Method and system for quantization for a general beamforming matrix in feedback information

Aspects of a method and system for utilizing Givens rotation expressions for quantization for a general beamforming matrix in feedback information. In one aspect of the invention, feedback information is computed at the receiving MIMO wireless device based on a geometric mean decomposition (GMD) method. The feedback information may include a matrix that describes a wireless medium. The matrix may represent a multiplicative product of at least one rotation matrix and at least one diagonal phase rotation matrix. Each of the rotation matrices may include at least one matrix element whose value is based on Givens rotation angle. The transmitting MIMO wireless device may subsequently transmit a plurality of signals via the wireless medium based on the received matrix information. The signal strength and/or signal to noise ratio (SNR) measurement (as measured in decibels, for example) associated with each of the transmitted plurality of signals may be about equal.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to wireless communication. More specifically, certain embodiments of the invention relate to a method and system for quantization for a general beamforming matrix in feedback information.

BACKGROUND OF THE INVENTION

Multiple input multiple output (MIMO) systems are wireless communications systems that are specified in resolution 802.11 from the Institute of Electrical and Electronics Engineers (IEEE). A MIMO system that receives a signal Y may compute a channel estimate matrix, H, based on the received signal. The signal may comprise information generated from a plurality of information sources. Each such information source may be referred to as a spatial stream. A transmitting MIMO system may utilize a plurality of transmitting antennas when transmitting the signal Y. A receiving MIMO system may utilize a plurality of receiving antennas when receiving the signal Y. The channel estimate matrix for a downlink RF channel, Hdown, may describe a characteristic of the wireless transmission medium in the transmission path from a transmitter, to a receiver. The channel estimate for an uplink RF channel, Hup, may describe a characteristic of the wireless transmission medium in the transmission path from the receiver to the transmitter.

According to the principle of reciprocity, a characteristic of the wireless transmission medium in the transmission path from the transmitter to the receiver may be assumed to be identical to a corresponding characteristic of the wireless transmission medium in the transmission path from the receiver to the transmitter. However, the channel estimate matrix Hdownmay not be equal to a corresponding channel estimate matrix for an uplink RF channel Hup. For example, a noise level, for example an ambient noise level, in the vicinity of the transmitter may differ from a noise level in the vicinity of the receiver. Similarly, an interference level, for example electro-magnetic interference due to other electro-magnetic devices, in the vicinity of the transmitter may differ from an interference level in the vicinity of the receiver. At a transmitter, or receiver, there may also be electrical cross-coupling, for example leakage currents, between circuitry associated with a receiving antenna, or a transmitting antenna, and circuitry associated with another receiving antenna, or another transmitting antenna.

The principle of reciprocity, wherein it may be assumed that Hup=Hdown, may also be based on the assumption that specific antennas at a transmitter or receiver are assigned for use as transmitting antennas, and/or assigned for use as receiving antennas. At the transmitter, a number of receiving antennas, NRX, utilized at the receiver may be assumed. At the receiver, a number of transmitting antennas, NTX, utilized at the transmitter may be assumed. If the assignments of at least a portion of the antennas at the transmitter are changed, the corresponding channel estimate matrix H′upmay not be equal Hdown. Similarly, if the assignments of at least a portion of the antennas at the receiver are changed, the corresponding channel estimate matrix H′downmay not be equal Hup. Consequently, after reassignment of antennas at the transmitter and/or receiver, the principle of reciprocity may not be utilized to characterize communications between the transmitter and the receiver when Hupdoes not equal H′down, when H′updoes not equal Hdown, or when H′updoes not equal H′down.

The principle of reciprocity may enable a receiving wireless local area network (WLAN) device A to receive a signal Y from a transmitting WLAN device B, and to estimate a channel estimate matrix Hdownfor the transmission path from the transmitting WLAN device B to the receiving WLAN device A. Based on the channel estimate matrix Hdown, the WLAN device A may transmit a subsequent signal Y, via an uplink RF channel, to the WLAN device B based on the assumption that the channel estimate matrix Hupfor the transmission path from the transmitting WLAN device A to the receiving WLAN device B may be characterized by the relationship Hup=Hdown. When the WLAN devices A and B are MIMO systems, corresponding beamforming matrices may be configured and utilized for transmitting and/or receiving signals at each WLAN device.

