KR101599189B1 - Channel Estimation Method for Large Scale MIMO Systems - Google Patents

Abstract

A problem of a memory space for big data is on the rise because of too many users and a limited memory space. In a big MIMO system, Toeplitz channel can help the performance be improved, as well as higher electricity efficiency. The present invention relates to a method for channel estimation, and more specifically, to a method for channel estimation in a big MIMO system. According to an embodiment of the present invention, provided are a Toeplitz channel division based on matrix vectorization while using Toeplitz matrix in a channel for a big MIMO system, and a Toeplitz Jacket matrix divided into Cooley-Tukey sparse matrix like a fast Fourier transform (FFT). According to another embodiment of the present invention, a multiple-input multiple-output (MIMO) communication system comprises a transmitter which transmits a signal by using multiple antennas; and a receiver which receives a signal by using multiple antennas and estimates a channel by using the received signal.

Description

[0001] The present invention relates to a channel estimation method for large scale MIMO systems,

The present invention relates to a channel estimation method, and more particularly, to a channel estimation method in a large scale MIMO system.

Multiple-input multiple-output (MIMO) antenna technology is emerging as an effective technology for increasing the capacity and robustness of wireless communication systems. Due to the very high spectral efficiency and reliability improvement in free space and the potential of actually achieving the theoretical predicted merits of MIMO in terms of power efficiency, large scale MIMO systems with tens to hundreds of antennas are of great interest have.

A large-scale MIMO system can be thought of as a system with several thousand terminals simultaneously using an antenna array of several hundred antennas on the same time-frequency resource. The basic premise of large-scale MIMO since then not only accommodates all the advantages of existing MIMO, but also has a much larger advantage. Overall, large-scale MIMO is an energy-efficient, secure, robust, and optimal means of enabling future fixed and mobile broadband networks to use spectrum efficiently.

In wireless MIMO communication, the channel between the transmitter and the receiver can be designed according to Kronecker-model in some cases. This model is possible when there is a certain relationship between different antennas. When this model is designed, the radio channel covariance matrix can be modeled as a two-matrix Kronecker product of a smaller dimension. When these conditions are met, it is important to have an algorithm that fits this particular problem to increase accuracy and reduce computational costs.

Korean Patent No. 10-1573001 (Nov. 21, 2015) Korean Patent No. 10-1263257 (2013.05.06)

SUMMARY OF THE INVENTION It is an object of the present invention to provide a channel estimation method in a MIMO communication system using vectorization based on Toeplitz channel matrix decomposition.

According to an aspect of the present invention, there is provided a channel estimation method including: receiving a signal; And estimating the channel using the received signal, wherein the estimating step estimates the channel using the following equation.

y ^(m) is the received signal vector of the m-th channel

x ^(m) is the transmission signal vector of the m-th channel

z ^(m) is the noise

≪ RTI ID = 0.0 > m <

I _N is a unit matrix

The Kronecker product is the Kronecker product.

Then, the channel matrix can be decomposed as shown in the following equation.

Meanwhile, a multiple-input multiple-output (MIMO) communication system according to another embodiment of the present invention includes: a transmitter for transmitting a signal using a plurality of antennas; And a receiver that receives a signal using a plurality of antennas and estimates a channel using the received signal, and the receiver estimates the channel using the above equation.

As described above, according to the embodiments of the present invention, channel estimation in a MIMO communication system becomes possible by using a vectorization technique based on Toeplitz channel matrix decomposition. This can improve memory efficiency, data processing speed, performance improvement, and power efficiency in the channel estimation process through channel matrix decomposition.

1 illustrates a forward fast algorithm,
FIG. 2 illustrates a reverse fast algorithm,
3 is a graph showing a large-scale MIMO capacity vs. CDF,
4 is a graph showing a large-scale MIMO capacity for the SNR difference,
5 is a diagram illustrating a MIMO communication system to which the present invention is applicable.

