KR20050046209A - A method for a channel estimation at a time-varying channel in an ofdm system with multiple transmit antennas - Google Patents

Abstract

The present invention relates to a channel estimation method in a time-varying channel in an orthogonal frequency division multiplex (OFDM) system using multiple transmit antennas and deploying pilots in a comb manner. In the OFDM method according to the present invention, a channel estimation method of a time-varying channel in a OFDM system generates a pilot symbol in a comb-type in which a pilot is inserted into a specific subcarrier at a predetermined interval in each OFDM symbol. Doing; b) transmitting a pilot symbol generated in a comb manner from a transmitter to a receiver through a time-varying channel using at least two or more multiple transmit antennas; c) receiving a signal transmitted through a multiple transmit antenna via a time varying channel; And d) estimating the channel in an interpolation manner using time correlation of time-varying channels. According to the present invention, the channel is estimated using time correlation of the channel, and the channel is estimated in consideration of the time variability of the channel, thereby enabling more accurate channel estimation compared to the general channel estimation method. In addition, as in the conventional channel estimation method, the complexity is reduced by estimating a channel for each subcarrier where a pilot is located.

Description

A method for a channel estimation at a time-varying channel in an OFDM system with multiple transmit antennas}

The present invention relates to a channel estimation method of a time-varying channel in an orthogonal frequency division multiplexing system. More specifically, an orthogonal frequency division multiplex (OFDM) system using multiple transmission antennas and arranging pilots in a comb manner ) Is a channel estimation method in a time-varying channel in a system.

When a signal is transmitted through a multipath channel, an inter-symbol interference ("ISI") is generated in the received signal by the multipath. In particular, in the case of high-speed data transmission, since the period of the symbol is smaller than the delay spread of the channel, the ISI becomes more severe, and a complex reception technique is required to compensate for the distortion caused by the ISI and accurately recover the transmission signal. In order to reduce the signal distortion caused by the ISI, the period of the symbol should be larger than the delay spread of the channel. Orthogonal Frequency Division Multiplexing (OFDM) has been proposed as a modulation scheme that can easily compensate for distortion in such a multipath channel. Unlike the transmission method using a single carrier, the OFDM method transmits data using a plurality of subcarriers having mutual orthogonality. That is, the OFDM scheme performs serial and parallel conversion on the input data by the number of subcarriers used for modulation, and modulates the converted data using the corresponding subcarriers to maintain the data rate while maintaining the symbol period in each subcarrier. Lengthens the number of subcarriers. Since subcarriers with mutual orthogonality are used, bandwidth efficiency is better than that of conventional frequency division multiplex (FDM), and symbol periods are lengthened.

In the OFDM system, modulation and demodulation processes of the transmitter and the receiver are performed by performing an Inverse Discrete Fourier Transform (IDFT) and a Discrete Fourier Transform (DFT), respectively. This is called an Inverse Fast Fourier Transform (IFFT) and Fast Fourier Transform (FFT). Can be implemented efficiently. In addition, if a guard interval longer than the delay spread of the channel is inserted for each transmitted symbol period, orthogonality between subcarriers is maintained, thereby preventing inter-carrier interference (ICI) from occurring. OFDM symbols are not overlapped so that ISI between adjacent symbols can be completely removed.

In addition, the OFDM transmission scheme has received much attention in the field of wireless communication systems because it is strong in multipath fading channels and has high bandwidth efficiency. IEEE 802.11a (United States) and ETSI HIPERLAN / 2 (Europe), which are WLAN standards using OFDM, have a transmission rate of up to 54 Mbps, which is digital audio broadcasting (DAB) and digital television broadcasting (DVB). It is applied to multimedia applications as well as high-speed Internet and intranet connections such as asymmetric digital subscriber lines (ADSL). In the near future, increasing the system transfer rate is inevitable in many applications. Recently, as a method for increasing the transmission rate, studies to maximize the capacity by using multiple transmit / receive antennas have been actively conducted.

Hereinafter, with reference to the accompanying drawings, a configuration and channel estimation method of a transmission and reception system of another OFDM system according to the prior art.