Beamforming is a method for signal processing that may allow a transmitting MIMO system to combine a plurality of spatial streams in a transmitted signal Y. Beamforming is also a method for signal processing that may allow a receiving MMO system to separate individual spatial streams in a received signal Y.

As a result of a failure of an assumed condition for the principle of reciprocity, a beamforming matrix at the transmitting WLAN device, and/or a beamforming matrix at the receiving WLAN device, may be configured incorrectly. In a transmitted signal Y, from the perspective of a signal associated with an ithspatial stream, a signal associated with a jthspatial stream may represent interference or noise. Incorrect configuration of one or more beamforming matrices may reduce the ability of the receiving WLAN device to cancel interference between an ithspatial stream and a jthspatial stream. Consequently, the received signal Y may be characterized by reduced signal to noise ratios (SNR). There may also be an elevated packet error rate (PER) when the receiving WLAN device decodes information contained in the received signal Y. This may, in turn, result in a reduced information transfer rate, as measured in bits/second, for communications between the transmitting WLAN device and the receiving WLAN device.

In some MIMO systems, a transmitting WLAN device may transmit a plurality of spatial streams based on channel state information at the transmitter (CSIT). The CSIT may be based on feedback information sent from the receiving WLAN device B to the transmitting WLAN device A. Based on the CSIT, the transmitting WLAN device A may compute estimated values for the channel estimate matrix Hdown.

In a typical MIMO system, the transmitting WLAN device A may transmit a plurality of information bits simultaneously via the plurality of transmitting antennas. The transmitting WLAN device A may allocate a portion of the plurality of information bits for transmission via at least a portion of the plurality of transmitting antennas. Each allocated portion of information bits may be error correction coded to enable the receiving WLAN device B to correctly detect the binary values associated with each of the transmitted information bits in a received signal. A received bit for which the receiving WLAN device detects an incorrect binary value may be referred to as a bit error. The rate, as measured over a time duration at which bit errors occur, may be referred to as a bit error rate (BER).

In some MIMO systems, the spatial streams transmitted by the transmitting WLAN device A may be characterized by the bit error rate. An error correction coding method may be characterized by the number of error correction bits that are transmitted with a given number of information bits. The ratio of information bits to the total number of error correction and information bits may be referred to as a coding rate. Spatial streams that are transmitted by a transmitting WLAN device A utilizing larger values for the coding rate, may be associated with higher BERs at the receiving WLAN device B in comparison to spatial streams that are transmitted utilizing smaller values for the coding rate. A larger value for the coding rate may be referred to as a weak coding rate in comparison to a smaller value of the coding rate. The error correction coding may enable the receiving WLAN device B to reduce the BER.

In some MIMO systems that utilize CSIT, the signal strength and/or signal to noise ratio (SNR) may vary among the transmitted spatial streams. In such MIMO systems that utilize higher, or weaker, coding rates, the BER performance may not be acceptable.

BRIEF SUMMARY OF THE INVENTION

A system and/or method for utilizing Givens rotation expressions for quantization for a general beamforming matrix in feedback information, substantially as shown in and/or described in connection with at least one of the figures, as set forth more completely in the claims.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention relate to a method and system for quantization for a general beamforming matrix in feedback information. Various embodiments of the invention may be utilized to enable communications within wireless communications systems between a transmitting multiple input multiple output (MIMO) wireless device and a receiving MIMO wireless device. In one aspect of the invention, feedback information may be computed at the receiving MIMO wireless device based on signals received from the transmitting MIMO wireless device. Any of a plurality of beamforming methods, for example geometric mean decomposition (GMD) or singular value decomposition (SVD), may be utilized. The feedback information may comprise a matrix that describes a wireless medium. The matrix may represent a multiplicative product of at least one rotation matrix and at least one diagonal phase rotation matrix. Each of the rotation matrices may comprise at least one matrix element whose value is based on Givens rotation angle. The transmitting MIMO wireless device may subsequently transmit a plurality of signals via the wireless medium based on the received matrix information. The signal strength and/or signal to noise ratio (SNR) measurement (as measured in decibels, for example) associated with each of the transmitted plurality of signals may be about equal.

