Linear transformation of symbols to at least partially compensate for correlation between antennas in space time block coded systems

A method is provided of transmitting signals from two or more antennas in a wireless telecommunications network, in which at least one data sequence is space-time block encoded. Before transmitting the data sequence, a linear transformation is applied to the data sequence, the linear transformation being adapted to use knowledge of correlation among the antennas to at least partially compensate the transmitted signals for said correlation. The linear transformation depends on the eigenvalues of an antenna correlation matrix. The linear transformation further depends on a ratio of symbol energy (Es) to noise variance (σ2). The method includes transmitting the encoded and transformed data sequence.

FIELD OF THE INVENTION

The present invention relates to methods of multiple antenna wireless transmission using space-time block encoding.

DESCRIPTION OF THE RELATED ART

Base station antennas are often placed high above ground and relatively close to each other. There may be no obstructions between them acting to scatter transmitted symbols, leading to high antenna correlation. It has been shown that such correlations reduce channel capacity and system performance in multiple-input multiple-output (MIMO) systems.

Specifically as regards Universal Mobile Telecommunications System (UMTS) networks, performance degradation due to antenna correlation is prevented merely by increasing the spacing of antennas. However, it has been found that in situations where the angular spread of radio waves reaching an antenna is relatively small or where there are no line of sight obstructions between antennas, antenna correlation is high (i.e. taking a value close to one) even when the antennas are well-separated.

Accordingly, those skilled in the art have recognised that antenna correlations tend to degrade the performance of MIMO systems.

SUMMARY OF THE INVENTION

A linear transformation (e.g., precoder) is provided for a space-time coded system, which alters transmitted signals to at least partially compensate for antenna correlation. The linear precoder combats the detrimental effects of antenna correlation by exploiting knowledge of antenna correlation made available to the transmitter.

An example of the present invention is a method of transmitting signals from two or more antennas in a wireless telecommunications network, in which at least one data sequence is space-time block encoded. Before transmitting the data sequence, a linear transformation is applied to the data sequence, the linear transformation being adapted to use knowledge of correlation among the antennas to at least partially compensate the transmitted signals for said correlation. The linear transformation depends on the eigenvalues of an antenna correlation matrix. The linear transformation further depends on a ratio of symbol energy (Es) to noise variance (σ2). The method includes transmitting the encoded and transformed data sequence.

It should be emphasized that the drawings of the instant application are not to scale but are merely schematic representations, and thus are not intended to portray the specific dimensions of the invention, which may be determined by skilled artisans through examination of the disclosure herein.

DETAILED DESCRIPTION

For ease of understanding a more general description is presented, followed by an explanation of implementation aspects in a mobile telecommunications network of Universal Mobile Telecommunications System (UMTS) type. It should be noted that the present invention has applications not only in UMTS, but also, by way of example and without limitation, in communication systems such as code division multiple access (CDMA) and wideband code division multiple access (W-CDMA).

MIMO systems, for example for use in UMTS, typically involve space-time block encoding. An example of space-time block encoding scheme for two transmit antennas is presented in S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Selected Areas in Communication, Vol. 16, No. 8, pp. 1451–1458, October 1998 and is also described in U.S. Pat. No. 6,185,258, which is incorporated herein by reference. The encoding and transmission sequence for this scheme is as follows: at a first transmission time instant t1symbols x1and x2are transmitted from antennas1and2respectively and at the next transmission instant t2symbols −x2* and x1* are transmitted from antennas1and2respectively, where * denotes complex conjugate. This transmission sequence Z can be represented in matrix form as

