DE102009033720A1 - Channel estimating method for two-way-relaying-system, involves amplifying training sequences with amplification matrix using amplify and forward relay, where amplification matrix is constant for time frame - Google Patents

Abstract

The method involves utilizing more than one antenna at transmission terminals (UT1, UT2) and a relay station (R). Training sequences are transmitted by the transmitting stations in a training phase at a successive time period in a time frame. The received training sequences are amplified with an amplification matrix using an amplify and forward relay, where the amplification matrix is constant for the time frame. A transmission signal for one of the antennas is generated from a linear combination of the received training sequences.

Description

The The present invention relates to a method for channel estimation in two-way relaying systems with amplify & forward relays.

With a two-way relaying method is a bidirectional data exchange realized between two users in only two time slots, though both participants and the relay station used in the Half duplex operation work. This will be a low cost achieved very high spectral efficiency, which allows high data rates. That's why two-way relaying is very important for the development of future mobile radio systems. It proves to be particularly advantageous that relay stations are used, which do not decode the signal (Decode & Forward) but amplify it only (Amplify & Forward): There are fewer signal propagation delays, the device complexity and thus the costs are less, the system can easily be extended by new coding methods, without the relay stations need to be replaced. However, two-way relaying systems with amplify and forward relays work only if both participants have both their own mobile channel to relay know as well as the channel between the other participant and the relay. Therefore, channel estimation methods for Two-way Relaying Systems with Amplify & Forward Relays of More Critical Importance.

Out The prior art has so far no channel estimation methods for Two-Way Relaying Systems with Amplify & Forward Relays known.

In contrast, channel estimation methods without relays have already been extensively studied (eg US 5,005,188 and US 5,912,876 ). However, these only concern a direct connection between the subscriber and the base station, so that the requirements of two-way relaying systems with amplify and forward relays are not investigated.

Out known in the art two-way relaying systems with decode & forward relays can be like classic transceiver systems in the Treat mobile phone, as this is for each participant only his own channel to the relay station is interesting. This one can be appreciated in the same way as the channel too a base station in the case of a system without relays. Against it Do not treat two-way relaying systems with Amplify & Foward Relays there for both participants not only their own channels important, but also the channels between each other participants and the base station. Such systems are in Although the literature is discussed, the channel estimation becomes however neglected and the channel known as perfect accepted (see [A] and [B]).

A Channel estimation for one-way relaying systems with Amplify & Forward relays is described for example in [C]. However, this approach is also not applicable in two-way relaying, as here only one of the two Terminals with channel state information is supplied in two-way relaying however, both terminals need this information.

task Therefore, the present invention is a method for channel estimation to provide in two-way relaying systems with amplify & forward relays, with which manages to overcome the disadvantages of the prior art, so that both participants with channel state information about the mobile channel between each of the two participants and the Relaystation be supplied with a transmission of Page information (feedback) prevents and thus exclusively transmit a sequence of known signals (pilots) in a training phase shall be.

According to the invention succeeds the solution of this task with the features of the first Claim. Advantageous embodiments of the invention Method are specified in the subclaims.

The Invention will become more apparent in the following with reference to drawings explained. Show it:

1 - Presentation of the scenario and its participants

2 - Representation of the two alternating transmission phases in two-way relaying systems

3 - tabular representation of a training phase

4 Representation of concrete gain matrices for the case M _R > min (M ₁ , M ₂ )

5 A channel estimation algorithm

6 - a Least Square Kathri-Rao factorization

7 - a best symmetric rank-one approximation

8th - a Rank-One Matrix reconstruction

With the present inventive method, the channel estimation in two-way relaying systems with amplify & forward relays with high estimation accuracy is to be realized, the number of antennas at the relay station (M _R ) and at terminal 1 (M ₁ ) and terminal 2 (M ₂ ) can be arbitrary. The focus is on the optimized choice of pilot sequences as well as the corresponding reinforcement matrices that relay uses in the training phase. Concrete rules on how to choose these sequences are described, depending on the antenna configuration.

When Application examples show two channel estimation algorithms, the underlying with the help of the described pilot sequences Task can cope, d. h., both participants can be supplied with the full channel state information become.