1 is a block diagram showing a configuration of a transmission / reception system of a general orthogonal frequency division multiplexing (OFDM)

The general OFDM transmission / reception system includes a signal mapping unit 21, a serial / parallel conversion unit 22, an inverse fast Fourier transform (IFFT) unit 23, a pilot insertion unit 24, a bottle / Serial converter 25, Rayleigh fading channel application unit 26, summer 27, serial / parallel converter 28, pilot remover 29, channel estimator 30, fast Fourier transform ( FFT) section 31, channel equalizer 32, parallel / serial converter 33, baseband demodulator 34.

First, when a binary source occurs, the signal mapping unit 21 of the transmitting side maps the data to be transmitted according to a modulation method, that is, a binary source, by using a normal QAM method, and mainly QPSK (Qualternary Phase Shift Keying), 16-QAM, 64 Use a modulation scheme such as QAM.

The data mapped by the signal mapping unit 21 is converted in parallel by the serial / parallel conversion unit 22 and inversely Fourier transformed by the inverse fast Fourier transform unit 23, and the pilot is inserted by the pilot insertion unit 24. After being inserted, it is converted into a serial form and output again to be transmitted from the parallel / serial converter 25. In this case, the transmitting side of the OFDM system inserts and transmits a pilot signal, which is a value known to the receiving side, between data to be transmitted in order to assist the demodulation of the receiving side.

Next, the data output in the serial form through the parallel / serial converter 25 are summed together with the noise in the summer 27 through the Rayleigh fading channel application unit 26 and the serial / parallel converter 28 Is sent).

Next, the pilot signal is removed from the pilot eliminator 29, and the channel estimator 30 removes the signal from the OFDM signal by using the pilot signal. Find the estimated value.

The signal output from the channel estimator 30 is input to the fast Fourier transform unit 31, Fourier transformed, and then transmitted to the channel equalizer 32. The channel equalizer 32 compensates for channel distortion due to non-ideal characteristics of the channel, that is, various noises, interference with adjacent channels, and multipath.

In this way, the signal passing through the channel equalizer 32 is converted into serial form again by the parallel / serial converter 33 and output as an output signal via the baseband demodulator 34.

On the other hand, in broadband mobile communication systems, radio channels are frequency selective and time varying. This indicates that the channel in the OFDM system is not the same on both the frequency axis and the time axis. In addition, when using multiple transmit antennas, received symbols in each subcarrier come in superimposed after the symbols transmitted from the multiple transmit antennas undergo fading independently. Therefore, in a mobile OFDM communication system using multiple transmit antennas, the channel is frequency selective and time-varying, so effective channel estimation is needed before demodulating OFDM symbols. In such an OFDM system, channel estimation is typically performed by inserting a pilot into a subcarrier already known in the time and frequency axis grids.

There are two ways to insert such pilots, block-type and comb-type. The block scheme refers to a scheme in which a pilot is inserted into all subcarriers of a specific OFDM symbol and the symbols are periodically repeated. In the block method, since the pilot is included in all subcarriers, it is relatively strong in the frequency selective characteristic of the channel, and is suitable for a slow channel change (slow-fading channel) in time, and does not require interpolation in the frequency domain. It is known to have a pilot symbol placement scheme that is relatively strong against selective fading.

In addition, the comb method refers to a method of inserting a pilot in a specific subcarrier at regular intervals in every OFDM symbol, and is known as a pilot symbol placement method that is stronger in fading than the block method. However, since the pilot symbols are inserted at regular intervals, the gain of the carrier must be estimated using the pilot symbols for each OFDM symbol.

Assuming that the ratio of data and pilot in the two schemes is the same, the comb scheme has a high retransmission rate. The comb method is therefore better suited for fast-fading channels.

In addition, the OFDM is a multi-carrier transmission scheme using a plurality of carriers, the signal transmission period is increased in proportion to the number of carriers. In this case, inter-symbol interference caused by the frequency selective channel generated in the high-speed data transmission can be eliminated, and as a result, it can be processed by approximating to the frequency non-selective channel. Referring to FIG. 1 again, such multi-channel signal processing may be implemented at high speed by using an inverse fast fourier transform (IFFT) at a transmitter and an FFT at a receiver.

FIG. 2 is a schematic block diagram of a mobile OFDM system using a general multiplexed transmission antenna, and FIG. 3 is a pilot comb-type pilot layout.

