METHOD AND APPARATUS OF TOPOLOGICAL PILOT DECONTAMINATION FOR MASSIVE MIMO SYSTEMS

Abstract

The presently claimed invention relates generally to a method and an apparatus for pilot decontamination for massive MIMO system and, more particularly, to a massive MIMO communication system based on channel estimation with topological interference alignment.

Claims

1. A method of topological pilot decontamination in a massive Multiple-Input Multiple-Output (MIMO) system, the system comprising one or more base stations (BSs), one or more user equipments (UEs), and a central controller, the method comprising: obtaining, by the central controller, a large scale fading matrix based on the channel gains obtained from the BSs; obtaining, by the central controller, a square topological matrix based on the large scale fading matrix; normalizing, by the central controller, the square topological matrix to form a normalized square topological matrix; obtaining, by the central controller, a pilot matrix by matrix decomposition based on the normalized square topological matrix and the number of pilot resources; obtaining, by the central controller, an optimized estimator projection matrix based on the pilot matrix and the square topological matrix; and performing, by an individual BS, a channel estimation based on the optimized estimator projection matrix and pilots transmitted by UEs where the pilots of all UEs are given by the pilot matrix.

2. The method of claim 1, wherein the pilot resources are located in an orthogonal domain including time domain, frequency domain, or code domain.

3. The method of claim 1, wherein the step of obtaining square topological matrix further comprises: transforming the large scale fading matrix to the square topological matrix by dividing each of the BSs, which serves multiple UEs, to virtual BSs, wherein each of the virtual BSs serves one UE and has the same parameters as its corresponding original BS.

4. The method of claim 1, wherein the step of normalizing the square topological matrix further comprises: normalizing channel gain vectors of each of the UEs in the square topological matrix with respect to a desired link channel gain, by multiplying the square topological matrix with a normalizing matrix, wherein the normalizing matrix is a diagonal matrix with the inverse of desired link channel gains as the diagonal values.

5. The method of claim 1, wherein the step of obtaining pilot matrix further comprises: obtaining a partial connectivity matrix by rounding negligible entries in the normalized square topological matrix to zero with a pre-defined threshold; obtaining a complimentary matrix based on the partial connectivity matrix by making non-diagonal elements with non-zero value in the partial connectivity matrix be zero, and assigning each of the zero elements in the partial connectivity matrix with an arbitrary value; obtaining a normalized pilot matrix by decomposing the complimentary matrix into a BS projection matrix and the normalized pilot matrix based on the number of the pilot resources, wherein both of the BS projection matrix and the normalized pilot matrix satisfy the following requirements: a product of the BS projection matrix and the normalized pilot matrix gives the complimentary matrix; and the BS projection matrix is of size K×T, while the normalized pilot matrix is of size T×K, where K is the number of UEs in all cells, and T is the number of the pilot resources; obtaining the pilot matrix by multiplying the normalized pilot matrix by a normalizing matrix.

6. The method of claim 5, wherein the normalized pilot matrix is obtained by a topological interference alignment computation, the computation comprising: generating a K×K random matrix A.sup.0 and setting i=0; processing iteratively the following steps: obtaining the singular value decomposition (SVD) of A.sup.i: A.sup.i=U.sup.iΣ.sup.iV.sup.i.sup.H, obtaining {tilde over (Σ)}.sup.i by forcing the smallest (K−T) singular values on the diagonal of Σ.sup.i to zero, and obtaining B.sup.i=U.sup.i{tilde over (Σ)}.sup.iV.sup.i.sup.H; obtaining A.sup.i+1 by forcing the diagonal elements to one and the corresponding elements with 0 in ${\tilde{D}}^{\frac{1}{2}}$  to zero as below: $A^{i+1}\left(j,k\right)=\{\begin{array}{cc}{\tilde{D}}^{\frac{1}{2}}\left(j,k\right)& \mathrm{if}.Math..Math.{\tilde{D}}^{\frac{1}{2}}\left(j,k\right)=0.Math..Math.\mathrm{or}.Math..Math.{\tilde{D}}^{\frac{1}{2}}\left(j,k\right)=1\\ B^i\left(j,k\right)& \mathrm{otherwise}\end{array};$ if A.sup.i+1 converges, break the iteration; otherwise, set i=i+1 and go to next iteration; obtaining the normalized pilot matrix as $\Psi ={\left(\stackrel{i}{.Math.}\right)}^{\frac{1}{2}}.Math.V^{i^H}.$

7. The method of claim 1, wherein the step of performing the channel estimation further comprises: sending, by each of the UEs, pilots indicated by its respective column of the pilot matrix.