Hereinafter, the present invention will be described in detail with reference to the drawings.

In the embodiment of the present invention, a vectorization based on Toeplitz channel matrix decomposition is proposed using a Kronecker product. Also, we propose the possibility of switching between antennas to maximize system throughput. Also, we propose an optimal switching between SB (statistical beamforming) with high correlation and SM (spatial multiplexing) with low correlation. This switching method improves performance and requires minimum feedback information. This is because the switching method depends only on the two channel statistics, the average SNR and the spatial correlation.

1. Toeplitz matrix structure

The Toeplitz matrix has a constant element along the diagonal and is a structure that transitions from the upper left to the lower right

procession

to be.

The Toeplitz matrix mentioned here is classified into two types as follows. The first classification is formed by a circulation matrix, where each row vector is rotated from left to right in relation to the previous column vector. In particular, the rotation as in equation (1)

About

to be. The second Toeplitz matrix is a negacycle matrix. Here,

About

to be.

This matrix shown in equation (1) is applied to various fields. For example, in the following equation

Represents the input to the column vector,

when

Is zero.

Therefore, the vector can be expressed as follows.

At this time, the matrix elements are as follows.

The vector

Lt; RTI ID = 0.0 >

Time-invariant filter of the discrete-time causal.

Toeplitz Jacket (TJ) matrix

Can be decomposed into sparse matrices so that a fast algorithm can be implemented as follows. Figures 1 and 2 show the forward fast algorithm and the reverse fast algorithm.

therefore,

Wow

, We can see that it becomes a unit matrix as follows.

The fast algorithm of Fig.

The high-speed algorithm of Fig.

A special case of the Toeplitz matrix is that each row of the matrix moves to the right one cycle from the top row

About

(5) and becomes a circulant matrix.

This matrix is used for cyclic coding for error correction including DFT (Discrete Fourier Transform).

In the Toeplitz procession,

The Toeplitz matrix, which deals with the role of the eigenvalue as it infinitely increases

For the sequence of

. A nonzero vector such as:

If there is a complex scalar

The matrix

.

in this case

Is an eigenvector of.

Eigenvalue

end

, It can be approximated using integration, and the Hermitian Toeplitz matrix

Eigenvalues for sequences

Dealing with the asymptotic role of

Which means that generality is not lost. This theorem has some technical requirements to be satisfied. For example, the coefficients associated with each other by

Fourier series is a condition that must exist.

So,

Function

, And vice versa. So the sequence of the matrix is sometimes

. if,

If it is Hermitian,

If so,

ego

Is a real number value.

If you make a reasonable assumption

Functions that are continuous in the range of

The Fourier series and the Toeplitz sequence can be represented by the same face.

2. System and Channel Model

The transmitting antenna

And the receive antenna is

And these antennas assume a large, spatially multiplexed point-to-multipoint MIMO system with thousands of antennas.

Represents a channel gain matrix using an m-th channel. At this time, it is assumed that these elements have an average of 0, a variance of 1 and follow the iid Gaussian distribution. The reception vector y (m) in the case of using the m-th channel is expressed by Equation (13).

here,

ego,

The elements i

. ≪ / RTI > In equation (14)

Has the Toeplitz structure as shown in Eq. (15).

Therefore, equation (13) can be rewritten as in equation (16).

Matrix vectorization and Kronecker product identity

(16) can be rewritten as Equation (17).

Several channel vector decomposition examples are presented here. For example, the following cases are assumed.

here,

Assuming that

, Where < RTI ID = 0.0 >

Lt; / RTI &

And receiving antenna

Lt; RTI ID = 0.0 > impulse < / RTI > Equation (18) can now be rewritten as Equation (19).

From Eq. (16) it can be written as

Therefore, the Kronecker product used in Eq. (17) can be expressed as Eq. (21).

sign

and

Assuming

And the received signal can be obtained by the matched filter as follows.

