KR101518991B1 - Apparatus and method for regularized coordinated beamforming in multiple antenna - Google Patents

Abstract

The present invention relates to an apparatus and method for normalized common beamforming in a multi-antenna system, and a transmitter for normalized common beamforming in a multi-antenna system includes a first beamforming vector for calculating a transmission beamforming vector using channel information, A second beamforming vector generator for normalizing the transmission beamforming vector, and a pre-coder for precoding and transmitting data using the normalized transmission beamforming vector, There is an advantage that the noise generated due to the constraint can be prevented from being greatly amplified.

Multiple antennas, Pilot, Coordinated Beamforming, Normalized transmit beamforming vectors.

Description

[0001] APPARATUS AND METHOD FOR REGULARIZED COORDINATED BEAMFORMING IN MULTIPLE ANTENNA [0002] BACKGROUND OF THE INVENTION [0003]

The present invention relates to co-ordinated beamforming (CBF) in a multi-antenna system, and more particularly to an apparatus and method for normalized co-beamforming that minimizes interference and noise.

There are a linear method and a non-linear method for precoding and post-processing methods for simultaneously transmitting data streams to multiple user terminals in a base station equipped with multiple antennas. Coordinated beamforming (CBF) corresponds to a linear method. Also, the linear scheme is divided into a unitary precoding scheme and a non-unitary precoding scheme, and the CBF corresponds to a non-unitary precoding scheme. That is, the CBF performs multi-user communication through a linear operation in the transmitter and receiver, but the precoding matrix of the transmitter is not a unitary matrix.

The CBF scheme calculates a precoding matrix and a reception beamforming vector (or matrix) using the downlink channel state information of the receivers in the transmitter. However, at this time, the precoding matrix and the reception beamforming vector do not generate inter-user interference (or multiple-access interference) after combining using the reception beamforming vector at the receiving apparatus. Must be satisfied. The precoding matrix and the reception beamforming vector satisfying the above properties are generally obtained through the iteration property.

In the CBF scheme, a base station can use the following two methods to transmit a reception beamforming vector to a terminal. The first method is to use pilot beamforming. After assigning a dedicated pilot so as not to be redundantly used in each terminal and performing beamforming of the pilot using the transmission beamforming vector corresponding to each terminal, the terminal estimates an effective channel, A matched filter is formed and used as a reception beamforming vector. In this method, pilots need to be allocated to each terminal without being overlapped (orthogonally), so that the number of dedicated pilots is required as the number of user streams increases. The second method is to quantize the transmission beamforming vector of each terminal and transmit it through a forwarding channel (downlink control channel). In this case, since the transmission beamforming vectors are different for each terminal, the capacity of the forwarding channel increases in proportion to the number of terminals.

The prior art uses an iterative algorithm based on zero-forcing to remove inter-user interference in calculating transmission and reception beamforming vectors. That is, the transmission / reception beamforming vector is updated by repeatedly updating the transmission / reception beamforming vector from the initial reception beamforming vector until the condition is satisfied. Therefore, when using the transmission and reception beamforming vectors obtained in the prior art, interference between users is eliminated in an ideal case (no channel error and no noise). However, the actual environment can not be ideal, and as a result, the noise is greatly amplified due to the restriction to completely eliminate interference between users. In particular, the lower the signal-to-noise ratio (SNR), the worse the performance is.

The regularized inversion technique combines the regular ZF-BF (Zero-Forcing Beamforming) technique with regularization. It adds a regularization factor to the inverse operation, By preventing the inverse of the ill-conditioned channel matrix, the above problem can be solved.

However, there is no known method of applying normalization in the case of a CBF in which a receiver has multiple antennas and a transmission / reception beamforming vector is calculated through an iterative algorithm, and a method of obtaining an optimal normalization element is also known It is not.

It is an object of the present invention to provide an apparatus and method for normalized coordinated beamforming in a multi-antenna system.

It is another object of the present invention to provide an apparatus and method for simultaneously minimizing interference and noise through normalized common beamforming in a multi-antenna system.

It is still another object of the present invention to provide an apparatus and a method for reducing an overhead using a pilot when calculating transmission and reception beamforming vectors in a multi-antenna system.