8. The method of claim 1, wherein the optimized estimator projection matrix is obtained by Minimum mean square error (MMSE) method as follows: $C_{\mathrm{jl}}=\sqrt{P_r.Math.t}.Math.B_{\mathrm{jl}}^{\frac{1}{2}}.Math.{{\Psi }_j^H\left(I+P_r.Math.t.Math.\underset{i=1}{\overset{L}{.Math.}}.Math..Math.{\Psi }_i.Math.B_{\mathrm{il}}.Math.{\Psi }_i^H\right)}^{-1},$ where Ψ.sup.H.sub.i is the pilot matrix of UEs in the i-th cell, B.sub.jl is the large scale fading matrix from the j-th cell's UEs to the l-th cell's BS, P.sub.r is the UE uplink transmit power, T is the number of pilot resources, and L is the number of cells.

9. The method of claim 1, wherein the step of performing the channel estimation further comprises: projecting the received pilots using the optimized estimator projection matrix.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Embodiments of the present invention are described in more detail hereinafter with reference to the drawings, in which:

[0045] FIG. 1 shows a graph illustrating channel fading in a wireless system;

[0046] FIG. 2 shows a BS projection matrix and a UE pilot matrix;

[0047] FIG. 3 shows pilot contamination and interference from other cell UEs;

[0048] FIG. 4 illustrates a flow chart of a method of topological pilot decontamination for massive MIMO systems according to the present invention; and

[0049] FIG. 5 illustrates a massive MIMO communication system framework based on channel estimation with topological interference alignment according to the present invention.

DETAILED DESCRIPTION

[0050] In the following description, methods for pilot decontamination in a massive MIMO system are set forth as preferred examples. It will be apparent to those skilled in the art that modifications, including additions and/or substitutions may be made without departing from the scope and spirit of the invention. Specific details may be omitted so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without undue experimentation.

[0051] As discussed above, consider a system with L cells. Each cell is assumed to have K single-antenna users and a BS with M antennas, where M>>K. For purposes of illustration, one assumes that all L cells use the same set of K pilot sequences.

[0052] As the number of BS antennas grows large, i.e., M.fwdarw.∞, the SINR (Signal to Interference plus Noise Ratio) of the k-th user in the j-th cell tends to the following limit

[00008]$\begin{array}{cc}{\mathrm{SINR}}_{k,j}^u=\frac{d_{j,k,j}^2}{\underset{l\ne j}{.Math.}.Math..Math.d_{j,k,l}^2}& \left(5\right)\end{array}$

where d.sub.j,k,l is the large-scale channel fading coefficient. From (5), the SINR depends only on the large-scale fading factors of the channels while the small-scale fading factors and noise are averaged out. So in massive MIMO, one can utilize the strong large scale fading for pilot contamination cancelation.

[0053] As discussed above for FIG. 1, not all the inter-cell interference links are strong enough. Only the UEs on the cell edge will create strong inter-cell interference, some UEs only introduce negligible interference. The partial connectivity enables orthogonal pilot transmission for more UEs than pilot slot number. One can use topological interference alignment to achieve this based on the partial connectivity.

[0054] FIG. 4 discloses a flow chart describing a method of topological pilot decontamination for massive MIMO systems of the presently claimed invention. In step 401, a large scale fading matrix is obtained from BSs. In step 402, a normalized square topological matrix is obtained base on the large scale fading matrix. In step 403, an uplink pilot matrix is obtained by matrix decomposition based on the square topological matrix and the number of pilot resources. In step 404, an optimized estimator projection matrix is obtained based on the pilot matrix and the square topological matrix. In step 405, channel estimation is performed using the optimized estimator projection matrix at the BSs. In step 406, transmitted signal is precoded and received signal is equalized based on the estimated channel state information (CSI).

[0055] FIG. 5 further illustrates a massive MIMO communication system framework based on channel estimation with topological interference alignment according to the present invention.