Various embodiments of the invention may exhibit improved bit error rate performance (BER) when utilizing weaker coding rates when compared to some conventional MIMO systems. As a result of improved BER performance, various embodiments of the invention may also enable higher information transfer rates between a transmitting MIMO wireless device and a receiving MIMO wireless device via a wireless medium.

Givens matrices may be utilized to reduce a quantity of information communicated in feedback information via an uplink RF channel. The feedback information may comprise specifications for a feedback beamforming matrix that may be utilized when transmitting signals via a corresponding downlink RF channel. The feedback beamforming matrix may represent a rotated version of an un-rotated beamforming matrix. The Givens matrices may be utilized to apply one or more Givens rotations to un-rotated beamforming matrix. The feedback beamforming matrix may be computed based on a matrix product of a plurality of Givens matrices. The feedback beamforming matrix may comprise comparable information content to the un-rotated beamforming matrix. The feedback beamforming matrix may be encoded utilizing fewer bits than may be required to encode the un-rotated beamforming matrix. Various embodiments of the invention may be utilized in wireless communications systems, including wireless data communications systems.

Feedback information may be utilized to reduce the likelihood that signals Y will be transmitted incorrectly during beamforming. Feedback comprises a mechanism by which a receiving WLAN device A may compute a channel estimate matrix Hdown. The computed channel estimate matrix may be utilized to compute feedback information that may be utilized by the WLAN device B to configure a beamforming matrix associated with the downlink RF channel. The feedback information may be communicated from the WLAN device A to the WLAN device B via the uplink RF channel. The feedback information may comprise a full description of the downlink RF channel. A full description of the downlink RF channel may comprise a frequency channel estimate for each subcarrier frequency associated with each spatial stream contained in the downlink RF channel. Each frequency channel estimate may be characterized in a Cartesian coordinate format, or in a polar coordinate format. In the Cartesian coordinate format, each frequency channel estimate may be represented as an in-phase (I) amplitude component, and a quadrature (Q) phase amplitude component. In the polar coordinate format, each frequency channel estimate may be represented as a magnitude (ρ) component, and an angle (θ) component.

In some conventional systems, a large quantity of feedback information may be communicated in the feedback direction. RF channel bandwidth that is dedicated for use in communicating feedback information may reduce the quantity of other types of information that may be communicated between the WLAN device A and the WLAN device B within a given time interval. The feedback information may be referred to as overhead within the uplink RF channel. The overhead may reduce the information transfer rate between the WLAN device A and the WLAN device B associated with non-feedback information.

FIG. 1is a block diagram of an exemplary system for wireless data communications, which may be utilized in connection with an embodiment of the invention. With reference toFIG. 1, there is shown a distribution system (DS)110, an extended service set (ESS)120, and an IEEE 802.x LAN122. The ESS120may comprise a first basic service set (BSS)102, and a second BSS112. The first BSS102may comprise a first 802.11 WLAN station104, a second 802.11 WLAN station106, and an access point (AP)108. The second BSS112may comprise a first 802.11 WLAN station114, a second 802.11 WLAN station116, and an access point (AP)118. The IEEE 802 LAN122may comprise a LAN station124, and a portal126. An IEEE 802.11 WLAN station, or IEEE 802.11 WLAN device, is a WLAN system that may be compliant with at least a portion of the IEEE 802.11 standard.