It is still another object of the present invention to provide an apparatus and method for normalized co-ordinated beamforming in a common pilot based wireless communication system such as an LTE (Long Term Evolution) system.

According to a first aspect of the present invention, there is provided a transmitter for normalized common beamforming in a multi-antenna system, comprising: a first beamforming vector generator for calculating a transmission beamforming vector using channel information; A second beamforming vector generator for normalizing the transmission beamforming vector, and a pre-coder for precoding and transmitting data using the normalized transmission beamforming vector.

According to a second aspect of the present invention there is provided a receiver for normalized common beamforming in a multi-antenna system, comprising: a receiver for receiving a beamforming vector from a first pilot signal beamformed by a reference transmit beamforming vector, An effective channel gain calculator for calculating an effective channel gain from the calculated reception beamforming vector; and a post-encoder for performing channel equalization using the effective channel gain and receiving data, .

According to a third aspect of the present invention, there is provided a transmission method for normalized common beamforming in a multi-antenna system, the method comprising: calculating a transmission beamforming vector using channel information; And normalizing the vector, and precoding and transmitting the data using the normalized transmission beamforming vector.

According to a fourth aspect of the present invention, there is provided a receiving method for normalized common beamforming in a multi-antenna system, the method comprising: receiving a first beamformed beamformed by a reference beamforming vector, Calculating an effective channel gain from the calculated reception beamforming vector, and performing channel equalization using the effective channel gain and receiving data.

As described above, by performing the normalized common beamforming in the multi-antenna system, there is an advantage that the noise generated due to the restriction to cancel the interference between users can be prevented from being greatly amplified. That is, joint beamforming can be performed in consideration of interference and noise. Therefore, in a low SNR wireless channel environment, a throughput significantly superior to the prior art can be obtained.

 In the normalized common beamforming scheme, the overhead can be reduced by using the pilot when transmitting the reception beamforming vector to the receiver, and the present invention can be applied to the common pilot based LTE system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. The following terms are defined in consideration of the functions of the present invention, and these may be changed according to the intention of the user, the operator, or the like. Therefore, the definition should be based on the contents throughout this specification.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will now be described with reference to an apparatus and method for normalized coordinated beamforming in a multi-antenna system.

In particular, an apparatus and a method for normalized common beamforming to perform normalized common beamforming to prevent an increase in noise due to interference restriction and to apply a pilot technique to reduce overhead will be described.

In addition, the present invention will be described with respect to a method of applying the present invention to a common pilot based system such as LTE (Long Term Evolution).

In order to perform the operation according to the present invention, the following assumptions are required. First, in order to obtain downlink channel information for all receivers, the transmitter uses an uplink sounding channel in a time division duplexing (TDD) scheme or a downlink sounding channel estimated by a terminal through a feedback channel The downlink channel information can be used. Finally, we assume a flat fading channel with slowly varying channels.

FIG. 1 illustrates a transmitter for performing normalized co-beamforming in a multi-antenna system in accordance with the present invention.

1, the transmitter includes a coder 101, a modulator 103, a demultiplexer 105, a pre-coder 107, an RF processor 109, a channel checker 111, a first beamforming vector A second beamforming vector generation unit 115, and a beamforming vector selection unit 117. The second beamforming vector generation unit 115,

The encoder 101 encodes transmission data according to a modulation level (for example, a Modulation and Coding Scheme (MCS) level) and outputs the encoded data. The modulator 103 modulates the encoded data from the encoder 101 according to the modulation level and outputs the modulated data. The demultiplexer 105 demultiplexes the modulation symbols provided from the modulator 103 to have the same number as the number of transmission antennas, and outputs a plurality of data streams.

The first beamforming vector generator 113 generates transmit and receive beamforming vectors using channel state information of the streams supplied from the channel determiner 311 and outputs the generated transmit beamforming vector values To the pre-coder 107, the second beamforming vector generator 115, and the beamforming vector selector 117. In a conventional iterative approach, a transmit / receive beamforming vector is generated using the channel state information. That is, the transmit / receive beamforming vector is updated from the initial beamforming vector repeatedly until the condition is satisfied.

The transmit / receive beamforming vector is expressed as Equation (1).

Where M is the transmit beamforming vector, m _k is the transmit beamforming vector value of the kth antenna, W is the receive beamforming vector, and w _k is the receive beamforming vector value of the kth antenna.

