcarrier as the first time-domain signal

It can be represented as the sum of two dogs. In addition, the transmission signal

Pilot signal

And data signal

As shown in FIG.

The

The pilot or data is entered into the frequency domain signal of the first subcarrier. And,

Indicates the position of the pilot signal,

Indicates the position of the data signal.

The channel estimation may be performed using a pilot signal, and the received pilot signal may be expressed as in Equation 2 below.

는

개의 다중 경로 채널을 통과한 수신 파일럿 신호를 나타낸다.

는 채널의

번째 복소 이득을 나타낸다.

는 백색 잡음을 나타낸다.here,

The

Receive pilot signals through two multipath channels are shown.

Of the channel

Second complex gain.

Indicates white noise.

If Equation 2 is expressed as a determinant, Equation 3 is as follows.

Assuming that the channel is invariant for one symbol block, the OFDM received signal may be Fourier transformed and expressed in the following equations in Equation 4 and Equation 5 in the frequency domain.

번째 부반송파가 파일럿 신호라면 채널 응답

는 다음의 [수학식 6]에 의해 추정할 수 있다.In the signal model of Equation 4

Channel response if the first subcarrier is a pilot signal

Can be estimated by the following Equation 6.

2. OMP algorithm

Compressive sensing (CS) algorithms can fully recover the original signal even if the signal is sparse, even at signals measured below the Nyquist rate. This is done by finding solutions in underdetermined linear equations. A sparse signal is a signal in which most of the signals have zero or relatively very small values. At this time, a signal which becomes mostly 0 through a linear transformation is also included in a sparse signal.

는 제외하고 파일럿 신호만으로 표현하면 다음의 [수학식 7]과 같다.The OFDM channel also has a value in the frequency domain, but can be said to be sparse in the time domain. Noise in Frequency Domain Signal of Equation 5 above

When expressed as a pilot signal only except for the following equation (7).

는

행렬을 나타낸다.

는

DFT 행렬을 나타낸다.here,

The

Matrix.

The

Represents a DFT matrix.

-최소화 방법은 과소 결정된 방정식에서는 유일해를 가지지 않고 무수히 많은 해를 찾는 방법이다.

-최소화 방법은 0이 아닌 부분만 찾는 방법이지만 모든 경우의 수를 찾는 NP-hard 문제이다.

-최소화 방법은 모든 원소 절대값의 합을 최소화하는 방법으로

개 정도의 측정값으로 스파스(sparse) 신호를 높은 확률로 복원할 수 있다. 위의 [수학식 7]의 선형 행렬

를

-최소화 방법으로 해를 구할 수 있는 지는 다음의 [수학식 8]과 같은 제한 합동 변환 특성(restricted isometry property : RIP) 조건을 만족하는 지로 확인할 수 있다.The compression-sensing algorithm can solve the underdetermined linear equations because it finds only the non-zero part of the sparse signal.

Minimization is a method of finding a myriad of solutions without having a unique solution in an underestimated equation.

-Minimization method finds only non-zero part but NP-hard problem finding number of all cases.

Minimize is a method that minimizes the sum of the absolute values of all elements.

With about a few measurements, the sparse signal can be recovered with high probability. Linear matrix of Equation 7 above

To

-Whether the solution can be obtained by the minimization method can be confirmed by satisfying the conditions of the restricted isometry property (RIP) as shown in [Equation 8].

는 제한 합동 변환 특성(RIP) 상수를 나타내고, 0에 가까울수록 의미가 있다. 그러나 모든 스파스(sparse) 신호에 대해 제한 합동 변환 특성(RIP) 조건을 확인하는 것은 NP-hard한 문제이기 때문에 사전에 선형 행렬

가 좋은 행렬인지 판단하는 방법으로는 적절하지 않다.here,

Represents the limiting joint transformation characteristic (RIP) constant, the closer to 0 is significant. However, it is a NP-hard problem to check the RIP condition for all sparse signals, so it is a linear matrix in advance.

It is not a suitable way to determine if is a good matrix.

에서 열(column) 간의 상호관계를 조사하여 판단할 수 있다. 선형 행렬 의 열(column)을

라 하고, 이들이 각각 정규화되어 있으면 최대 상호 상관은 다음의 [수학식 9]와 같다.Linear matrix in a more realistic way

This can be determined by examining the interrelationships between columns. Linear matrix Column of

If they are normalized, the maximum cross correlation is as shown in Equation 9 below.

-최소화와

-최소화가 같은 유일해를 가지게 되는 조건은 다음의 [수학식 10]과 같다.By using the cross-correlation value according to [Equation 9]

Minimize and

-The condition that minimizes the same solution is as shown in [Equation 10].