A WLAN is a communications networking environment that comprises a plurality of WLAN devices that may communicate wirelessly via one or more uplink and/or downlink RF channels. The BSS102or112may be part of an IEEE 802.11 WLAN that comprises at least 2 IEEE 802.11 WLAN stations, for example, the first 802.11 WLAN station104, the second 802.11 WLAN station106, and the AP108, which may be members of the BSS102. Non-AP stations within BSS102, the first 802.11 WLAN station104, and the second 802.11 WLAN station106, may individually form an association with the AP108. An AP, such as AP108, may be implemented as an Ethernet switch, bridge, or other device in a WLAN, for example. Similarly, non-AP stations within BSS112, the first 802.11 WLAN station114, and the second 802.11 WLAN station116, may individually form an association with the AP118. Once an association has been formed between a first 802.11 WLAN station104and an AP108, the AP108may communicate reachability information about the first 802.11 WLAN station104to other APs associated with the ESS120, such as AP118, and portals such as the portal126. The WLAN station104may subsequently communicate information wirelessly via the BSS102. In turn, the AP118may communicate reachability information about the first 802.11 WLAN station104to stations in BSS112. The portal126, which may be implemented as, for example, an Ethernet switch or other device in a LAN, may communicate reachability information about the first 802.11 WLAN station104to stations in LAN122such as the 802 LAN station124. The communication of reachability information about the first 802.11 WLAN station104may enable WLAN stations that are not in BSS102, but are associated with ESS120, to communicate wirelessly with the first 802.11 WLAN station104.

The DS110may provide an infrastructure which enables a first 802.11 WLAN station104in one BSS102, to communicate wirelessly with a first 802.11 WLAN station114in another BSS112. The DS110may also enable a first 802.11 WLAN station104in one BSS102to communicate with an 802 LAN station124in an IEEE 802 LAN122, implemented as, for example a wired LAN. The AP108, AP118, or portal126may provide a means by which a station in a BSS102, BSS112, or LAN122may communicate information via the DS110. The first 802.11 WLAN station104in BSS102may communicate information wirelessly to a first 802.11 WLAN station114in BSS112by transmitting the information wirelessly to AP108, which may transmit the information via the DS110to AP118, which in turn may transmit the information wirelessly to station114in BSS112. The first 802.11 WLAN station104may communicate information wirelessly to the 802 LAN station124in LAN122by transmitting the information wirelessly to AP108, which may transmit the information via the DS110to the portal126, which in turn may transmit the information to the 802 LAN station124in LAN122. The DS110may utilize wireless communications via an RF channel, wired communications, such as IEEE 802 Ethernet, or a combination thereof.

A WLAN station or AP may utilize one or more transmitting antennas, and one or more receiving antennas when communicating information. A WLAN station or AP that utilizes a plurality of transmitting antennas and/or a plurality of receiving antennas may be referred to as a multiple input multiple output (MIMO) system.

FIG. 2is a block diagram of an exemplary MIMO system that may be utilized in connection with an embodiment of the invention. With reference toFIG. 2there is shown a baseband processor272, a transceiver274, an RF front end280, a plurality of receiving antennas276a, . . . ,276n, and a plurality of transmitting antennas278a, . . . ,278n. The transceiver274may comprise a processor282, a receiver284, and a transmitter286.

The processor282may perform digital receiver and/or transmitter functions in accordance with applicable communications standards. These functions may comprise, but are not limited to, tasks performed at lower layers in a relevant protocol reference model. These tasks may further comprise the physical layer convergence procedure (PLCP), physical medium dependent (PMD) functions, and associated layer management functions. The baseband processor272may perform functions in accordance with applicable communications standards. These functions may comprise, but are not limited to, tasks related to analysis of data received via the receiver284, and tasks related to generating data to be transmitted via the transmitter286. These tasks may further comprise medium access control (MAC) layer functions as specified by pertinent standards.

The receiver284may perform digital receiver functions that may comprise, but are not limited to, fast Fourier transform processing, beamforming processing, equalization, demapping, demodulation control, deinterleaving, depuncture, and decoding. The transmitter286may perform digital transmitter functions that comprise, but are not limited to, coding, puncture, interleaving, mapping, modulation control, inverse fast Fourier transform processing, beamforming processing. The RF front end280may receive analog RF signals via antennas276a, . . . ,276n, converting the RF signal to baseband and generating a digital equivalent of the received analog baseband signal. The digital representation may be a complex quantity comprising I and Q components. The RF front end280may also transmit analog RF signals via an antenna278a, . . . ,278n, converting a digital baseband signal to an analog RF signal.