A two-way relaying scenario is characterized by two terminals UT ₁ and UT ₂ , which want to exchange data with one another with the aid of a relay station R (see FIG. 1 ). The two terminals UT ₁ and UT ₂ are equipped with M ₁ or M ₂ antennas, the relay station with M _R antennas. The specifics of "two-way relaying" is that first both terminals send UT ₁ and UT ₂ simultaneously to R (where the transmissions interfere) and subsequently R sends an amplified version of that signal to both terminals. These two transmission phases alternate (s. 2 ).

From a network infrastructure cost perspective, it is desirable to keep the complexity of the relay stations low. The use of "amplify &foward" relays is therefore obvious. These are characterized by merely amplifying the received signal and sending it out directly without decoding it. r Tx = G · r Rx

Signalen können beide Terminals volle Kenntnis über alle an der Übertragung beteiligten Kanalkoeffizienten gewinnen, vorausgesetzt, dass bei der Wahl von den Verstärkungsmatrizen und Pilotsymbolen nachfolgende Designregeln eingehalten werden:

• – Die Anzahl der Pilotsymbole N_P muss mindestens so groß sein, wie die Summe der Anzahl der Antennen beider Terminals NP ≥ M1 + M2
• – Die Pilotsequenzen sollten zueinander und untereinander orthogonal sein:
  

However, these simple relay stations are unable to participate in the separation of the two interfering data streams. This task falls completely to the user terminals. With the help of channel knowledge at UT ₁ and UT ₂ , the data streams can be completely separated. In order to gain the channel knowledge, a training phase is necessary. In this case, for a preselected set of N _R gain matrices G ( i ) , i = 1, 2, ..., N R . each of a sequence of N _P pre-selected pilot symbols x 1, j , x 2, j , j = 1, 2, ..., N P transmitted from both terminals (see Table 3). From the received

Signals, both terminals can gain full knowledge of all channel coefficients involved in the transmission, provided that the following design rules are followed in the selection of the gain matrices and pilot symbols:

• - The number of pilot symbols N _P must be at least as large as the sum of the number of antennas of both terminals N P ≥ M 1 + M 2
• The pilot sequences should be orthogonal to each other and to each other:
  

definiert, wobei G( i ) = G1·diag{G3(i, :)}·GT2 , i = 1, 2, ..., NR To construct the reinforcement matrices, first the matrices

defined, where G ( i ) = G 1 · Diag {G 3 (i, :)} · G T 2 , i = 1, 2, ..., N R

• – G₃: N_R ≥ M_R
• – G₃ sollte orthogonale Spalten haben
  
• – G₁, G₂ sollten orthogonale Matrizen sein
• – G –1 / 2·G₁ sollte: → Für M_R ≤ min(M₁, M₂): Keine Nullen enthalten → Sonst: Maximal min(M₁, M₂) von null verschiedene Werte pro Spalte haben

The matrices G ₁ , G ₂ , G ₃ must then satisfy the following conditions:

• - G ₃ : N _R ≥ M _R
• - G ₃ should have orthogonal columns
  
• - G ₁ , G ₂ should be orthogonal matrices
• - G -1 / 2 · G ₁ should be: → For M _R ≤ min (M ₁ , M ₂ ): do not contain any zeros → otherwise: have maximum min (M ₁ , M ₂ ) nonzero values per column

In The following embodiments will be two concrete Channel estimation algorithms are presented, both described on the Pilot sequences are based. This is the one in the publication [D] presented non-iterative TENCE and an itertive improvement the channel estimation with the "SLS-based refinement for TENCE "(see also [E])

(a) TENCE

• Notation:

• - scalars = italic letters a, b, ...
• - Vectors = lowercase bold letters a, b, ...,
• - Matrices = bold capital letters A, B, ...,
• Tensors = bold calligraphic letters
• - Euclidean norm of a vector: || α || ₂ , Frobenius norm of a matrix: || A || _F , Higher-Order Frobenius Standard of a Tensor: || A || _H.
• - Matrix transpose: A ^T , conjugate transpose (Hermitian): A ^H , matrix inverse: A ^-1 , Moore-Penrose pseudo-inverse: A ⁺ .
• - Kronecker product: A⊗B,
• - column-wise Kronecker product (Khatri-Rao product): A⟡B,
• - elemental product (Schur product): A⊙B,
• - elemental division (inverse Schur product): A⊘B
• - Matrix unfolding of a tensor
  
  along dimension n:
  
• - Product between matrix
  
  and tensor
  
  in dimension n (n-mode product):
  
• - Vectorization of a matrix or a tensor by Stacking all elements in a vector: α = vec {A}
• - Sequence of two tensors along dimension n: [A⎵ _n B].
• - zero matrix of size p × q: 0 _{p × q} , matrix of ones of the largest p × q: 1 _{p × q} ,
• - unit matrix of size p × p: I _p (ones on the diagonal, otherwise 0),
• - unit tensor of size p × p × p: I _{3, p} (ones on the space diagonal, otherwise 0).