The second beamforming vector generation unit 115 normalizes the transmission beamforming vector values from the first beamforming vector generation unit 113. [ At this time, the transmission beamforming vector M from the second beamforming vector generator 115 is normalized as shown in Equation (2) below, whereby noise increase due to user interference restriction can be prevented.

는 프로베니우스놈(frobenius norm) 연산을 의미한다.Here, M _reg is the normalized transmission beamforming vectors, I is the identity matrix or a unit vector, M is the transmission beamforming vector received from the first beam-forming vector generation section 113, (and) ^H is the Hermitian (Hermitian) operation, and (and) ^-1 is the inverse operation (inverse operation), and P is the transmission power, and N _o is the noise power, and H _k is a channel matrix of the k th MS, m _k is the k-th transmission Beamforming vector value,

Means the frobenius norm operation.

The channel check unit 111 checks the channel state of streams for transmitting data to receivers located in the service area. For example, the channel identifying unit 111 estimates the channel state of the streams using the sounding signals transmitted by the receivers through the uplink channel. In another embodiment, the channel check unit 111 checks the channel state included in the feedback signal received from the receivers.

The beamforming vector selector 117 selects the value of the reference transmission beamforming vector m _j according to the following Equation (3), and provides it to the pre-coder 107. That is, the receiver selects a value of the transmission beamforming vector for increasing the beamforming signal strength with respect to the radio channel, and determines the reference transmission beamforming vector as a reference transmission beamforming vector.

Where H _k is the channel matrix of the k th UE and m _j is the j th transmit beamforming vector value.

The pre-coder 107 multiplies the first transmit signal by the first transmit signal vector m _j from the beamforming vector selector 117 to form a reference beam, 109). Also, the pre-coder 107 generates a second pilot signal as follows to output to the RF processor 109 so as to compensate for channel distortion of a signal received at the receiver.

The preamble encoder 107 pre-encodes the normalized transmit beamforming vector values provided from the second beamforming vector generator 115 and the data stream to be transmitted through each antenna provided from the demultiplexer 105, And outputs it. That is, the pre-coder 107 multiplies the data to be transmitted in each stream by the normalized transmission beamforming vector provided from the second beamforming vector generator 115 to form a beam for each stream. This can be expressed as Equation (4) below. Here, the pre-coder 107 is output to the first antenna 1 RF signal to a processor (109-1) and output to the RF processor _t N (109-N _t), the N _t th antenna signal.

Where m _k ^R is a normalized transmit beamforming vector value of the kth antenna, b _k is a data stream transmitted through the kth antenna, and? Is a factor for normalizing the transmit power.

Wherein the RF processor (109-1 to 109-N _t) converts the data stream received from the encoder 107, the line to an analog signal. Then, the RF processor (109-1 to 109-N _t) is the analog signal the actual transferable high frequency: convert (RF Radio Frequency) signal to be transmitted via the antenna.

2 shows a receiver for performing normalized co-beamforming in a multi-antenna system according to the present invention.

2, the receiver includes an RF processor 201, a post coder 203, a channel estimator 205, an effective channel gain calculator 209, a channel equalizer 211, a demodulator 213, And a decoder 215.

The RF processors 201-1 to 201- _NR convert a radio frequency (RF) signal received through each antenna into a baseband signal and output the baseband signal. The received signal includes a signal by a data subcarrier and a signal by a pilot subcarrier.

The channel estimator 405 estimates a channel with a transmitter using the pilots included in the signals provided from the RF processors 401-1 to 401- _NR , and calculates a reception beamforming vector. Here, the pilot is divided into a first pilot and a second pilot, the first pilot is used to form a reference beam at a transmitter to estimate a reception beamforming vector, and the second pilot is used to compensate for channel distortion at a receiver It is used for. The reception beamforming vector value is calculated by Equation (5).