In operation, the processor282may receive data from the receiver284. The processor282may communicate received data to the baseband processor272for analysis and further processing. The baseband processor272may generate data to be transmitted via an RF channel by the transmitter286. The baseband processor272may communicate the data to the processor282. The processor282may generate a plurality of bits that are communicated to the receiver284. The processor282may generate signals to control the operation of the modulation process in the transmitter286, and of the demodulation process in the receiver284.

FIG. 3Ais an exemplary diagram illustrating beamforming that may be utilized in connection with an embodiment of the invention. Referring toFIG. 3Athere is shown a transmitting mobile terminal302, a receiving mobile terminal322, and a plurality of RF channels342. The transmitting mobile terminal302comprises a transmit filter coefficient block V304, a first source signal s1306, a second source signal s2308, a third source signal s3310, and a plurality of transmitting antenna312,314, and316. The receiving mobile terminal322comprises a receive filter coefficient block U*324, a first destination signal ŝ1326, a second destination signal ŝ2328, a third destination signal ŝ3330, and a plurality of receiving antenna332,334, and336. An exemplary mobile terminal may be a WLAN station104, for example. A corresponding matrix V may be associated with the transmit filter coefficient block V304. A corresponding matrix U* may be associated with the receive filter coefficient block U*324. The matrices V and U* may be utilized in connection with beamforming.

In operation, the transmitting antenna312may enable transmission of a signal x1, the transmitting antenna314may enable transmission of a signal x2, and the transmitting antenna316may enable transmission of a signal x3. In a beamforming operation, each of the transmitted signals x1, x2, and x3may be a function of a weighted summation of at least one of the plurality of the source signals s1, s2, and s3. The weights may be determined by the beamforming V matrix such that:
X=VSSequation[1a]
where X may be a 3×1 vector representation of the transmitted signals x1, x2, and x3, for example:

X=[x1x2x3]equation⁢[1⁢b]
SSmay be a 3×1 vector representation of the source signals s1, s2, and s3, for example:

SS=[s1s2s3]equation⁢[1⁢c]
and V may be a 3×3 matrix representation of the beamforming V matrix, for example:

The receiving antenna332may receive a signal y1, the receiving antenna334may receive a signal y2, and the receiving antenna336may receive a signal y3. The plurality of RF channels342may be characterized mathematically by a transfer coefficient matrix H. The transfer coefficient matrix H may also be referred to as a channel estimate matrix.

The plurality of received signals y1, y2, y3, may be expressed as a function of the plurality of transmitted signals x1, x2, x3, and the transfer coefficient matrix H in the following equation, for example:
Y=HX+Nequation[2a]
where Y may be a 3×1 vector representation of the received signals y1, y2, and y3, for example:

Y=[y1y2y3]equation⁢[2⁢b]
H may be a 3×3 matrix representation of the transfer coefficient matrix, for example:

H=[h11h12h13h21h22h23h31h32h33]equation⁢[2⁢c]
and N may be a 3×1 vector representation of noise that may exist in the communications medium, for example:

When utilizing singular value decomposition (SVD), the matrix H from equation[2a] may be represented as in the following equation:
H={tilde under (U)}S{tilde under (V)}*  equation[3a]
where {tilde under (U)} may represent a column orthogonal matrix, {tilde under (V)}* may represent an Hermitian transpose of an orthogonal matrix {tilde under (V)}, and S may represent a diagonal matrix, for example. The matrix S may comprise a plurality of nonzero matrix diagonal elements, the values of which may correspond to at least a portion of singular values associated with the matrix H.

A matrix V may be represented according to the following equation:
V={tilde under (V)}{tilde under (D)}  equation[3b]
where {tilde under (D)} may represent a diagonal steering matrix. The matrix V may represent a rotated version of the matrix {tilde under (V)}. Each of the rows within the matrix {tilde under (V)} may comprise one or more matrix elements that may each be represented as a complex number. The matrix may {tilde under (D)} rotate the matrix {tilde under (V)} such that the last row of the matrix V may comprise a corresponding number of matrix elements, each of which may be represented as a real number. The matrix V may be referred to as being phase invariant based on the equation[3b].

A matrix U may be similarly represented by a matrix multiplication product of the matrix {tilde under (U)}, and the steering matrix {tilde under (D)}. The equation[3a] may be represented:
H={tilde under (U)}{tilde under (D)}S {tilde under (D)}*{tilde under (V)}*equation[4]

Various embodiments of the invention may utilize decomposition methods other than SVD. The embodiments may include utilizing methods based on geometric mean decomposition (GMD), for example. When utilizing GMD, the matrix S may be represented as in the following equation:
S=QRP*equation[5]
where matrices Q and P may represent column orthogonal matrices, and the matrix R may represent an upper diagonal matrix. The matrix elements associated with the matrix R may each be represented as a real number. Values associated with each of the diagonal matrix elements in the matrix R may be equal such that rii=rjj, where riimay represent an ithdiagonal matrix element and rjjmay represent a value associated with a jthdiagonal matrix element. The value associated with a diagonal matrix element may be about equal to a geometric mean value for at least a portion of the singular values associated with the matrix S. When utilizing GMD, one representation of the equation[3a] may be as shown in the following equation:
H={tilde under (U)}Q{tilde under (D)}R{tilde under (D)}*P*{tilde under (V)}*equation[6a]
where the beamforming V matrix may be defined:
V={tilde under (V)} P{tilde under (D)}  equation[6b]
and the beamforming U matrix may be defined:
U={tilde under (U)}Q{tilde under (D)}  equation[6c]

In the equation[6a], the matrix S, from equation[3a] may be equal to the matrix multiplication product Q{tilde under (D)}R{tilde under (D)}*P*. This product may further be represented as the matrix R, a matrix multiplication product Q{tilde under (D)} and a matrix multiplication product {tilde under (D)}*P*. The matrix multiplication product {tilde under (D)}*P* may represent a rotated version of the matrix P*. However, the matrix P, as represented in equations [5] and [6a], may not possess a property of phase invariance that would ensure that a matrix computed based on the matrix multiplication product {tilde under (D)}R{tilde under (D)}* is a real-valued matrix. Consequently, the matrix computed based on the matrix multiplication product {tilde under (D)}R{tilde under (D)}* from equation[6a] may comprise one or more matrix elements, the values of which may each be represented as a complex number.

When utilizing GMD, another representation of the equation[3a] may be as shown in the following equation:
H={tilde under (U)}{tilde under (D)}QRP*{tilde under (D)}*{tilde under (V)}*equation[6d]

In the equation[6d], the matrix H may be represented as a matrix multiplication product of the matrix multiplication product QRP*, the matrix multiplication product {tilde under (U)}{tilde under (D)}, and the matrix multiplication product {tilde under (D)}*{tilde under (V)}*. The matrix multiplication product {tilde under (D)}*{tilde under (V)}* may possess the phase invariant property as indicated in equation[3b]. As a result, the matrix R in equation[6d] may comprise matrix elements, the values of which may each be represented as a real number.

Various metrics may be defined based on equation[6d]. One metric may be based on the matrix multiplication product P*{tilde under (D)}*{tilde under (V)}*. This metric may be utilized in connection with the matrix V this is associated with the transmit filter coefficient block V304as in the following equation:
V={tilde under (V)}{tilde under (D)}P  equation[7a]
where the matrix {tilde under (V)}{tilde under (D)}P may be derived based on the matrix multiplication product P*{tilde under (D)}*{tilde under (V)}*.