• Data Model:

• - Sending phase 1: The terminals send to the relay:
  
  Here are:
  
  The symbol vectors emitted by the terminals,
  
  - the channel matrices between the antennas of the relay and the individual terminals and
  
  - the additive noise at the relay. It is assumed that non-frequency-selective channel fading.
• - Transmit phase 2: The relay amplifies the signal by multiplication with a gain matrix
  
  and then send to both terminals. The received signals can be described by y 1 = H T 1 * G * (H 1 .x 1 + H 2 .x 2 + n R ) + n 1 y 2 = H T 2 * G * (H 1 .x 1 + H 2 .x 2 + n R ) + n 2 . Here are:
  
  the received signals at the two terminals and
  
  the additive noise at the terminals. It is assumed that the channels are reciprocal, forward and reverse channels are therefore identical.
• Training phase: In a sequence of N _R consecutive frames, a sequence of N _P pilot symbols is transmitted by the terminals in each case. From frame to frame, the relay changes its amplifiers kung matrix. y 2, i, j = H T 1 ·G (I) ·H 1 .x 1, j + H T 1 ·G (I) ·H 2 .x 2, j + n ~ 1, i, j y 2, i, j = H T 2 ·G (I) ·H 1 .x 1, j + H T 2 ·G (I) ·H 2 .x 2, j + n ~ 2, i, j where: • y _{1, i, j} , x _{2, i, j are} the received signal from pilot j in frame i, • G ^{(i) is} the gain matrix that uses the relay in frame i, • x _{1, j} , x _{2, j are} the transmit vectors for pilot j, n ~ _{1, i, j} , n- _{2, i, j,} the combined noise term of pilot j in frame i consisting of its own additive noise and the amplified noise at the relay station. Here i = 1, 2, ..., N _R and j = 1, 2, ..., N _P. It turns out that the required number of frames N _R must be at least M _R. To minimize the training effort, N _R = M _{R is} selected.
• - Tensor data model: The received signals can be expressed more compactly in tensor notation:
  
  Here is:
  
  the relay amplification tensor,
  
  the common channel matrix and
  
  the overall pilot matrix.
• - Disassembly of Relay Gain Tensor:
  
  in which
  
  the relay factor matrices are. The relationship between G ^{( i )} and G _n is given by G ^{( i )} = G ₁ · diag {G ₃ (i, :)} · GT / 2 where diag {G ₃ (i, :)} is a diagonal matrix, whose diagonal corresponds to the i-th row of G ₃ .
• - With the help of this representation for the relay amplification tensor, the following relation for terminal 1 results: (G -1 3 · [Y 1 ] (3) T = (H T 1 ·G 1 ) ⟡ (X T ·H T ·G 2 )
• The matrix on the left side of the equation can be calculated from the training data and is ideally equal to the Khatri-Rao product of two matrices. The goal is to split off the factors. Since this relationship under the influence of disturbances only approximately applies, the matrix can not be exactly decomposed into Khatri-Rao factors, but only approximately. This is done using the least-squares-Khatri-Rao-Factorization algorithm, which is described in 6 is described. Since it is based on column-wise rank-1 approximations by means of the singular value decomposition, Eckart-Young's theorem implies that the decomposition is optimal with respect to the mean square error.
• - The factorization is only unique except for a scaling ambiguity per column. Consequently, for the two factors F1 and F2, which are determined from the least-squares-Khatri-Rao-Factorization: F 1 = H T 1 ·G 1 · Λ F 2 = X T ·H T ·G 2 · Λ -1 where: • Λ = diag {λ} is a diagonal matrix with unknown scaling factors
  