이 되고, 기준 빔을 사용하지 않는 수신기일 때(k≠j), 수신 빔포밍 벡터는 f(ㆍ)에 의한 직교 벡터로 산출된다. 상기 f(ㆍ)는 2x1 벡터에 대해서 하나의 직교 벡터를 출력하는 함수이다. 예를 들어, [p, q]^T 인 벡터에 대해 쉽게 [q*, -p*]^T 와 같은 직교 벡터를 구할 수 있다. y_{k , pilot -A} 는 제 1 파일럿을 수신한 신호이다.Here, when the receiver using the reference beam (j = k), the reception beamforming vector is

And the receiver does not use the reference beam (k? J), the reception beamforming vector is calculated as an orthogonal vector by f (?). F (?) Is a function for outputting one orthogonal vector with respect to a 2x1 vector. For example, we can easily find an orthogonal vector such as [q *, -p *] ^ T for a vector of [p, q] ^ T. y _{k , pilot -A} is the signal that received the first pilot.

The effective channel gain calculation unit 209 calculates the effective channel gain for the second pilot signal using the calculated reception beamforming vector value from the channel estimation unit 205. [ The effective channel gain is expressed by Equation (6).

는 k 번째 수신 빔포밍 벡터값이고, (ㆍ)^H는 허미션(Hermitian) 연산이고, y_{k , plot -B}은 제 2 파일럿에 의한 수신신호, β는 송신전력을 일반 화(normalization)하기 위한 인자, m_k ^R은 k 번째 안테나의 정규화된 송신 빔포밍 벡터값,

는 k 번째 단말의 수신빔포밍 벡터에서의 위상에러이다.here,

Is the k-th receive beamforming vector value, (and) ^H is the Hermitian (Hermitian) operation is, y _{k, plot -B} is received by the second pilot signal, β is to General Chemistry (normalization) the transmit power M _k ^R is the normalized transmit beamforming vector value of the kth antenna,

Is the phase error at the reception beamforming vector of the k < th >

The channel equalizer 211 performs equalization on the effective channel gain from the effective channel gain calculator 209 through an inverse number.

The post encoder 203 detects received data using effective channel information provided from the channel equalizer 211. This is shown in Equation (7) below.

는 k 번째 수신 빔포밍 벡터값이고, (ㆍ)^H는 허미션(Hermitian) 연산이고, y_k은 데이터 부반송파에 의한 수신신호, n_k'는 잡음이다.Here,

( ^H ) is a Hermitian operation, y _k is a received signal by a data subcarrier, and n _k 'is a noise.

The demodulator 213 demodulates the signal received from the post coder 203 according to the modulation level (Modulation and Coding Scheme) level.

The decoder 215 decodes the signal supplied from the demodulator 213 according to the modulation level to detect original data.

FIG. 3 illustrates a transmitter operation for performing normalized common beamforming in a multiple antenna system in accordance with the present invention.

Referring to FIG. 1, in step 301, the transmitter checks channel states of streams for transmitting data to receivers located in a service area. For example, the transmitter can estimate the channel state of the streams using the sounding signal transmitted by the receivers through the uplink channel, or check the channel state included in the feedback signal provided from the receivers.

In step 303, the transmitter generates transmission and reception beamforming vectors using channel state information of each stream. The generated transmit beamforming vector values are generated using the channel state information in a conventional approach. That is, the transmit / receive beamforming vector is repeatedly updated from the initial beamforming vector until the value is satisfied with the threshold value.

Then, the transmitter normalizes the transmission beamforming vector values generated in step 305. [ By normalizing the transmission beamforming vector, it is possible to prevent an increase in noise due to user interference limitation (see Equation (2)).

In step 307, the transmitter multiplies the reference transmit beamforming vector by a first pilot to form a reference beamforming, thereby performing a pre-coding. At this time, the reference transmission beamforming vector is selected according to the criterion of Equation (3).

In step 309, the transmitter transmits a second pilot signal as follows to compensate for channel distortion in the receiver.

In step 311, the transmitter transmits a data stream to be transmitted through each antenna using a normalized transmission beamforming vector.

Thereafter, the transmitter terminates the normalized common beamforming procedure.

The operation of the transmitter for applying the normalized common beamforming in a common pilot based system such as 3GPP LTE is shown in FIG.

4 shows a flow diagram of a transmitter operation for performing normalized common beamforming in a multi-antenna system in accordance with the present invention.

Referring to FIG. 4, the transmitter derives a transmit / receive beamforming vector for all code words (reference transmit beamforming vector) of a codebook in step 401, and calculates a sum -rate) to the maximum.