As further background, it is known that the performance of MIMO systems can sometimes be improved by precoding. Precoding means applying a linear transformation to symbols. A so-called optimal linear precoder for space-time coded systems that assumes knowledge of, and compensates for, the transmit antenna correlations was proposed in H. Sampath, A. Paulraj, “A Linear precoding for space-time coded systems with known fading correlations” IEEE Communications Letters, Volume: 6 Issue: 6, June 2002, Page(s): 239–241. This precoder is a function of both the matrices of eigenvectors and eigenvalues of the antenna correlation matrix R. Specifically, the optimal precoder L, which is optimal in the sense that the average Pairwise Error Probability (PEP) between two codewords is minimised, is proved to be:
L=VrΦfVeH(1)
where R1/2=UrΛrVr, with Urand Vrbeing the matrices of eigenvectors of the matrix R1/2and Λrbeing the matrix of eigenvalues of R1/2. R is the antenna correlation matrix. Φf2=(γI−Λr−2Λe−2), with I being the identity matrix, and EEH=UeΛeVe, E being the matrix of the minimum distance of the code, with Ueand Vebeing the matrices of eigenvectors of EEHand Λebeing the matrix of eigenvalues of EEH. γ>0 is a constant that is computed from the transmit power and (·)+ denotes that the expression in the parenthesis takes its actual computed value if positive else is set to zero if negative.

A linear precoder that exploits knowledge of antenna correlation is included in a space-time coded MIMO system so as to enhance performance. Let us consider a multiple-input multiple output (MIMO) telecommunications network consisting of M transmit antennas and N receive antennas, as shown inFIG. 1. The transmitter, for example a base station for mobile telecommunications, has some knowledge about the channel, namely the antenna correlation matrix R. There is a channel matrix H which describes the physical characteristics of the propagation channel. More specifically, each entry hjiof the N×M channel matrix H represents the channel response between transmit antenna i and receive antenna j. The space-time encoder of the transmitter maps the input data sequence x=(x1,x2, . . . xQ) to be transmitted into an M×Q matrix Z of codewords, that are split on a set of M parallel sequences. I.e., each of the M rows of the matrix Z represents one of Q distinct codewords. These codewords are then transformed by a M×M linear transformation denoted L in order to adapt the code to the available antenna correlation information. The resulting sequences, which are represented by rows of a new transformed M×Q matrix C=LZ, are sent from the M transmit antennas over Q time intervals.

The receive signal (at the mobile) is assumed to be a linear combination of several multipaths reflected from local scatterers, which result in uncorrelated fading across the receive antennas and therefore uncorrelated rows of matrix H. However, limited scattering at the transmitter (e.g. a base station, can result in antenna correlation and hence correlated columns of channel matrix H. A correlation among the M transmit antennas is described by the M×M matrix R, referred to as the (transmit) antenna correlation matrix. The signal received by the N receive antennas over Q time periods is represented by an N×Q matrix Y. The received signal included in the matrix Y is then a superposition of M transmitted sequences corrupted by an additive white Gaussian noise characterised by the N×Q matrix Σ and with covariance matrix equal to σ2IN:
Y=HC+Σ=HLZ+Σ(2)

The linear transformation L is determined so as to minimise a given criterion, namely an upper bound on the pairwise error probability (PEP) of a codeword. The determination of L, as described here, assumes for mathematical simplification that the transmitter possesses perfect knowledge of the antenna correlation matrix. This precoder L is a function of both the matrices of eigenvectors and eigenvalues of the antenna correlation matrix. Specifically, the optimal precoder L, which minimises the average PEP is:
L=VrΦfVeH(3)
where R1/2=UrΛrVr, with Urand Vrbeing the matrices of eigenvectors of the correlation matrix R1/2and Λrbeing the matrix of eigenvalues of R1/2. R is the antenna correlation matrix.

Φf2=(γ⁢⁢I-(Esσ2)-1⁢Λr-2⁢Λe-2)+,
with I being the identity matrix and EEH=UeΛeVe, where E is the matrix of the minimum distance of the code, with Ueand Vebeing the matrices of eigenvectors of EEHand Λethe matrix of eigenvalues of EEH. Also, γ>0 is a constant that is computed from the transmit power POand (·)+ denotes that the expression in the parenthesis takes it actual computed values if positive else is set to zero if negative. It will be seen that there is an additional term

(ESσ2)-1,
where Esis the symbol energy and σ2is the noise variance. This term was included so as to account for Signal-to-Noise Ratio, which is Es/σ2.

Since an orthogonal space-time code is considered, EEH=ζI, where ζ is a scalar, Λe=ζI and Ve=I. This gives:
L=VrΦf(4)
Application to a Two-antenna Transmission System

The next step is to apply both the linear precoder L of Equation (4) and the matrix of codewords for Alamouti space-time block coding, namely

For power Po=1, where λr,1,λr,2are the eigenvalues and [w1, w2] is the strongest eigenvector of the matrix R1/2, the linear precoder is characterised as follows:

1) When the antenna correlation is less than one, λr,1,λr,2≠0 and

β=(1λr,22-1λr,12)/(ESσ2)≤1,
the precoder can be written as:

2) When the antenna correlation is zero, the eigenvalues of the matrix R1/2are equal and therefore β=0. In this case the precoder becomes

L=12⁡[w1w2*w2-w1*]
which is equivalent to the Alamouti orthogonal space-time coding.

3) When the antenna correlation is one, one eigenvalue of matrix R1/2is zero resulting in a matrix Φfwith all elements but one equal to zero. In this case the precoder becomes

L=[w10w20],
which is equivalent to a beamformer.

The proposed reconfigurable scheme is thus equivalent to orthogonal space-time block coding for antenna correlation equal to zero, and to beamforming for antenna correlation equal to one. For intermediate antenna correlation values it performs well and is robust to antenna correlation variations.

The Decoder

The space-time decoder at the receiver is similar to the one used with Space-Time Block Codes (and described in the Alamouti paper referred to above), except that the linear transformation matrix L is taken into account. The received signal described in Equation (2) can be seen as Y=└y1y2┘=HeqZ+Σ=HLZ+Σ, where Heq=└heq,1heq,2┘=HL. The space-time block decoder for the proposed approach can then be seen as identical with the conventional one under the assumption that the effective channel is now Heq. Hence, to recover the transmitted signals x1and x2, the following operations are realised:
{circumflex over (x)}1=(heq,1)*y1−heq,2(y2)*
{circumflex over (x)}2=(heq,2)*y1+heq,1(y2)*
It will be seen that knowledge of the equivalent channel Heq(or its estimate) is required at the receiver in order to recover the transmitted signals x1and x2.
UMTS System Implementation

A UMTS transmitter2and receiver4are shown inFIG. 2. The UMTS frequency division duplex (FDD) downlink transmission-reception scheme includes antenna correlation dependent linear precoding as explained above. The transmitter2has some knowledge about the channel, namely the antenna correlation matrix R. In a UMTS network operating FDD downlink (e.g., from base station to mobile station), the antenna correlation information is obtained as feedback channel estimates6provided as bits sent by receiver4(i.e. the mobile station). The relevant modules are, at the transmitter, a linear precoder (L)8, a processor (COR,10) which determines the antenna correlation matrix (R), and an R to L converter12. The relevant modules at the receiver are a processor (COR,14) which determines the antenna correlation matrix (R), an R to L converter16, and a space-time decoder18.

At the transmitter2, the linear precoder (L)8is applied to the space-time encoded symbols provided from a space-time block encoder20after channel coding, rate matching interleaving, and modulation (shown as functional clock22) in known fashion. The linear precoder L coefficients are computed based on the antenna correlation matrix R in the R to L converter12. The computation of R (in a functional block denoted COR,10) is based on channel estimates6fed back from the receiver4. It is performed by averaging over time-sequential channel estimates (running average) using a forgetting factor. The forgetting factor aims to weight the contribution of each new channel estimate as compared to the past channel estimates. It will thus be seen that fast fading is not tracked but only slowly varying antenna correlations. This information is fed back to the transmitter using a low-rate feedback link, as available in UMTS. In a UMTS uplink channel there is a number of bits available for communicating information to the transmitter about the received signal. The outputs of the linear precoder8are spread/scrambled9and subject to addition of Common Pilot Channel (CPICH) coding 11 bits before transmission.

At the receiver4, received signals are used to provide channel estimates in a channel estimation block26so as to be used to compute the antenna correlation matrix R in processor14(as at the transmitter). The signals are also despread28and applied to a space-time block decoder24. At the receiver4the space-time block decoder (STD,24) has essentially the same structure as a conventional one (described in the Alamouti paper and patent referred to above), but needs to consider instead of the channel estimates, the equivalent channel, defined as the linear transformation of the channel according to the coefficients of L, that is Heq=└heq,1heq,2┘=HL. As shown inFIG. 2, the linear precoder L coefficients are estimated at the receiver from the processor (COR,14) which determines the antenna correlation matrix (R) and the R to L converter16present at the receiver4. The outputs of the space-time decoder24are provided to a combiner30and then channel decoded, inverse rate matched, deinterleaved and demodulated in known fashion (shown inFIG. 2as functional block32).

Alternative UMTS Implementation

An alternative implementation is now described, in which instead of the linear transformation matrix L being determined at the transmitter from channel estimates provided by the receiver, the coefficients of linear transformation matrix L are provided by the receiver.

In this alternative embodiment, which is shown inFIG. 3, the transmitter2′ is given the coefficients of the precoder L by the receiver4′. In this UMTS transmitter2′ and receiver4′ operating with frequency division duplex (FDD) downlink, these coefficients are feedback bits sent by the mobile station. The proposed UMTS network is depicted inFIG. 3, where the UMTS FDD downlink transmission-reception scheme includes antenna correlation dependent linear precoding as explained previously. The relevant module at the transmitter is a linear precoder (L)8′. The relevant modules at the receiver are a processor (COR,14′) which determines the antenna correlation matrix (R), an R to L converter16′, and a space-time decoder24′.

At the transmitter, the linear precoder (L) is applied to the space-time encoded symbols provided from the space-time block encoder20′ after channel coding, rate matching, interleaving, and modulation (shown as functional block22′) in known fashion. The outputs from the linear precoder8′ are spread/scrambled9′ and subject to the addition of Common Pilot Channel (CPICH) 11′ bits before transmission. The linear precoder L coefficients are provided by the receiver4′ as explained below and fed back over air to the transmitter.

At the receiver, the computation of R (in a functional block denoted COR14′) is based on channel estimates provided from the channel estimator lock26′. It is performed by averaging over time sequential channel estimates (running average) using a forgetting factor. The forgetting factor aims to weight the contribution of each new channel estimate as compared to the past channel estimates; the aim being to take account of slowly-varying antenna correlations but not fast fading. The linear precoder (L) coefficients are computed based on the antenna correlation matrix R in the R to L converter16′.

At the receiver4′, received signals are both used to provide channel estimates in a channel estimation block26′, and are also despread28′ and applied to a space-time decoder24′. At the receiver, the space-time block decoder (STD)24′ has identical structure to the conventional one (described in the Alamouti paper and patent referred to above), but needs to consider instead of the channel estimates, the equivalent channel, defined as the linear transformation of the channel according to the coefficients of L, that is Heq=└heq,1heq,2┘=HL. The outputs of the space-time decoder are provided to a combiner30′ and then channel decoded, inverse rate matched, deinterleaved and demodulated in known fashion (shown inFIG. 3as functional block32′).

General

It is believed that this approach has natural extensions to the cases in which there are three or more transmit antennas. Extensions to such cases are also considered to lie within the scope of the present invention.

While the particular invention has been described with reference to illustrative embodiments, this description is not meant to be construed in a limiting sense. It is understood that although the present invention has been described, various modifications of the illustrative embodiments, as well as additional embodiments of the invention, will be apparent to one of ordinary skill in the art upon reference to this description without departing from the spirit of the invention, as recited in the claims appended hereto. Consequently, the method, system and portions thereof and of the described method and system may be implemented in different locations, such as network elements, the wireless unit, the base station, a base station controller, a mobile switching center and/or a radar system. Moreover, processing circuitry required to implement and use the described system may be implemented in application specific integrated circuits, software-driven processing circuitry, firmware, programmable logic devices, hardware, discrete components or arrangements of the above components as would be understood by one of ordinary skill in the art with the benefit of this disclosure. Those skilled in the art will readily recognize that these and various other modifications, arrangements and methods can be made to the present invention without strictly following the exemplary applications illustrated and described herein and without departing from the spirit and scope of the present invention It is therefore contemplated that the appended claims will cover any such modifications or embodiments as fall within the true scope of the invention.