[0056] Referring to FIG. 5, in step 501, a central controller obtains a large scale fading matrix from BSs. Then a normalized square topological matrix is calculated based on the large scale fading matrix in step 502. In step 503, the central controller derives an uplink pilot matrix by matrix decomposition based on the square topological matrix and the number of pilot resources. Then, in step 504, an optimized estimator projection matrix is obtained based on the pilot matrix and the square topological matrix. In step 505, the central controller informs BSs the pilot matrix and the projection matrix. Then, at BSs side, in step 506, BSs feedback the pilot matrix to respective UEs. And UEs send uplink pilots to BSs in step 507. In step 508, BSs perform channel estimation using the optimized estimator projection matrix for the received pilots. Lastly, in step 509, for data transmission, transmit signal or equalize receiver signal can be precoded based on the estimated channel.

[0057] As for step 502, regarding that cases whose large scale fading matrix is not square, such as each BS serving 2 UEs, one has to transform the large scale fading matrix into a square matrix. For example, each BS is divided into 2 virtual BSs, and each virtual BS corresponding to on UE. Then one normalizes the channel gain of each UE based on the desired link. In this way, the diagonal becomes 1.

[0058] In order to further explain step 502, an example is used for further illustration. Accordingly, there are 3 BSs, and 2 UEs/BS. An original large scale fading matrix is provided as follows:

##STR00002##

[0059] When the number of UEs is not equal to the number of BSs, the large scale fading matrix is transformed to a square matrix by treating BS serving multiple UEs as multiple BSs such that the large scale fading matrix is extended to a square matrix by the virtual BSs as shown in the below matrix.

[00009]$\hspace{1em}.Math.\left[\begin{array}{cccccc}0.8& 1.25& 0.1& 0.08& 0.03& 0.4\\ 0.8& 1.25& 0.1& 0.08& 0.03& 0.4\\ 0.4& 0.35& 1& 2& 0.15& 0.75\\ 0.4& 0.35& 1& 2& 0.15& 0.75\\ 0.01& 0.2& 0.06& 0.12& 0.5& 1\\ 0.01& 0.2& 0.06& 0.12& 0.5& 1\end{array}\right]$

[0060] The normalized square topological matrix is determined by normalizing the channel gain of each UE according to the desired link (diagonal elements). In this example, the diagonal elements are

×diag(1.25, 0.8, 1, 0.5, 2, 1)

[0061] After normalizing each column to channel gain in desired link, and incorporating desired link channel gain in the algorithm, a normalized square topological matrix is obtained as follows.

[00010]$\hspace{1em}\left[\begin{array}{cccccc}1& 1& 0.1& 0.04& 0.06& 0.4\\ 1& 1& 0.1& 0.04& 0.06& 0.4\\ 0.5& 0.28& 1& 1& 0.3& 0.075\\ 0.5& 0.28& 1& 1& 0.3& 0.075\\ 0.0125& 0.16& 0.06& 0.06& 1& 1\\ 0.0125& 0.16& 0.06& 0.06& 1& 1\end{array}\right]$

[0062] According to an embodiment of the present invention, the normalized square topological matrix is obtained as follow:

[0063] transforming the large scale fading matrix to 2-dim matrix {circumflex over (D)} L×KL, the (l,n)-th entry of which is

[00011]${\hat{d}}_{\ln }=b_{\mathrm{kkjl}}.Math.,.Math.k=n-K-K.Math..Math.\frac{n-1}{K}.Math.,.Math.j=.Math.\frac{n-1}{K}.Math.+1.$

[0064] transforming it to a square matrix D KL×KL the (i,n)-th entry of which is

[00012]${\stackrel{\mathrm{.Math.}}{d}}_{\mathrm{in}}={\hat{d}}_{\ln },l=.Math.\frac{i-1}{K}.Math.+1.$

[0065] obtaining the normalized square topological matrix by normalizing each column based on the diagonal {umlaut over (D)}

[00013]$\stackrel{\mathrm{.Math.}}{D}=\stackrel{\mathrm{.Math.}}{D}.Math..Math.{\mathrm{diag}\left(\stackrel{\mathrm{.Math.}}{D}\right)}^{-1}.$

[0066] In order to clearly explain the step 503 of pilot matrix design, an example will help to understand. For example, one has 4 time slots as pilot resources, 6 BSs and 6 UEs. All UEs use same desired channel. Assume the large scale fading matrix is

##STR00003##

[0067] By rounding the negligible entries in the large scale fading matrix to 0 with a pre-defined threshold 0.1, one obtains the partial connectivity matrix.