Then, the transmitter calculates a normalized transmission beamforming vector using the transmission beamforming vector searched in step 403, as in FIG.

Then, in step 405, the transmitter transmits a normalized transmission beamforming vector to compensate for channel distortion in a receiver through port 5 of LTE used for a dedicated pilot, and transmits the normalized reference beam index reference beam index) to the receiver through a control channel.

In step 407, the transmitter transmits the beamformed data to the normalized transmission beamforming vector through ports 0 to 3.

At this time, the receiver calculates its own reception beamforming vector through the reference beamforming index received through the control channel, and obtains the effective channel gain using the signal received through the port 5. After receiving the data using the receive beamforming vector, equalization is performed through the effective channel gain to obtain a sufficient statistic of data.

Thereafter, the transmitter terminates the normalized common beamforming procedure.

Figure 5 shows a flow diagram of a receiver operation for performing normalized common beamforming in a multiple antenna system in accordance with the present invention.

Referring to FIG. 5, in step 501, the receiver estimates a valid channel using a dedicated pilot tone.

In step 503, the receiver determines whether the user is a reference beam user. Each receiver can know through the control information (MAP) whether or not it is a reference beam user (i.e., a terminal using the reference transmission beamforming vector) or not.

이 되고, 기준 빔을 사용하지 않는 수신기일 때(k≠j), 수신 빔포밍 벡터는 f(ㆍ)에 의한 직교 벡터로 산출된다. 상기 f(ㆍ)는 2x1 벡터에 대해서 하나의 직교 벡터를 출력하는 함수이다. 예를 들어, [p, q]^T 인 벡터에 대해 쉽게 [q*, -p*]^T 와 같은 직교 벡터를 구할 수 있다. y_{k , pilot -A} 는 제 1 파일럿을 수신한 신호이다.Then, the receiver calculates a reception beamforming vector from the reference transmission beamforming vector for the signal of the first pilot (see Equation (5)). That is, when the receiver uses a reference beam (j = k), the reception beamforming vector is

And the receiver does not use the reference beam (k? J), the reception beamforming vector is calculated as an orthogonal vector by f (?). F (?) Is a function for outputting one orthogonal vector with respect to a 2x1 vector. For example, we can easily find an orthogonal vector such as [q *, -p *] ^ T for a vector of [p, q] ^ T. y _{k , pilot -A} is the signal that received the first pilot.

Then, the receiver calculates an effective channel gain for the second pilot signal from the calculated reception beamforming vector in step 507 (see Equation (6)).

In step 509, the receiver receives data using a reception beamforming vector and performs channel equalization (see Equation (7)).

Thereafter, the receiver terminates the normalized common beamforming procedure.

As described above, the transmission beamforming vector for minimizing the system-wide MSE (Mean Squared Error) in obtaining the transmission and reception beamforming vectors for performing the coordinated beamforming is obtained, It is possible to solve the noise increase problem due to the limitation. In addition, a pilot use technique may be applied to reduce the overhead in performing the common beamforming.

While the present invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiments, but is capable of various modifications within the scope of the invention. Therefore, the scope of the present invention should not be limited by the illustrated embodiments, but should be determined by the scope of the appended claims and equivalents thereof.

1 is a block diagram of a transmitter for performing normalized common beamforming in a multi-

2 shows a receiver for performing normalized common beamforming in a multi-antenna system according to the present invention,

3 is a flow chart of a transmitter operation for performing normalized common beamforming in a multi-antenna system according to the present invention;

FIG. 4 is a flowchart of a transmitter operation for performing normalized common beamforming in a multi-antenna system according to the present invention, and FIG.

5 is a flow diagram of a receiver operation for performing normalized common beamforming in a multiple antenna system in accordance with the present invention.

Claims (16)

A transmitter for normalized common beamforming in a multiple antenna system, A beamforming vector generator for calculating a transmission beamforming vector using channel information, A pre-coder for multiplying a first transmit beamforming vector by a first transmit beamforming vector to form a reference beam and precoding the data using the transmit beamforming vector; And an RF processor for transmitting the first pilot signal and the precoded data to a receiver. The method according to claim 1, Wherein the beamforming vector generator comprises: And updates the transmit / receive beamforming vector repeatedly from the initial beamforming vector until the condition is satisfied. The method according to claim 1, Wherein the beamforming vector generator comprises: and normalizes the transmit beamforming vector that minimizes a system-wide MSE (Mean Squared Error). The method of claim 3, Wherein the transmit beamforming vector is normalized by Equation (8).

Here, M _reg is the normalized transmission beamforming vectors, I is the identity matrix or a unit vector, M is the transmission beamforming vector received from the first beam-forming vector generation section 113, (and) ^H is the Hermitian (Hermitian) operation, and (and) ^-1 is the inverse operation (inverse operation), and P is the transmission power, and N _o is the noise power, and H _k is a channel matrix of the k th MS, m _k is the k-th transmission Beamforming vector value,

Means the frobenius norm operation. The method according to claim 1, And a beamforming vector selector for selecting the reference transmission beamforming vector for forming the reference beam among the calculated transmission beamforming vectors. The method according to claim 1, Wherein the preamble encoder multiplies the transmit beamforming vector by a second pilot signal to multiply the reference transmit beamforming vector by a first pilot signal and then compensate for channel distortion for a signal received at the receiver, And the RF processor transmits the second pilot signal to the receiver. A receiver for normalized common beamforming in a multiple antenna system, A channel estimator for calculating a reception beamforming vector from a first pilot signal beamformed by a reference transmission beamforming vector, An effective channel gain calculator for calculating an effective channel gain from the calculated reception beamforming vector; A post coder that performs channel equalization using the effective channel gain and receives data; And an RF processor for receiving the first pilot signal and data from a transmitter. 8. The method of claim 7, Wherein the channel estimator calculates a reception beamforming vector using Equation (9).

Here, when the receiver using the reference beam (j = k), the reception beamforming vector is

(K ≠ j), the reception beamforming vector is calculated as an orthogonal vector by f (·), and f (·) is a single orthogonal vector for a 2 × 1 vector _{Yk, and pilot-A} denotes a signal that has received the first pilot. A transmission method for normalized common beamforming in a multiple antenna system, Calculating a transmission beamforming vector using channel information, Multiplying a first transmit signal by a first transmit beamforming vector to form a reference beam, Precoding data using the transmission beamforming vector; And transmitting the first pilot signal and the precoded data to a receiver. 10. The method of claim 9, The transmission beamforming vector may include: Wherein the transmit and receive beamforming vectors are updated and calculated from the initial beamforming vector repeatedly until a predetermined condition is satisfied. 10. The method of claim 9, further comprising the step of normalizing the transmit beamforming vector to minimize a system-wide MSE (Mean Squared Error). 12. The method of claim 11, Wherein the transmit beamforming vector is normalized by < EMI ID = 10.0 >

Here, M _reg is the normalized transmission beamforming vectors, I is the identity matrix or a unit vector, M is the transmission beamforming vector received from the first beam-forming vector generation section 113, (and) ^H is the Hermitian (Hermitian) operation, and (and) ^-1 is the inverse operation (inverse operation), and P is the transmission power, and N _o is the noise power, and H _k is a channel matrix of the k th MS, m _k is the k-th transmission Beamforming vector value,

Means the frobenius norm operation. 10. The method of claim 9, And selecting the reference transmit beamforming vector to form the reference beam among the calculated transmit beamforming vectors. 10. The method of claim 9, Multiplying the transmission beamforming vector by a second pilot signal to compensate for channel distortion of a signal received at the receiver, And transmitting the transmission beamforming vector multiplied to the second pilot signal to the receiver. A receiving method for normalized common beamforming in a multiple antenna system, Calculating a reception beamforming vector from a first beamformed beamformed by a reference transmission beamforming vector; Calculating an effective channel gain from the calculated reception beamforming vector; Performing channel equalization using the effective channel gain; And receiving the first pilot signal and data from a transmitter. 16. The method of claim 15, Wherein the step of calculating the reception beamforming vector comprises: (11). &Lt; EMI ID = 11.0 >

Here, when the receiver using the reference beam (j = k), the reception beamforming vector is

(K ≠ j), the reception beamforming vector is calculated as an orthogonal vector by f (·), and f (·) is a single orthogonal vector for a 2 × 1 vector _{Yk, and pilot-A} denotes a signal that has received the first pilot.

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