  These are determined by taking advantage of the structure of the problem. Two cases have to be considered: • Case 1: M _R <min (M ₁ , M ₂ ) - In this case a solution is directly possible. For this purpose, the matrix L is calculated: L = [F + 1 (X T 1 ) + · F 2 ] ⊘ (G -1 2 ·G 1 ) Subsequently, with the 7 algorithm 2 of the vector λ determined. In this case, the G -1 / 2 · G ₁ matrix must consist only of non-zero elements. • Case 2: M _R ≥ min (M ₁ , M ₂ ) - In this case, the solution after λ requires that the matrix G -1 / 2 · G ₁ maximally min (M ₁ , M ₂ ) be non-zero values per Column has. A solution after λ is possible, in which the matrix L is calculated as follows:
  
  Subsequently, the missing elements in L according to algorithm 3 in 8th refilled. Here: - g ~ _{m is} the m-th column of the matrix G ~ = G -1 / 2 · G ₁ and - f ~ _{2, m is} the m-th column of the matrix F 2 = (X T 1 ) + · F 2 The matrix L thus obtained is then treated as in case 1: with algorithm 2 7 the vector λ can be obtained. In both cases, the final estimates for H ₁ and H _{2 are} given by
  
  
• - In addition to the already derived design rules for the factor matrices G _n , it is noticeable that all three matrices must be inverted. This necessarily requires that they all have full rank. To optimize the numerical stability, G _{n is} therefore chosen so that its columns are orthogonal to each other. Moreover, the matrix inversion is easy to calculate in this case, since only the conjugate transposed must be suitably scaled.
• - In addition, the pseudo-inverse of the pilot matrices X ₁ and X _{2 must be} formed. This necessarily requires that X _{1 has} at least rank M ₁ and X ₂ at least rank M ₂ . In addition, the calculation of H _{2 is} only possible if X ₁ and X ₂ are mutually orthogonal. Moreover, with the same argument as before, these matrices should be chosen so that the lines are orthogonal to each other. Incidentally, these conditions require that N _P ≥ M ₁ + M ₂ . Since the training effort increases with N _P , the least expensive choice is N _P = M ₁ + M ₂ ,
• - This justifies all established design rules for the relay gain tensor G as well as for the pilot matrices X ₁ and X ₂ . An example of G satisfying the established rules is described in claim 8, an example of X ₁ and X ₂ can be found in claim 11.

(b) SLS-based refinement

Based on the same training data, it can be an iterative Specify algorithm that is non-iterative TENCE improved the estimation accuracy for the Channel matrices achieved with slightly increased computational effort.

The algorithm is based on the statement that the training data contains the following structure:

Thus, the quality of the channel estimation can be estimated by the norm of the so-called residual tensor:

wobei

und α∊R, α > 0 einen Regularisierungsparameter zur Verbesserung der numerischen Stabilität darstellt. Da dies ein nichtlineares Least-Squares-Problem ist, lässt es sich nur iterativ lösen.This allows the establishment of the following cost function:

in which

and αεR, α> 0 represents a regularization parameter for improving the numerical stability. Since this is a nonlinear least squares problem, it can only be solved iteratively.

The iteration is initialized as follows:

wobei H ^₁, H ^₂ die TENCE-Lösungen darstellen. Die Matrizen

sind so definiert, dass für beliebige A gilt:

Die Iteration wird solange wiederholt bis die Bedingung

erfüllt ist, wobei δ ein Schwellenparameter ist. Am Ende der Iterationen sind die verbesserten Kanalschätzungen gegeben durch (H ^₁ + ΔH_1,k) sowie (H ^₂ + ΔH_2,k).In iteration step k, the following calculations take place:

where H ^ ₁ , H ^ _{2 represent} the TENCE solutions. The matrices

are defined such that for any A:

The iteration is repeated until the condition

is satisfied, where δ is a threshold parameter. At the end of the iterations, the improved channel estimates are given by (H ^ ₁ + ΔH _{1, k} ) and (H ^ ₂ + ΔH _{2, k} ).

Simulations have shown that α = 100, δ = 10 ^{-3 are} suitable values for the design parameters of the algorithm. In addition, only between 2 and 4 iterations were always necessary.