As shown in FIG. 2, in a mobile OFDM system using a general multiplexed antenna, the pilot symbols 1a and 1b of the first and second transmitters Tx # 1 and Tx # 2 are respectively the first and the second. After the inverse Fourier transform through the inverse fast Fourier transformers (IFFT: 3a, 3b), they are transmitted through the multiple transmit antennas (5a, 5b) of the transmitter, respectively. In addition, the signal received through the multiple transmit antenna 7 of the receiving end is Fourier transformed Fast Fourier Transformer (FFT) 9, wherein the pilot symbol 11 of the receiving end is removed through a pilot canceller to use the pilot signal. The channel estimator obtains a channel estimate from the OFDM signal. A detailed method of estimating the channel will be described later.

Referring to FIG. 3, a general comb-type pilot is configured to insert a pilot in a specific subcarrier at regular intervals in every OFDM symbol.

Meanwhile, channel estimation methods using the block and comb methods include methods of applying a least square ("LS") and a minimum mean-square error (MMSE). The LS method does not need advance information on channel and noise and has a low complexity.

The OFDM signal transmission is performed in symbol units, and intersymbol interference occurs during the multipath radio channel. In order to prevent such inter-symbol interference, a guard interval is inserted between the symbols. That is, the interference between signals is prevented by providing a guard period longer than the maximum delay time of the channel. When the last part of the symbol is copied and inserted into the guard interval, it is called Cyclic Prefix. This prevents the destruction of orthogonality due to signal delay.

In the OFDM scheme, since each subchannel is approximated as a frequency non-selective fading channel, the equalizer in each subchannel is in the form of a single tap, and the equalizer coefficients are inverses of the estimated subchannel. Channel estimation is needed. The channel estimator can be derived by applying least square (LS) or minimum mean-square error (MMSE) criterion in the frequency domain. The LS channel estimator is simple in structure but does not reflect the statistical characteristics of the channel. Since it is not used, it is sensitive to noise. The MMSE channel estimator uses the second order moments of the channel, such as autocorrelation and cross-correlation, so that the computational increase is significantly higher than that of the LS estimator, but the overall estimation error considering noise is minimized, so that for fading channels with severe nulls Excellent performance.

Channel estimation in the OFDM scheme can be largely classified into pilot-symbol-aided (PSA) channel estimation and decision-directed (DD) channel estimation according to the type of data used for channel estimation. have. The PSA technique is suitable for fast fading channels, where pilots are placed in consideration of the channel's coherence bandwidth, coherence time, and bandwidth efficiency reduction due to the use of pilot tones. Since the DD technique estimates the channel of the next symbol period using the detection data, it is suitable for a slow fading channel having a high fixed or time correlation.

Hereinafter, a general channel estimation method using the LS method in a mobile OFDM system using a multiplexed antenna using the above-described comb method will be described.

For convenience, a case of using two transmission antennas will be described. It is apparent to those skilled in the art that this can be easily extended for the case of using more transmit antennas.

First, the frequency axis signal received at the p-th subcarrier containing the pilot at the nth time. Is expressed as

here, Is the frequency axis pilot transmitted from the m th antenna, the p th subcarrier at the n th time, Is the corresponding frequency axis channel value, Is 0 and the variance is White Gaussian additive noise, Is , Is to be. Also, Represents a transpose.

In order to express the number of pilots contained in one OFDM symbol as P, and to use the minimum pilot required for channel estimation, this is the smallest multiple of 2 larger than L (the maximum length of the channel). P pilots are inserted at equal intervals between subcarriers within a symbol, and their positions are Set to.

According to Equation 1, the necessary and sufficient conditions for LS channel estimation are to be. To satisfy this, a pilot of the (n + 1) th symbols is required. But required by the corresponding channel Increases to 4 After all, necessary To fix the following assumptions,

here, Is the channel of the n th time corresponding to the m th transmit antenna. Therefore, Equation 1 may be expressed as follows.

here, Is , Is , Is And

to be.

therefore, The least squares (LS) estimation of is performed as follows.

here, Denotes a pseudo inverse matrix. It is expressed by Equation 5 by Equations 3 and 4.

Since is unbiased, the least squares error (MSE) of channel estimation is

here Is the probability, Indicates a trace. Meanwhile, pilots of different transmit antennas must be orthogonal to obtain the minimum MSE of LS channel estimation. Thus, as an easy example, the pilot is designed as follows.