를

-최소화 방법으로 풀어보면 다음의 [수학식 11]과 같다.Next, the measurement signal with noise

To

-When solved by the method of minimization is as shown in [Equation 11].

는

보다 크거나 같다.here,

The

Is greater than or equal to

-최소화 문제를 선형 문제로 변환하여 풀면 계산 복잡도가 대략

에 해당하는 많은 연산을 필요로 한다. 이에 따라 본 발명에서는 계산량을 줄이기 위해 OMP 알고리즘을 이용하여 채널을 추정한다. OMP 알고리즘을 이용하여 채널을 추정하는 과정을 정리하면 다음의 [표 1]과 같다.Equation 11

Solve by minimizing and minimizing a problem into a linear problem.

It requires a lot of operations. Accordingly, in the present invention, the channel is estimated using the OMP algorithm to reduce the amount of computation. The process of estimating the channel using the OMP algorithm is summarized in the following [Table 1].

,

,

input :

,

,

Print :

,

And

repeat

until

는 수신된 신호에 포함된 파일럿 심벌(pilot symbol)을 나타낸다.

는 기 설정된 파일럿 심벌을 FT(Fourier transform)하여 획득된 측정 행렬(sensing matrix)을 나타낸다.

는 에러(error)를 나타낸다.

는 선택된 인덱스들을 원소로 하는 서포트 집합을 나타낸다.

는 추정된 시변 채널(time varying channel)을 나타내다.here,

Denotes a pilot symbol included in the received signal.

Denotes a measurement matrix obtained by Fourier transform (FT) a preset pilot symbol.

Indicates an error.

Indicates a support set whose elements are the selected indices.

Denotes an estimated time varying channel.

를 공집합으로 두고, 잔차(residual) 벡터

을 수신된 신호에 포함된 파일럿 심벌

로 한다. 그 다음으로 상관 관계를 확인하는 단계는

의 값을 구하고 가장 큰 값의 인덱스를 서포트 집합

에 추가한다. 마지막으로 업데이트 단계는

로 새로운 시변 채널(time varying channel)

을 구하고 잔차(residual) 벡터

을

로 갱신한다.The OMP algorithm is a greedy algorithm that repeats the process of finding solutions from highly correlated elements in three steps. Initialization phase is support set

With the empty set, the residual vector

The pilot symbol included in the received signal

. The next step is to check the correlation

Find the value of and support the index of the largest value.

Add to Finally, the update phase

New time varying channel

Find the Residual Vector

of

Update to.

The OMP algorithm repeats the checking and updating steps until the end condition is satisfied. At this time, the termination condition of the OMP algorithm should be a condition that can find the sparsity of the channel. When the termination condition is obtained from the residual vector obtained for each iteration in the OMP algorithm, the following Equation 12 is obtained.

에서는 잡음이 남게 된다. 따라서 종료 조건은

로 하고 잡음은 가우시안 분포를 가지고 있으므로

은 실험적으로 구해진 5.43으로 설정한다.If channel estimation is correct

Will leave noise. Therefore, the termination condition

And the noise has a Gaussian distribution

Is set to 5.43 obtained experimentally.

2 is a flowchart illustrating a time domain equalization method according to a preferred embodiment of the present invention.

The time domain equalizer 100 receives an OFDM signal transmitted from an external device (S210), and separates a pilot symbol from the received OFDM signal (S220). Then, the time domain equalizer 100 selects the support (S230), adds the selected support to the support set (S240), and includes the signal received through the measurement matrix and the support set. A one sparse time varying channel is estimated from the pilot symbol (S250). In this case, the time domain equalizer 100 measures residuals and measurements indicating a result of subtracting an estimated one sparse time varying channel from a pilot symbol included in a received signal. The index with the largest correlation is selected as the support by multiplying the sensing matrix.

The time domain equalization apparatus 100 repeatedly performs a support selection step, a support addition step, and a channel estimation step to estimate a one sparse time-varying channel corresponding to a pilot symbol included in the received signal (S260). Thereafter, the time domain equalizer 100 equalizes the OFDM received signal by obtaining an inverse function of the estimated channel (S270).

3 to 8 are graphs for explaining the performance of the channel estimation technique according to an embodiment of the present invention.

In order to test the performance of the channel estimation scheme according to the present invention, a symbol error rate (SER) is compared with a time domain equalization method using a conventional LS (least squares) technique.