Bibliography

• [A] - Hammerstrom, M. Kuhn, C. Esli, J. Zhao, A. Wittneben, and G. Bauch, "MIMO two-way relaying with transmit CSI at the relay," in Proc. IEEE 8th Workshop on Sig. Proc. Adv. In Wireless Comm. (SPAWC 2007), Helsinki, Finland, June 2007.
• [B] - T. Unger and A. Klein, "Maximum sum of non-regenerative two-way relaying in systems with different complexities", in Proc. IEEE 9th Intl. Symp. On Personal, Indoor and Mobile Radio Comm. (PIMRC 2008), Cannes, France, Sept. 2008.
• [C] - P. Lioliou and M. Viberg, "Least-squares based channel estimation for MIMO relays", in Proc. ITG / IEEE Workshop on Smart Antennas (WSA '08), pp. 90-95, Darmstadt, Germany, Feb. 2008.
• [D] - F. Roemer and M. Haardt, "Tensor-based channel estimation (TENCE) for two-way relaying with multiple antennas and spatial reuse," in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing (ICASSP), (Taipei, Taiwan), pp. 3641-3644, Apr. 2009, invited paper.
• [E] - F. Roemer and M. Haardt, "Structured Least Squares (SLS) based enhancements of tensor-based channel estimation (TENCE) for two-way relaying with multiple antennas," in Proc. International ITG Workshop on Smart Antennas (WSA 2009), (Berlin, Germany), Feb. 2009

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited patent literature

• - US 5005188 [0004]
• US 5912876 [0004]

Claims (10)

Method for channel estimation in a two-way relaying system with amplify & forward relays, in which - M ₁ > 1 antennas at the transmitting station 1, - M ₂ > 1 antennas at the transmitting station 2 and - M _R > 1 antennas the relay station are used, characterized in that in a training phase both transmitting stations simultaneously in a time slot (frame) in N _P ≥ (M ₁ + M ₂ ) successive times the training sequences

send, the amplify & forward relay the received signals with a constant for the time slot i gain matrix

amplified, wherein the transmission signal for the n-th antenna from the linear combination of the received signals with the n-th row of G ^{( i)} is formed. Method according to Claim 1, characterized in that the training sequence extends over N _R ≥ M _R time slots, the same matrices X ₁ and X _{2 being} transmitted in each time slot, but the associated gain matrices G ⁽ⁱ⁾ , i = 1, 2, ..., N _{R are} different. Method according to one of claims 1 or 2, characterized in that the reinforcement matrices G ^{( i )} are constructed as follows

Method according to one of claims 1 to 3, characterized in that the rank of G ₁ , G ₂ and G _{3 is} equal to M _R and satisfy the following conditions: G -1 / 2 · G ₁ has: → For M _R ≤ min (M ₁ , M ₂ ) Entries other than zero → Otherwise: Maximum min (M ₁ , M ₂ ) nonzero values per column A method according to claim 4, characterized in that the matrices G ₁ , G ₂ , G ₃ satisfy the following conditions: - G ₃ has orthogonal columns

G ₁ , G ₂ are orthogonal matrices. Method according to claim 4 or 5, characterized in that the matrices G ₁ , G ₂ , G _{3 are selected} according to the following rule: G ₃ contains the first M _R columns of an N _R × N _R DFT matrix G ₂ is one Unit matrix of size M _R × M _R. G ₁ is for M _R ≤ min (M ₁ , M ₂ ) an M _R × M _R DFT matrix - G ₁ is calculated for M _R > min (M ₁ , M ₂ )

in which

an M _R × M _R DFT matrix, S is a matrix resulting from the cyclic shift of the vector

arises, and ⨀ represents the elemental product. Method according to one of claims 1 to 6, characterized in that the matrices of the training sequences X ₁ and X _{2 have} the rank M ₁ or M ₂ . Method according to one of claims 1 to 7, characterized in that the matrices of the training sequences X ₁ and X ₂ are chosen so that they are mutually orthogonal, ie

Method according to one of claims 1 to 8, characterized in that the matrices of the training sequences X ₁ and X _{2 are selected} according to the following rule: - X ₁ contains the first M ₁ rows of an N _P × N _P DFT matrix - X ₂ contains the rows M ₁ + 1 to M ₁ + M _{2 of} an N _P × N _P DFT matrix. Method according to one of claims 1 to 9, characterized in that the channel matrices H ₁ and H ₂ after the in 5 estimated algorithm can be estimated.