However, according to the assumption of Equation 2, a change in a channel within two OFDM symbol periods causes a performance decrease due to channel estimation. In other words, when the Doppler frequency is high, there is a problem that sufficient accuracy in channel estimation cannot be guaranteed.

Meanwhile, in June 2003, I. Barhumi et al. The article was published in the title of "Optimal training design for MIMO OFDM systems in mobile wireless channels" in Volume 51, No. 6, 1615-1624, of On Signal Processing.

In the paper of I. Barhumi et al., A channel estimation mean square error (MSE) is calculated in an orthogonal frequency division multiplexing (OFDM) system using multiple transmission antennas having a block-type pilot pattern or a comb-based pilot pattern. This is a paper on the design of pilot for channel estimation in order to minimize. To this end, the number of pilot subcarriers required for channel estimation is required by (transmission antenna × channel length = P). In order to minimize the channel estimation MSE, two conditions must be satisfied by the equation derived from the above paper.

In the first condition, pilots should be arranged at equal intervals within one OFDM symbol. The second condition is that the pilot signal of any reference transmit antenna and the other transmit antenna pilot signals must be orthogonal, as well as the signal delayed by the channel of this antenna must be orthogonal to the other antenna signals (phase shift orthogonal). . In other words, a signal that is cyclically shifted (range: channel length) of another antenna signal on the time axis should also be orthogonal to the reference antenna signal.

If the two conditions are satisfied, the MSE of channel estimation can be minimized. However, the scheme is designed on the premise that the number of pilot subcarriers required for channel estimation, that is, the channel is constant during P. In other words, in the case of a system having a block-type pilot pattern, the total number of subcarriers should be greater than P, and the accuracy of channel estimation is clearly deteriorated when the channel is time-varying for data symbols following the pilot symbol. In addition, to track a channel, a complicated equalizer using various algorithms is accompanied. In addition, in the case of a system having a comb-based pilot pattern, if a minimum pilot subcarrier (channel length) is used for one symbol to reduce the pilot load, the premise that the channel does not change for as many symbols as the number of transmit antennas is required. Do. Therefore, when the channel is time-varying, there is a problem that the accuracy of channel estimation is similarly degraded.

An object of the present invention for solving the above problems is to provide a more accurate channel estimation method using the time correlation of time-varying channels in an orthogonal frequency division multiplexing system (OFDM) using multiple transmit antennas and pilot placement in a comb method It is for.

In addition, another object of the present invention for solving the above problems is to provide a channel estimation method of a time-varying channel in which the increase in complexity is reduced by estimating the channel by a linear interpolation method for each subcarrier where a pilot is located in an orthogonal frequency division multiplexing system. will be.

As a means for achieving the above object, the channel estimation method of a time-varying channel in an orthogonal frequency division multiplexing system (OFDM) according to the present invention, a) a comb method of inserting a pilot to a specific subcarrier at regular intervals in each OFDM symbol ( comb-type) to generate a pilot symbol; b) transmitting the pilot symbol generated by the comb method to a receiving end through a time-varying channel using at least two or more multiple transmitting antennas; c) receiving a signal transmitted through the multiple transmit antenna via the time-varying channel; And d) estimating a first channel of the time-varying channel in an interpolation scheme using a time correlation between a second channel and a third channel.

Here, the time-varying channel is characterized in that the channel is estimated in a Least Square (LS) method.

Here, the interpolation method is preferably a linear interpolation method.

In addition, when the pilot is designed using the time correlation of the channel, it is designed to satisfy the required rank for the multi-channel estimation in each symbol period in order to reduce the performance decrease over time of the channel. It features.

In addition, when two antennas are used as the multiplex antennas, a frequency axis signal transmitted by a pth subcarrier containing a pilot at an nth time is used. Is expressed as in Equation 8.

, Where Is , The frequency axis channel value ( ) , And additional noise ( )silver In this case, the channel of the n + 1 th time corresponding to the m th transmit antenna And channel at n + 2th time Is nth And n + 3th When the linear interpolation channel estimation method is used as the time correlation, it can be expressed as Equation (9).

Is the frequency axis pilot transmitted from the mth antenna and the pth subcarrier at the nth time,

It is characterized by designing a pilot to be.

Therefore, according to the present invention, the channel estimation is performed using the time correlation of the channel, so that the channel estimation is possible more accurately than the general channel estimation method. By estimating the channel for each subcarrier, the increase in complexity is reduced.