의 지연을 갖는 2-path 채널과

의 지연을 갖는 6-path의 다중 경로 채널을 이용한다. 이때, 도플러 주파수는 10Hz, 100Hz, 1kHZ로 하여 각 채널에서 실험한다.In the performance experiment, a 64-QAM OFDM system with 256 subcarriers is used. The bandwidth of the signal is 10 MHz and the carrier frequency is 5.9 GHz. In addition, there are 32 pilots in which 64 pilot intervals and 8 subcarriers are arranged for pilots. Channel estimation is made up to a 32 sample delay. The channel we used for the performance experiment

2-path channel with a delay of

Use a 6-path multipath channel with a delay of. At this time, the Doppler frequency is 10Hz, 100Hz, 1kHZ experiments in each channel.

3 is a graph illustrating a result of experimenting with a symbol error rate when the Doppler frequency is 10 Hz in the 2-path channel, and FIG. 4 is a graph showing a result of experimenting with a symbol error rate when the Doppler frequency is 100 Hz in the 2-path Channel. 5 is a graph illustrating a result of experimenting with a symbol error rate when the Doppler frequency is 1 kHz in a 2-path channel. Here, the horizontal axis represents the signal to noise ratio (SNR), and the vertical axis represents the symbol error rate (SER). In addition, the line ① represents the test result of the channel estimation according to the conventional LS (least squares) technique, and the line ② represents the test result of the channel estimation according to the present invention.

정도로 가장 낮은 심벌 에러율(SER)이 나오는 것을 확인할 수 있다. 이와 같이, 본 발명에 따른 채널 추정이 종래의 방법에 의한 채널 추정보다 성능이 향상됨을 알 수 있다.Referring to FIG. 3, when the signal-to-noise ratio (SNR) is 15 dB to 35 dB, it can be confirmed that the present invention is about 3 dB superior to the conventional method. In addition, when the signal-to-noise ratio (SNR) is 36 dB, the present invention

It can be seen that the lowest symbol error rate (SER) is obtained. As such, it can be seen that the channel estimation according to the present invention improves performance over the channel estimation by the conventional method.

FIG. 6 is a graph illustrating a result of experimenting with a symbol error rate when the Doppler frequency is 10 Hz in a 6-path channel, and FIG. 7 is a graph showing a result of experimenting with a symbol error rate when the Doppler frequency is 100 Hz in a 6-path Channel. 8 is a graph illustrating a result of experimenting with a symbol error rate when the Doppler frequency is 1 kHz in a 6-path channel. Here, the horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the symbol error rate (SER). In addition, the line ① represents the test result of the channel estimation according to the conventional LS (least squares) technique, and the line ② represents the test result of the channel estimation according to the present invention.

6 to 8, it can be seen that even in a multipath channel, channel estimation according to the present invention improves performance over channel estimation by a conventional method.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, It will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the appended claims.

100: time domain equalizer, 110: signal receiver,
130: channel estimation unit

Claims (4)

A signal receiver which receives an OFDM signal transmitted from an external device and separates a pilot symbol from the received OFDM signal; And
A support, which is an index indicating a non-zero element position in a sparse channel vector, is selected and added to a support set, and a measurement matrix of a preset pilot symbol and the support set are provided. By estimating the original sparse time varying channel from the pilot symbols acquired through the signal receiver through the selection of the support, adding the support, and performing channel estimation repeatedly, the sparse time varying channel is obtained. And a channel estimator for estimating, and obtaining an inverse function of the estimated sparse time-varying channel to equalize the received OFDM signal. The method of claim 1,
The channel estimator multiplies the residual matrix representing the result of subtracting the estimated one sparse time-varying channel from the pilot symbol acquired through the signal receiver and the measurement matrix, thereby supporting the index having the largest correlation. The time domain equalizer using the OMP algorithm in an OFDM system, characterized in that the selection. Receiving an OFDM signal transmitted from an external device;
Separating pilot symbols from the received OFDM signal;
Selecting a support that is an index indicating the position of a nonzero element in a sparse channel vector;
Adding the selected support to a support set;
Estimating a one sparse time-varying channel from a pilot matrix obtained from a measurement matrix of a preset pilot symbol and the OFDM signal received through the support set;
Estimating a sparse time-varying channel by repeatedly performing the support selection step, the support addition step, and the channel estimation step; And
Equalizing the received OFDM signal by obtaining an inverse function of the estimated sparse time-varying channel. The method of claim 3,
Selecting an index having the largest correlation by multiplying the measurement matrix by a residual representing a result of subtracting the estimated one sparse time-varying channel from the pilot symbol obtained from the OFDM signal received in the support selection step; A time domain equalization method using OMP algorithm in an OFDM system.

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