Toeplitz

An example of a channel is shown below.

As a result, the following equation (24) can be obtained.

In the receiver, the reception capacity can be expressed by Equation (25).

In a similar way, Eq. (23) can be written as Eq. (26) and its capacity can be obtained as Eq. (27).

3. Simulation

To analyze the meaning of the Toeplitz channel decomposition, a monte-carlo simulation was performed. 3 and 4 show results of a more realistic scenario, where the channel coefficients

Is a real number with a Gaussian distribution with an average of 0 and a variance of 0.5 and a complex number of imaginary parts. channel

Is random, so the capacity is also a random variable with a special distribution. The CCDF (Complimentary Cumulative Distribution Function) is used as an important unit for measuring the capacity of such a channel. This curve basically suggests the probability that the MIMO capacity will be above a certain threshold.

4. MIMO communication system

5 is a diagram illustrating a MIMO communication system to which the present invention is applicable. As shown in FIG. 5, the MIMO communication system is constructed to include a transmitter 100 that transmits signals using a plurality of antennas and a receiver 200 that receives signals using a plurality of antennas.

The receiver 200 estimates the channel using the received signal from the transmitter 100. [ Specifically, the receiver 200 estimates the channel by calculating H ^(m) described above in "2. System and channel model ".

Channels are modeled according to the Kronecker-model. Meanwhile, in order to save memory due to limited memory space, the receiver 200 decomposes the channel matrix using a Toeplitz channel matrix technique based on vectorization in a large scale MIMO communication system. Thereby, the radio channel covariance matrix is modeled as a Kronecker product of small-dimensional matrices.

In the embodiment of the present invention, vectorization based on the Toplitz channel matrix decomposition using Kronecker product is presented, and the Toeplitz Jacket matrix is decomposed into a Cooley-Tukey sparse matrix like the Fourier transform. In order to maximize throughput of the system, we proposed the possibility of switching between antennas.

It is common to adjust between the coding and modulation modes according to the SNR. Embodiments of the present invention have suggested the possibility of proper switching between SM under conditions with high correlation and SM under conditions with low correlation. This switching method increases the performance and requires minimum feedback information because it depends only on the spatial correlation with the two channel characteristics, that is, the average SNR.

5. Toeplitz inverse matrix

The Toeplitz inverse of Eq. (1) can be seen in the following example.

Example 1.

In the case of

Example 2.

In the case of

Example 3.

In the case of

Example 4. For a Circulant Jacket matrix

, Where operator

silver

It means "Sookmyung".

Example 5.

In the case of

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 in form and details may be made therein without departing from the spirit and scope of the present invention.

100: Transmitter
200: receiver

Claims (8)

The receiver receiving the signal; And
And the receiver estimating the channel using the received signal,
Wherein the estimating step estimates the channel using the following equation,

y ^(m) is the received signal vector of the m-th channel
x ^(m) is the transmission signal vector of the m-th channel
z ^(m) is the noise

≪ RTI ID = 0.0 > m <

I _N is a unit matrix
Is the Kronecker product,
The H is decomposed into a product of a Toffler's matrix Tn and diagonal matrices, and is processed by a fast algorithm, as expressed by a Cj (Circulant Jacket) matrix as shown in the following equation.

delete delete delete delete A transmitter for transmitting a signal using a plurality of antennas; And
And a receiver for receiving the signal using a plurality of antennas and estimating the channel using the received signal,
The receiver estimates the channel using the following equation,

y ^(m) is the received signal vector of the m-th channel
x ^(m) is the transmission signal vector of the m-th channel
z ^(m) is the noise

≪ RTI ID = 0.0 > m <

I _N is a unit matrix
Is the Kronecker product,
The H is represented by a Cj (Circulant Jacket) matrix and is decomposed into a product of a Toffler's matrix Tn and diagonal matrices and processed by a fast algorithm. Communication system.

delete delete

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