Hereinafter, a channel estimation method of a time-varying channel in an orthogonal frequency division multiplexing system according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

As described above, in the case of using a coarse pilot arrangement, a channel estimation at the receiving end generally requires as many symbols as the number of transmit antennas in time and requires the assumption that the channel does not change during that time. It is difficult to apply the channel estimation method. In addition, as described above, in order to estimate the multi-channel of the n-th symbol period according to the multiple transmit antennas, pilot for two symbol periods is required.

In order to reduce the performance decrease due to the channel change, channel estimation is required in each symbol period. Accordingly, in order to reduce the influence of Doppler while satisfying a rank required for multi-channel estimation, the channel correlation is used. Referring to FIG. 4, a channel estimation method in a time-varying channel will be described in detail.

FIG. 4 is a diagram illustrating a channel estimation method in a time-varying channel in an OFDM system using a multiple transmit antenna and arranging pilots in a comb manner according to the present invention. Reference numerals 13a, 13b, 13c, and 13d of FIG. 4 denote symbols in which pilots are inserted in a comb manner for each symbol period, and shaded portions indicate pilots are inserted.

4, in the case of using two transmit antennas according to an embodiment of the present invention, and of Wow Is represented by the time correlation of. That is, the channel of the n + 1 th time corresponding to the m th transmit antenna according to the linear interpolation method And channel at n + 2th time Is the nth And n + 3th It can be expressed as a time correlation.

When the linear interpolation method is used, this is expressed as follows (see FIG. 4).

Here, using more sophisticated interpolation methods, such as high-dimensional polynomial interpolation, allows more accurate channel estimation but increases complexity. On the other hand, Equation 8 is

here, Is , The frequency axis channel value ( ) , And additional noise ( )silver , And

Therefore, by the LS method, the multiple channels are estimated as follows.

finally, Can be designed as follows.

Although the above embodiment illustrates the case of using two transmit antennas, it is apparent to those skilled in the art that the channel can be easily estimated even in the case of two or more transmit antennas.

On the other hand, computer simulation was performed to prove the efficiency of the channel estimation method according to the present invention. The simulation environment is as follows. L = 8, iid (independent identically distributed), and the correlation in time is Jakes' model Follow. In the OFDM system, the number of subcarriers in one symbol is 64 and the length of the guard interval is 16. P is set to 8 to satisfy the minimum number of pilots for channel estimation. In addition, QPSK is used as a modulation method and two transmission antennas are tested. The performance of the system was measured by MSE of LS channel estimation.

5 is a normalized Doppler frequency Is 0 and 0.02, the MSE performance according to SNR is shown for the general channel estimation technique and the channel estimation technique according to the present invention.

The normalized Doppler frequency If 0, that is, if the channel does not change in time, that is, time-invariant channel, it can be seen that the general channel estimation technique has a gain of about 1 dB in terms of signal-to-noise ratio (SNR). However, normalized Doppler frequency Is 0.02, the general channel estimation technique generates an error floor. On the other hand, the technique according to the present invention shows that there is no change in performance even though the channel changes quickly in time. In the MSE of 10 ⁻² , it can be seen that the channel estimation scheme according to the present invention gains about 2 dB over the general estimation scheme (see reference numerals a, b, c, and d of FIG. 5).

6 shows a block method, a general estimation method, and a comb method using the estimation method according to the present invention at SNR = 24 ms. MSE performance is shown. For proper comparison of the block and comb methods, the pilot method inserts one pilot symbol after seven data symbols in proportion to the pilot and data ratios. As shown in FIG. 6, the block scheme exhibits the same performance as the comb scheme in time-invariant channels. Normalized Doppler Frequency As is increased, its performance is drastically reduced, making practical use impossible at high Doppler frequencies. In the comb method, the general channel estimation technique shows better performance than the channel estimation technique according to the present invention when the channel changes slowly in time. This is because the pilot design of the general channel estimation scheme is designed with an orthogonal matrix to satisfy the minimum MSE, but the pilot design according to the channel estimation technique according to the present invention does not satisfy the orthogonal matrix. In the channel estimation scheme according to the present invention, if the pilot design satisfies the orthogonal matrix, both techniques show the same performance when the channel changes slowly in time. On the other hand, for channels that change quickly in time, i.e., the normalized Doppler frequency In the large case, as in FIG. 5, it can be seen that the channel estimation technique according to the present invention performs much better than the general channel estimation technique (see reference numerals e, f, and g of FIG. 6).

As a result, as described above, the paper of I. Barhumi et al. Is for designing a transmission pilot for minimizing channel estimation MSE in an OFDM system using multiple transmission antennas. Placed at equal intervals, designed to satisfy the satellite transition orthogonality, and is applied to the LS (least square) method for channel estimation, but if the channel does not change, but the optimal channel estimation method. If the channel is time-varying, the accuracy of the channel estimation is degraded.

According to the present invention, there is provided a channel estimation scheme and a pilot design considering a case where a channel is time-varying in an OFDM system using a multiplexed transmission antenna having a comb-based pilot pattern. That is, the pilot subcarriers according to the present invention are arranged at equal intervals within one OFDM symbol, and the pilot is designed to satisfy orthogonality, and the LS method using a simple interpolation method is applied in consideration of time-varying channels in channel estimation. That is, in the pilot design, only orthogonality needs to be satisfied, and the LS channel can be estimated along with a simple interpolation method in consideration of the time-varying channel.

According to the present invention, even when the channel is time-varying, there is almost no difference in performance from when the channel is not changed, and thus more accurate channel estimation is possible than the channel estimation method of the previous paper.

While the invention has been shown and described in connection with specific embodiments thereof, it will be appreciated that various modifications and changes can be made without departing from the spirit and scope of the invention as indicated by the claims. It is obvious to those who have.

As described above, the channel estimation method according to the present invention maintains the accuracy of channel estimation without performance loss in time-varying channels by performing channel estimation considering the Doppler effect using the channel correlation. Able to know.

In addition, according to the present invention, since simple linear interpolation and channel estimation are performed independently for each subcarrier, complexity is not only reduced, but also the performance of the OFDM system can be improved by designing a pilot suitable for the channel estimation technique.

1 is a block diagram showing a configuration of a transmission / reception system of a general orthogonal frequency division multiplexing (OFDM)

2 is a schematic block diagram of a mobile OFDM system using multiple transmit antennas according to the prior art.

3 is a pilot layout of a comb-type in general.

FIG. 4 is a diagram illustrating a channel estimation method in a time-varying channel in an OFDM system using a multiple transmit antenna and arranging pilots in a comb manner according to the present invention.

5 is a diagram illustrating a mean square error (MSE) and a signal-to-noise ratio (SNR) according to a channel estimation technique and a general channel estimation technique according to the present invention.

6 is a mean square error (MSE) and a normalized Doppler frequency according to a channel estimation technique and a general channel estimation technique according to the present invention. ).

Claims (5)

In the channel estimation method of time-varying channel of Orthogonal Frequency Division Multiplexing (OFDM) system, a) generating a pilot symbol in a comb-type of inserting a pilot in a specific subcarrier at regular intervals in each OFDM symbol; b) transmitting the pilot generated in the comb manner from a transmitter to a receiver through a time-varying channel using at least two multiple transmit antennas; c) receiving a signal transmitted through the multiple transmit antenna via the time-varying channel; And d) estimating a first channel of the time-varying channel by an interpolation method using a time correlation between a second channel and a third channel Channel estimation method comprising a. The method of claim 1, Step d), The time-varying channel is a channel estimation method of estimating the channel in a least square (Least Square (LS)) method. The method of claim 1, The interpolation method is a channel estimation method, characterized in that the linear interpolation method. The method of claim 1, When designing a pilot using the time correlation of the channel, the channel estimation method is designed to satisfy the necessary rank for multi-channel estimation in each symbol period in order to reduce the performance decrease according to the time-varying channel. . The method of claim 3, In the case of using two antennas as the multiplexed transmission antennas, a frequency axis signal transmitted from a pth subcarrier containing a pilot at nth time Is , Where Is , The frequency axis channel value ( ) , And additional noise ( )silver When I say Channel of n + 1th time corresponding to mth transmit antenna And channel at n + 2th time Is nth And n + 3th Using the linear interpolation channel estimation as a time correlation, Is expressed as: Is the frequency axis pilot transmitted from the mth antenna and the pth subcarrier at the nth time, And a pilot is designed to be a channel estimation method.