[0068] The dominant entries in the partial connectivity matrix greater than or equal to the threshold 0.1 will be rounded up to 0, and the negligible entries less than the threshold 0.1 can be arbitrary value X. That means, dominant interference needs to be forced to zero, and weak interference (shadow/path loss) can be arbitrary value. Then, one obtains the complementary matrix as follows:

##STR00004##

[0069] With the complimentary matrix, one can compute and obtain a pilot matrix by matrix decomposition. Recall that one has 4 time slots as pilot resources. Then, one decomposes the complimentary matrix into a BS projection matrix Φ.sub.6×4 and an UE pilot matrix Ψ.sub.4×6 as follows.

##STR00005##

[0070] Both of the BS projection matrix and the normalized pilot matrix satisfy the following requirements: a product of the BS projection matrix and the UE pilot matrix gives the complimentary matrix; and the BS projection matrix is of size K×T, while the normalized pilot matrix is of size T×K, where K is the number of columns of the complimentary matrix, and T is the number of the pilot resources.

[0071] Matrix decomposition can be computed by alternating projection algorithm. The pilot matrix is determined based on the UE pilot matrix.

[0072] According to an embodiment of the present invention, a pilot matrix is obtained by the following steps:

[0073] obtaining a partial connectivity matrix D by rounding negligible elements with a pre-defined threshold d.sub.th as follows:

{umlaut over (D)}({umlaut over (D)}≦d.sub.th)=0,D={umlaut over (D)}.

[0074] obtaining complimentary matrix D of the partial connectivity matrix as follows:

[00014]${\tilde{d}}_{\mathrm{in}}=\{\begin{array}{cc}1& i=n\\ 0& d_{\mathrm{in}}\ne 0,.Math.\mathrm{and}.Math..Math.i\ne n\\ X& \mathrm{else}\end{array}$

[0075] obtaining the matrix decomposition for this complimentary matrix as follows:

({tilde over (D)}).sup.1/2=Φ{tilde over (Ψ)}

[0076] changing back the pilot power based on the normalizing matrix as follows:

{circumflex over (Ψ)}={circumflex over (Ψ)}diag({umlaut over (D)}).sup.−1

[0077] In brief, one obtains a pilot matrix by decomposing the complimentary matrix based on the number of pilot resources (e.g., time slots).

[0078] For obtaining channel estimation, according to an embodiment of the present invention, each UE sends the pilots indicated by respective column of the pilot matrix, the estimator projection matrix is calculated using MMSE based on the square topological matrix and the pilot matrix, and channel estimation is performed using the estimator projection matrix.

[0079] According to an embodiment of the present invention, the estimator projection matrix C.sub.jl is calculated and the channel estimation is performed by the below equations:

[00015]$C_{\mathrm{jl}}=\sqrt{P_r.Math.t}.Math.B_{\mathrm{jl}}^{\frac{1}{2}}.Math.{{\Psi }_j^H\left(I+P_r.Math.t.Math.\underset{i=1}{\overset{L}{.Math.}}.Math..Math.{\Psi }_i.Math.B_{\mathrm{il}}.Math.{\Psi }_i^H\right)}^{-1}$$\mathrm{where}$${\Psi }_i=\hat{\Psi }\left(:,\left(i-1\right).Math.K+1:\mathrm{iK}\right)..Math.{\hat{H}}_{\mathrm{jl}}=C_{\mathrm{jl}}.Math.Y_l.$

where Ψ.sup.H.sub.i is the pilot matrix of UEs in the i-th cell, B.sub.jl is the large scale fading matrix from the j-th cell's UEs to the l-th cell's BS, P.sub.r is the UE uplink transmit power, T is the number of pilot resources, and L is the number of cells.

[0080] In the present invention, topological interference alignment is utilized to design the pilot with low interference. Using less time slots, interference-free pilots for more UEs can be transmitted.

[0081] In the present invention, obtaining normalized square topological matrix based on the large scale fading matrix is a pre-processing process, which is able to deal with the cases when the number of UE is not equal to the number of BS, and different UEs need different channels. Obtaining estimator projection matrix based on the pilot matrix and the square topological matrix is a post-processing process, which is able to get optimized projection matrix, especially at low SNR case.

[0082] The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art.

[0083] The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalence.