WO2009006040A2

WO2009006040A2 - Method and apparatus for determining beamforming weights for an antenna array

Info

Publication number: WO2009006040A2
Application number: PCT/US2008/067581
Authority: WO
Inventors: Nicholas W. Whinnett
Original assignee: Motorola, Inc.
Priority date: 2007-06-29
Filing date: 2008-06-20
Publication date: 2009-01-08
Also published as: WO2009006040A3; GB0712533D0; GB2450522A; GB2450522B

Abstract

A beamforming processor (133) determines responses for transmit elements (109-115) and receive elements (125-131) for each antenna elements (101-107) of an antenna array. A channel response processor (205) estimates a channel response for each propagation channel between one of the plurality of antenna elements (101-107) and a remote station in response to a signal received from the remote station. A receive compensation processor (207) compensates the channel responses for the receive elements (125-131) but not the transmit elements (109-115). An Eigen beamforming processor (209) then executes an Eigen beamforming algorithm based on the compensated channel responses. The resulting beamform weights are then compensated for the response of the transmit elements (109-115) in a transmit compensation processor (211).

Description

METHOD AND APPARATUS FOR DETERMINING BEAMFORMING WEIGHTS

FOR AN ANTENNA ARRAY

Field of the invention

The invention relates to a method and apparatus for determining beamforming weights for an antenna array and in particular to beamforming using an Eigen beamforming algorithm.

Background of the Invention

In wireless radio communication systems antenna arrays comprising a plurality of antenna elements are used to provide transmit diversity or beamforming that results in improved communication quality. In particular, by varying the phase of a signal applied to all antenna elements of a transmit antenna array, a directional transmit pattern can be achieved and the radiated power can be concentrated in one or more directional beams.

In a number of communication systems such beamforming is used to direct the transmitted power towards a desired recipient. For example, in systems such as Wireless Local Area Networks (WLANs) , Wide Area Networks (WANs) and cellular communication systems, the base stations can comprise transmit antenna arrays such that transmissions to individual remote stations can be concentrated towards the remote stations by a directional beam being formed. In order to determine the beamforming weights to apply to each antenna element, a beamforming algorithm is executed. One such technique is known as the Eigen beamforming algorithm. In this algorithm, the propagation channel response from each of the antenna elements to the remote stations is estimated. In many systems, the propagation channel response from the individual antenna element to the remote station (the downlink propagation channel) can be determined from knowledge of the propagation channel response from the remote station to the antenna element (the uplink propagation channel) . Therefore, the downlink response can be determined from an uplink signal received from the remote station.

In the Eigen beamforming algorithm a spatial correlation matrix reflecting the correlations between the estimated propagation channel responses for each of the antenna elements is generated. The dominant Eigen vector for this spatial correlation matrix is determined and the conjugate of the individual coefficients of this vector represents the appropriate weights for each antenna element. The Eigen vector is typically calculated using an algorithm known as the power iteration algorithm.

Further description of the Eigen beamforming algorithm can e.g. be found in F. W. Vook, T. A. Thomas, and X. Zhuang, "Transmit Diversity and Transmit Adaptive Arrays for Broadband Mobile OFDM Systems," Proc. IEEE WCNC 2003. New Orleans, LA, March 18-20, 2003.

The Eigen beamforming approach has been found to provide very high performance in many systems including e.g. WLAN, WAN and cellular systems. However, a problem with

CE17159N4V the Eigen beamforming algorithm is that even if the propagation channel is accurately determined, the responses of the individual transmit and receive paths also impact on the optimal beamforming weights that should be applied for each antenna element.

One approach to overcome this problem is to continuously adapt the responses of the individual transmit and receive paths such that their responses are substantially identical (both between the transmit and receive paths as well as between the paths for different antenna elements) . However, such continuous adaptation is complex and tends to lead to impractical and complex systems.

A more frequently applied approach is to measure the responses of the individual transmit and receive paths and to compensate the estimated propagation channel responses accordingly prior to applying the Eigen beamforming algorithm. Such conventional Eigen beamforming systems tend to comprise calibration functionality which measures the frequency response of the receive and transmit functionality for each individual antenna element. The determined propagation channel is then modified by multiplying the determined channel response by the response of the transmit path and dividing it by the response of the receive path. The resulting response is then used to calculate the spatial correlation matrix.

However, although this approach may be useful in many situations, it tends to provide suboptimal performance. Indeed it has been found that the approach for many practical propagation channels and systems result in

CE17159N4V significant degradation compared to the performance achieved for ideal and identical transmit and receive paths .

Hence, an improved system for determining beamforming weights would be advantageous and in particular a system allowing improved beamforming, improved communication quality, practical implementation and/or improved performance would be advantageous .

Summary of the Invention

Accordingly, the Invention seeks to preferably mitigate, alleviate or eliminate one or more of the above mentioned disadvantages singly or in any combination.

According to an aspect of the invention there is provided an apparatus for determining beamforming weights for an antenna array comprising a plurality of antenna elements with each antenna element having an associated transmit element and receive element, the apparatus comprising: first means for determining a receive path response for each receive element associated with one of the plurality of antenna elements; second means for determining a transmit path response for each transmit element associated with one of the plurality of antenna elements; means for estimating a channel response for each propagation channel between one of the plurality of antenna elements and a remote station in response to a signal received from the remote station; first compensating means for compensating the channel response for each antenna element by the receive path response for

CE17159N4V the antenna element to generate compensated channel responses for the plurality of antenna elements; beamforming means for determining beamforming weights for the plurality of antenna elements by performing Eigen- beamforming in response to the compensated channel responses; and second compensating means for modifying the beamforming weight for each antenna element in response to a multiplication of the beamforming weight and a complex conjugate of the transmit path response for each antenna element.

The invention may provide an improved apparatus for determining beamforming weights. An improved beamforming may be achieved resulting in improved communication quality, reduced transmit power, reduced performance and/or improved capacity of a communication system utilising the apparatus. The invention may allow a practical, low complexity and/or low cost implementation. In particular, the invention may easily be implemented in many existing systems using Eigen beamforming.

The invention in particular exploits the specific characteristics of Eigen beamforming to perform an improved two stage compensation for characteristics of the receive and transmit paths. In particular, the inventor has realised that for an Eigen beamforming based apparatus, improved performance can be achieved by performing receive path compensation prior to Eigen beamforming weight determination and transmit path compensation following this weight determination. In particular, receive path only compensated propagation channel responses are generated and these are then used to determine the spatial correlation matrix used by the

CE17159N4V Eigen beamforming algorithm. The transmit path compensation is only performed following the Eigen beamforming and is specifically performed by directly modifying the antenna element weights determined by the Eigen beamforming algorithm.

The receive element for an antenna element may comprise the functionality used in converting a signal received by the antenna element to (e.g. complex) base band. The transmit element for an antenna element may comprise the functionality used in converting from (e.g. complex) base band to the signal fed to the antenna element.

According to another aspect of the invention there is provided a method of determining beamforming weights for an antenna array comprising a plurality of antenna elements with each antenna element having an associated transmit element and receive element; the method comprising: determining a receive path response for each receive element associated with one of the plurality of antenna elements; determining a transmit path response for each transmit element associated with one of the plurality of antenna elements; estimating a channel response for each propagation channel between one of the plurality of antenna elements and a remote station in response to a signal received from the remote station; compensating the channel response for each antenna element by the receive path response for the antenna element to generate compensated channel responses for the plurality of antenna elements; determining beamforming weights for the plurality of antenna elements by performing Eigen-beamforming in response to the compensated channel responses; and modifying the

CE17159N4V beamforming weight for each antenna element in response to a multiplication of the beamforming weight and a complex conjugate of the transmit path response for each antenna element.

These and other aspects, features and advantages of the invention will be apparent from and elucidated with reference to the embodiment (s) described hereinafter.

Brief Description of the Drawings

Embodiments of the invention will be described, by way of example only, with reference to the drawings, in which

FIG. 1 is an illustration of a base station in accordance with some embodiments of the invention;

FIG. 2 is an illustration of an apparatus for determining beamforming weights in accordance with some embodiments of the invention;

FIG. 3 illustrates performance results for different beamforming approaches; and

FIG. 4 is an illustration of a method of determining beamforming weights in accordance with some embodiments of the invention.

Detailed Description of Some Embodiments of the Invention

CE17159N4V The following description focuses on embodiments of the invention applicable to a base station for a WLAN, WAN or cellular communication system. In the specific example, an OFDM (Orthogonal Frequency Division Multiplexing) communication is described but it will be appreciated that the invention is not limited to this application but may be applied to many other systems and transmission schemes .

FIG. 1 illustrates an example of elements of a base station for an OFDM base station. In the specific example, the base station is a WiMAX™ (Worldwide Interoperability for Microwave Access) base station.

The base station comprises an antenna array which in the example comprises four antenna elements 101-107. For each of the antenna elements 101-107, the base station comprises a transmit element 109-115 coupled to the antenna element 101-107 via a duplexer 117-123. For each of the antenna elements 101-107, the base station furthermore comprises a receive element 125-131 coupled to the antenna element 101-107 via the duplexer 117-123.

In the specific example, the base station communicates with remote stations using a Time Division Duplex (TDD) communication scheme where uplink (from the remote stations to the base station) and downlink (from the base station to the remote stations) are time duplexed on the same frequency. In this example, the duplexers may simply be implemented as switches that connect the transmit elements 109-115 to the antenna elements 101-107 during the transmit time interval and the receive elements 125-

CE17159N4V 131 to the antenna elements 101-107 during the receive time interval.

Each of the receive elements 125-131 comprises functionality for converting the received antenna signal from the associated antenna element 101-107 into a complex base band signal. Thus, the receive elements 125- 131 comprise filtering, amplification and down-conversion functionality as will be known to the skilled person. Each of the transmit elements 109-115 comprises functionality for converting a complex base band signal into a radio frequency signal which is fed to the associated antenna element 101-107. Thus, the transmit elements 109-115 comprise up-conversion, filtering and amplification functionality as will be known to the skilled person. It will be appreciated that the receive elements 125-131 and transmit elements 109-115 may share some functionality. For example, they may use a common local oscillator as a frequency reference.

The receive elements 125-131 and transmit elements 109- 115 are coupled to a base band processor which is responsible for generating the OFDM base band signal to be transmitted and to demodulate the received OFDM base band signal to generate the received data (for clarity the base band processor is not illustrated in FIG. 1) .

The base station of FIG. 1 uses beamforming to direct the transmissions towards the desired remote station (s). Accordingly, the base station comprises a beamforming processor 133 which calculates individual weights for each of the antenna elements 101-107. The beamforming processor 133 is coupled to the transmit elements 109-115

CE17159N4V and the determined antenna weights are fed to the transmit elements 109-115 and applied to each transmitted signal by the individual transmit element 109-115. In the example, each antenna weight is determined as a single complex value (for a given update time interval) which is multiplied with the complex base band transmit signal prior to up-conversion . In other examples, the antenna weights may e.g. be applied in the base band processor.

The beamforming processor 133 uses an Eigen beamforming algorithm which is based on estimates of the downlink propagation channel from each of the antenna elements 101-107 to the remote station to which the OFDM signal is transmitted.

In the system of FIG. 1, the downlink propagation channel responses are determined from measurements of the uplink channel. Specifically, as the system uses TDD communication, it is assumed that there is close reciprocity between the uplink and downlink propagation channels. It will be appreciated that reciprocity may also be assumed in some systems using frequency separation between uplink and downlink transmissions although the correlation in such cases will tend to be smaller. Also, it will be appreciated that other means of estimating the downlink propagation channel response may be used.

In the specific example, the uplink transmissions can e.g. comprise training symbols for which the beamforming processor 133 determines the received phase and gain. It can then determine the response of the propagation channels from the measured phase and gain relative to the

CE17159N4V known transmitted training symbol. Alternatively in the case of Eigen beamforming systems the user data symbols can be used to determine the relative gain and phase between the uplink transmissions received on antennas 101-107.

A problem for Eigen beamforming systems is that the total response affecting the received and transmitted signal is not only that of the propagation channel but also includes the responses of the individual transmit elements 109-115 and receive elements 125-131. Specifically, even if a common reference frequency is used, component variations, small timing differences, and differences between the components etc. result in the transmit and receive path responses being different for the different transmit elements 109-115 and receive elements 125-131.

In order to compensate for these responses, it is necessary to first measure the responses of each path, and the base station of FIG. 1 comprises a calibration processor 135 which determines a response for each of the transmit elements 109-115 and each of the receive elements 125-131.

It will be appreciated that any suitable means of determining the response of the receive elements 125-131 and transmit elements 109-115 may be used and that a number of different approaches will be known to the skilled person.

For example, a calibration transceiver may be coupled to each of the antenna elements 101-107 (e.g. for each

CE17159N4V antenna element 101-107 a sensor may be electromagnetically coupled to the feed line of the antenna element 101-107) . A known signal may then be fed phase aligned to all transmit elements 109-115 and the calibration transceiver can measure the resulting phase and gain of the signals fed to the individual antenna elements. These values can then be fed to the calibration processor 135 which determines a transmit path response for each transmit element 109-115. Similarly, the calibration transceiver can inject the same phase aligned signal to all receive elements 125-131 via the electromagnetic coupling to the antenna element feed line. The resulting receive path response for each receive element 125-131 is then determined by the calibration processor 135. The transmit and receive path responses can specifically be determined as a gain and phase for each transmit element 109-115 and receive element 125-131. The gain and phase are in the specific example represented as a calibration coefficient in the form of a complex value for each element.

In the Eigen beamforming algorithm, a spatial correlation matrix is calculated and one or more Eigen vectors are then determined for this correlation matrix.

Conventionally, compensation for the receive and transmit path responses is performed by an element-wise multiplication of the responses represented by the transmit and receive calibration coefficients and the received signal vector prior to the generation of the spatial correlation matrix estimate. Specifically, a compensated propagation channel response is calculated from:

CE17159N4V x^zΘc

where z is the received signal vector (comprising a complex base band sample for each antenna element) , c is a vector comprising the calibration coefficients (one complex value for each antenna element) and ® denotes element wise multiplication. For an OFDM system there may be one such vector per sub-carrier and per OFDM symbol, and c is calculated per sub-carrier (or per group of sub- carriers) .

The compensated response x comprises a compensation for both the receive and transmit paths and is typically calculated as:

where H_Tx and H_11x are the measured responses of the transmit paths and receive paths respectively. Note that H_Tx and H_11x may be normalized e.g. such that the first element of each is equal to unity. The spatial correlation matrix is then calculated from x as:

R_xx == ∑> x x

where x^H denotes x transposed and conjugated and ^• denotes normal vector multiplication. The summation may be performed over time (e.g. OFDM symbols in an OFDM system), over frequency (e.g. sub-carriers in an OFDM system), or a combination of both.

CE17159N4V For Eigen-beamforming the weight vector is then determined as the complex conjugate of the eigenvector corresponding to the largest Eigenvalue of R_xx, This value is typically found by using a power iteration algorithm as known to the skilled person.

However, the inventor of the current invention has realised that this approach tends to lead to suboptimal performance and in particular that the conventional approach tends to lead to determination of suboptimal antenna weights and thus to degraded communication performance of the base station and communication system as a whole.

As will be described in the following, the beamforming processor 133 of the base station of FIG. 1 uses a different approach to compensating for the responses of the receive elements 125-131 and transmit elements 109- 115 which leads to improved beamforming weights and thus improved performance of the base station and communication system as a whole. Furthermore, low complexity is maintained thereby allowing easy implementation .

FIG. 2 illustrates functional elements of the beamforming processor 133. In the example, the base station is an OFDM base station and as will be described in the following, the process is repeated individually for each subcarrier of the OFDM signals. Thus, transmit path responses and receive path responses are individually determined for each individual sub-channel (or per group of sub-channels) . For each user the propagation channel

CE17159N4V responses may be determined from all or a sub-set of subchannels assigned to the user. The antenna weights are specific to each user and may be common for all sub- carriers or for groups of sub-channels assigned to the user. All of the responses and antenna weights are calculated as a single complex value which is constant for at least one antenna weight update interval.

The beamforming processor 133 comprises a receive response processor 201 which determines a receive path response for each of the receive elements 125-131. Similarly, the beamforming processor 133 comprises a transmit response processor 203 which determines a transmit path response for each of the transmit elements 109-115. In the example, the receive response processor 201 and the transmit response processor 203 simply receive the complex calibration coefficients which reflect the individual receive and transmit path response from the calibration processor 135. However, it will be appreciated that any suitable way of determining the response may be used and that the functionality described with reference to the calibration processor 135 may e.g. be implemented in the receive response processor 201 and transmit response processor 203.

The beamforming processor 133 furthermore comprises a channel response processor 205 which generates an estimate of the channel response of the propagation channel between each of the antenna elements 101-107 and the antenna of the remote station. In the example, the uplink transmissions from the remote station are used to determine the downlink response. As the system uses TDD communication, the downlink channel response is simply

CE17159N4V determined from an assumption of reciprocity between the uplink and downlink channel.

Thus, for each antenna element, the channel response processor 205 receives the received complex base band signal from the remote station and from this it calculates the downlink propagation channel response (for each antenna element) . This process is performed for all or for a subset of OFDM subcarriers assigned to each user. In the example, one of the antenna elements 101 is used as a reference antenna element and the channel response for other antenna elements 103-107 is referenced to this reference antenna element 101. This substantially facilitates operation as it removes the necessity of determining absolute phase/amplitude values in favour of determining relative phase/amplitude values. For example, as the same transmitted signal is received by all antenna elements 101-107, the relative complex value channel response for the antenna elements 103-107 can simply be determined by comparing the received complex base band sample (s) of the individual antenna elements 103-107 with that of the reference antenna element 101. Alternatively the complex value channel response for the antenna elements 103-107 can simply be the unmodified received complex base band sample (s) of the individual antenna elements 103-107.

The receive response processor 201 and the channel response processor 205 are coupled to a receive compensation processor 207 which receives the determined channel responses and receive path responses for all antenna elements 101-107 and subcarriers. The receive compensation processor 207 then, for each antenna element

CE17159N4V 101-107 and subcarrier, compensates the determined channel response for the receive path response in order to generate compensated channel responses. However, the compensation prior to applying the Eigen beamforming algorithm is purely for the response of the receive elements 125-131 and does not include any compensation for the responses of the transmit elements 109-115.

Specifically, the receive compensation processor 207 generates the compensated channel response for each antenna element 101-107 in response to a division of the channel response for the antenna element 101-107 by the receive path response for the antenna element 101-107 for the subcarrier (s) corresponding to the channel response. Furthermore, the receive response processor 201 may normalise the receive path response for each receive element 127-131 relative to a receive path response for the reference antenna element 101. Thus, the responses of the receive elements 127-131 may be determined relative to the response of a reference receive element 125.

In the example, the receive compensation processor 207 determines the compensated channel by applying the following formula for each channel response and associated subcarrier:

where z is a vector comprising the channel responses, H_11x is a vector comprising the receive path responses,

CE17159N4V H_11x is the receive path response for a reference antenna element of the plurality of antenna elements and(÷)denotes element-wise division.

Thus, representing the channel response index by k, the receive compensation processor 207 calculates the following for all values of k:

The receive compensation processor 207 is fed to an Eigen beamforming processor 209 which determines the beamforming weights for the antenna elements 101-107 by performing an Eigen-beamforming based on the compensated channel responses.

Specifically, the Eigen beamforming processor 209 calculates a spatial correlation matrix from the compensated channel responses. In the specific example, a spatial correlation matrix is calculated for each OFDM subcarrier :

where N is the total number of channel responses processed. The N channel responses may be obtained over all subcarriers assigned to the user in the uplink, or over multiple groups of sub-carriers, as well as over time. In this way there may be a single spatial correlation matrix and a single weight which is applied

CE17159N4V over all subcarriers assigned to a user in the downlink. As another example, multiple spatial correlation matrices may be calculated for a user in which case there will be multiple weights, each corresponding to a group of sub- carriers .

For each spatial correlation matrix, the Eigen beamforming processor 209 then proceeds to determine the beamforming weights. Specifically, the beamforming weights are components of a beamforming vector given as the complex conjugate of the Eigenvector which corresponds to the largest Eigenvalue of R_xx (the so called Principal Eigenvector) . The Principal Eigenvector can specifically be found using the well-known power iteration method. The power iteration method is an iterative procedure, an example of which is described in the following equations in the case of 4 antennas:

χ = R_»v_B

^V«₊l =

The operation of this algorithm will be well known to the person skilled in the art and will for brevity not be described in further detail.

It will be known to those skilled in the art that the complex conjugate operations may be performed in a number of alternative ways e.g. x(k) may be conjugated prior to estimating the spatial correlation matrix in which case the beamforming weight equals the Principal Eigenvector.

The Eigen beamforming processor 209 is coupled to a transmit compensation processor 211 which is further

CE17159N4V coupled to the transmit response processor 203. The transmit compensation processor 211 receives the determined beamforming weights and the transmit path responses and compensates for the transmit path responses by modifying the beamforming weights in response thereto.

Specifically, each weight is compensated for the response of the transmit element 109-115 which is associated with the antenna element to which the beamform weight applies.

The transmit compensation processor 211 generates the compensated beamform weight for each antenna element in response to a multiplication of the beamforming weight for the first antenna element and a transmit path response for the first antenna element. As the compensation is intended to compensate for the following phase shift of the transmit element 109-115, the transmit path response used is the conjugate of the response measured for the transmit elements 109-115. This is done individually for each subcarrier to be used for the signal transmission using the beamforming weights.

Thus a very simple to implement yet highly accurate and reliable transmit path compensation is achieved. The described approach provides for the use of a simple multiplication applied directly to the beamforming weights without requiring e.g. complex divisions to be applied. The direct multiplication of the transmit path response value and the beamform weights furthermore provide a highly efficient compensation for the impact of the different transmit path responses on the transmitted signal and thus results in improved beamforming.

CE17159N4V Furthermore, the transmit response processor 203 may normalise the transmit path response for each transmit element 111-115 relative to a transmit path response for the reference antenna element 101. Thus, the responses of the transmit elements 111-115 may be determined relative to the response of a reference transmit element 109.

In the specific example, the transmit compensation processor 211 generates a vector, u, which comprises compensated beamforming weights from:

where v is a vector representing the beamforming weights (specifically the conjugate of the principal eigenvector v) , H_Tx is a vector comprising the transmit path responses, I H_Tx I is the transmit path response for a reference antenna element of the plurality of antenna elements, ^* indicates a conjugate value and Vindicates a bitwise multiplication .

Thus, representing the subcarrier by k, the transmit compensation processor 211 calculates the following for all values of k to be used with beamforming weight v for transmission by this user :

CE17159N4V In case that multiple spatial correlation matrices and multiple beamforming weight sets v are calculated for a user, then there would be one such equation per weight set v.

It will be known to those skilled in the art that the complex conjugate operations may be performed in a number of alternative ways e.g. the conjugates on the right hand side of the equation above could be removed and replaced with a conjugate applied to the left hand side of the equation, in which case a further conjugation step would be required to calculate the final compensated beamforming weights u(k).

In some embodiments, the weights comprised in the vectors u(k) may be used directly. Thus, these vectors may be fed to the transmit elements 109-115 where the complex base band samples of the signal to be transmitted (in the specific example the OFDM subcarrier symbols) are multiplied by the corresponding beamform weight before being up-converted.

However, in the specific example, the beamforming weights are normalised such that the weights correspond to a combined nominal gain for the antenna array. Thus, the beamforming weights are normalised such that the effective transmit gain is independent of the beamforming calculation. In the example, the absolute value of the weights are scaled such that the overall gain of the weights corresponds to a predetermined value (i.e. to a nominal gain) . This may substantially facilitate

CE17159N4V implementation and may for example reduce or eliminate transmit power fluctuations faster than the speed of a potential power control loop.

In the specific example, the transmit compensation processor 211 normalises the beamforming weights by, for each subcarrier k, calculating the vector:

The coefficients of w(k) are then fed to the transmit elements 109-115 where they are applied as beamforming weights .

In some embodiments, the transmit compensation processor 211 normalises each individual beamforming weight such that it corresponds to a nominal gain for each antenna element. Thus, in such embodiments, the calculated compensated weight is scaled such that the amplitude/power of each weight is always maintained constant and only the phase is modified. This may ensure that the beamforming is still in the right direction (i.e. that the transmitted signals tend to be received coherently at the remote station antenna) while e.g. facilitating implementation as a reduced dynamic range is required for each of the transmit elements 109-115 and in particular for the power amplifiers of such elements.

Thus, the beamforming approach of the beamforming processor 133 uses a two-stage compensation approach wherein the receive path response compensation in the form of a division by the measured receive path response

CE17159N4V is applied to the propagation channel responses and the transmit path compensation is applied to the calculated beamforming weights in the form of a multiplication by the conjugate of the measured transmit path response. Thus, in the approach the receive elements are compensated prior to applying the Eigen beamforming whereas the transmit elements are compensated after the Eigen beamforming.

The inventor has realised that for Eigen beamforming such a compensation approach provides improved performance. Specifically, the Eigenvalues and Eigenvectors of the spatial correlation matrix R_xx are a function of the spatial channel alone, rather then a function of the combined channel and transmit responses. As a result the spread of Eigenvalues is reduced leading to more energy being concentrated in the principal Eigenvector. Accordingly, an improved beamforming and communication is achieved.

FIG. 3 illustrates an example of the performance of the described beamforming relative to the prior art approach. FIG. 3 specifically illustrates simulation results for a WiMAX™ pedestrian B channel model with zero angular spread. The solid lines represent the prior art, while the dashed lines (labelled EBF2) represent the described approach. The performance is shown relative to that of an ideal Maximum Ratio Transmission (ideal in the sense of signal to noise ratio and calibration) . As can be seen the described approach significantly outperforms the prior art approach.

CE17159N4V FIG. 4 illustrates an example of a method of determining beamforming weights for an antenna array in accordance with some embodiments of the invention. The antenna array comprises a plurality of antenna elements with each antenna element having an associated transmit element and receive element.

The method initiates in step 401 wherein a receive path response is determined for each receive element.

Step 401 is followed by step 403 wherein a transmit path response is determined for each transmit element.

Step 403 is followed by step 405 wherein a channel response is estimated for the propagation channel between each of the plurality of antenna elements and a remote station in response to a signal received from the remote station .

Step 405 is followed by step 407 wherein the channel response for each antenna element is compensated by the receive path response for the antenna element to generate compensated channel responses for the plurality of antenna elements. Specifically, the compensation may be by a division of a channel response for each antenna element by the receive path response for each receive element .

Step 407 is followed by step 409 wherein beamforming weights for the plurality of antenna elements are determined by performing an Eigen-beamforming in response to the compensated channel responses.

CE17159N4V Step 409 is followed by step 411 wherein each beamforming weight for the plurality of antenna elements is modified in response to a multiplication of the beamforming weight and a complex conjugate of the transmit path response for each antenna element.

In the previous description, references to specific signals and values are described with reference to a specific implementation. However, it will be appreciated that depending on the specific implementation the described signals may be represented by corresponding representations of the signals. For example, as appropriate the reference to a complex value may include a reference to the complex conjugate of that value as appropriate.

It will be appreciated that the above description for clarity has described embodiments of the invention with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units or processors may be used without detracting from the invention. For example, functionality illustrated to be performed by separate processors or controllers may be performed by the same processor or controllers. Hence, references to specific functional units are only to be seen as references to suitable means for providing the described functionality rather than indicative of a strict logical or physical structure or organization.

The invention can be implemented in any suitable form including hardware, software, firmware or any combination

CE17159N4V of these. The invention may optionally be implemented at least partly as computer software running on one or more data processors and/or digital signal processors. The elements and components of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way. Indeed the functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. As such, the invention may be implemented in a single unit or may be physically and functionally distributed between different units and processors .

Although the present invention has been described in connection with some embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the accompanying claims. Additionally, although a feature may appear to be described in connection with particular embodiments, one skilled in the art would recognize that various features of the described embodiments may be combined in accordance with the invention. In the claims, the term comprising does not exclude the presence of other elements or steps.

Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by e.g. a single unit or processor. Additionally, although individual features may be included in different claims, these may possibly be advantageously combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. Also the inclusion of a feature in one category of claims does not imply a limitation to this

CE17159N4V category but rather indicates that the feature is equally applicable to other claim categories as appropriate. Furthermore, the order of features in the claims does not imply any specific order in which the features must be worked and in particular the order of individual steps in a method claim does not imply that the steps must be performed in this order. Rather, the steps may be performed in any suitable order.

CE17159N4V

Claims

1. An apparatus for determining beamforming weights for an antenna array comprising a plurality of antenna elements with each antenna element having an associated transmit element and receive element, the apparatus comprising : first means for determining a receive path response for each receive element associated with one of the plurality of antenna elements; second means for determining a transmit path response for each transmit element associated with one of the plurality of antenna elements; means for estimating a channel response for each propagation channel between one of the plurality of antenna elements and a remote station in response to a signal received from the remote station; first compensating means for compensating the channel response for each antenna element by the receive path response for the antenna element to generate compensated channel responses for the plurality of antenna elements; beamforming means for determining beamforming weights for the plurality of antenna elements by performing Eigen-beamforming in response to the compensated channel responses; and second compensating means for modifying the beamforming weight for each antenna element in response to a multiplication of the beamforming weight and a complex conjugate of the transmit path response for each antenna element.

CE17159N4V

2. The apparatus of claim 1 further comprising means for adjusting an amplitude of the beamforming weights to correspond to a combined nominal gain for the antenna array.

3. The apparatus of claim 1 further comprising means for adjusting an amplitude of the beamforming weights to correspond to a nominal gain for each antenna element.

4. The apparatus of claim 1 wherein the first means is arranged to normalise the receive path response for each receive element relative to a receive path response of a first of the receive elements.

5. The apparatus of claim 1 wherein the second means is arranged to normalise the transmit path response for each transmit element relative to a transmit path response of a first of the transmit elements.

6. The apparatus of claim 1 arranged to determine the beamforming weights for a single subcarrier of an Orthogonal Frequency Division Multiplex, OFDM, signals.

7. The apparatus of claim 1 wherein the antenna array is arranged to support a time division duplex communication wherein the signal received from the remote station is an uplink signal and the beamforming weights are downlink beamforming weights.

8. The apparatus of claim 1 wherein the beamforming means is arranged to determine a spatial correlation matrix from the compensated channel responses of each

CE17159N4V antenna element and to determine the beamforming weights in response to the spatial correlation matrix.

9. The apparatus of claim 1 wherein each of the receive path responses, each of the transmit path responses, each of the channel responses, and each of the beamforming weights are represented by a single complex value.

10. The apparatus of claim 1 wherein the first compensating means is arranged to generate a compensated channel response for a first antenna element in response to a division of a channel response for the first antenna element by a receive path response for a receive element associated with the first antenna element.

11. The apparatus of claim 10 wherein the first compensating means is arranged to calculate a vector, x, comprising the compensated channel responses from:

Tn_11xI is a receive path response for a reference antenna element of the plurality of antenna elements and(÷)denotes element-wise division.

12. The apparatus of claim 1 wherein the second compensating means is arranged to calculate a vector, u, comprising compensated beamforming weights from:

CE17159N4V

where v is a vector comprising the beamforming weights, H_Tx is a vector comprising the transmit path responses,

a transmit path response for a reference antenna element of the plurality of antenna elements, ^* indicates a conjugate value and Vindicates a bitwise multiplication .

13. A method of determining beamforming weights for an antenna array comprising a plurality of antenna elements with each antenna element having an associated transmit element and receive element; the method comprising: determining a receive path response for each receive element associated with one of the plurality of antenna elements; determining a transmit path response for each transmit element associated with one of the plurality of antenna elements; estimating a channel response for each propagation channel between one of the plurality of antenna elements and a remote station in response to a signal received from the remote station; compensating the channel response for each antenna element by the receive path response for the antenna element to generate compensated channel responses for the plurality of antenna elements;

CE17159N4V determining beamforming weights for the plurality of antenna elements by performing Eigen-beamforming in response to the compensated channel responses; and modifying the beamforming weight for each antenna element in response to a multiplication of the beamforming weight and a complex conjugate of the transmit path response for each antenna element.

CE17159N4V