Another metric may be based on the matrix multiplication product {tilde under (U)}{tilde under (D)}Q This metric may be utilized in connection with the matrix U*, associated with the receive filter coefficient block U*324as in the following equation:
U*=Q*{tilde under (D)}*{tilde under (U)}*equation[7b]
where the matrix Q*{tilde under (D)}*{tilde under (U)}* may be derived based on the matrix multiplication product {tilde under (U)}{tilde under (D)}Q.

In various embodiments of the invention, the metric {tilde under (V)}{tilde under (D)}P may be utilized by a receiver322for sending channel feedback information to a transmitter302. The metric {tilde under (V)}{tilde under (D)}P may be computed based on the matrix multiplication product P*{tilde under (D)}*{tilde under (V)}*. The transmitter302may utilize the feedback information when transmitting subsequent signals to the receiver322. Based on the matrix V, as in equation[7a], the transmitter302may transmit subsequent spatial streams s1, s2, and s3such that the signals transmitted via the corresponding transmitting antennas312,314, and316are each characterized by approximately equal signal strength and/or SNR measurements. A signal strength and/or SNR may be measured in decibels (dB), for example. The metric {tilde under (U)}{tilde under (D)}Q may be utilized at the receiver322when receiving the subsequent signals transmitted by the transmitter302.

In a MIMO system that utilizes beamforming as shown inFIG. 3A, the values associated with the matrices V, H, and U* may be such that the value of the transmitted signal simay be approximately equal to the value of the corresponding received signal ŝi, where the index i may indicate an ithspatial stream. In various embodiments of the invention that utilize GMD, the matrix V, associated with the transmit filter coefficient block V304, may be computed based on the metric {tilde under (V)}{tilde under (D)}P, and the matrix U*, associated with the receive filter coefficient block U*324, may be computed based on the metric {tilde under (U)}{tilde under (D)}Q as shown in equations [7a] and [7b]. The receiver322may compute a channel estimate, Hdown, for a downlink RF channel based on a received signal from the transmitter302. The transmitter302may compute a channel estimate, Hup, for an uplink RF channel based on a received signal from the receiver322. The transmit filter coefficient block V304may set values associated with the matrix V, utilized for communications via the downlink RF channel, based on the channel estimate Hup.

When the receiver322sends feedback information to the transmitter302via the uplink RF channel, the receiver322may compute values associated with a matrix V that may be based on the channel estimate Hdown. The receiver322may subsequently communicate the computed matrix V to the transmitter302via the uplink RF channel. The transmitter302may subsequently set values associated with the matrix V, utilized for communications via the downlink RF channel, based on the channel estimate Hdown.

FIG. 3Bis an exemplary diagram illustrating channel feedback, which may be utilized in connection with an embodiment of the invention. Referring toFIG. 3B, there is shown a transmitting mobile terminal302, a receiving mobile terminal322, and a communications medium344. The communications medium344may represent a wireless communications medium. The transmitting mobile terminal302may transmit a signal vector X to the receiving mobile terminal322via the communications medium344. The communications direction from the transmitting mobile terminal302to the receiving mobile terminal322may be referred to as a downlink direction. The signal vector X may comprise a plurality of spatial streams simultaneously transmitted via transmitting antennas312,314and316, for example. The signal vector X may be beamformed by the transmitting mobile terminal302based on a beamforming matrix V. The signal vector X may travel through the communications medium344. The signal vector X may be altered while traveling through the communications medium344. The transmission characteristics associated with the communications medium344may be characterized by a transfer function H. The signal vector X may be altered based on the transfer function H. In the downlink direction, the transfer function H may be referred to as Hdown. The altered signal vector X may be represented as the signal Y. The receiving mobile terminal322may receive the signal Y. The receiving mobile terminal322may determine one or more values associated with the transfer function Hdownbased on the signal Y received via the communications medium344.

The receiving mobile terminal322may compute one or more values associated with a matrix V based on the information related to the transfer function Hdown. The receiving mobile terminal322may communicate information related to the matrix V to the transmitting mobile terminal302as feedback information. The feedback information (Hdown) may represent feedback information based on the information related to the transfer function Hdown. The receiving mobile terminal322may communicate the feedback information (Hdown) via a transmitted signal vector Xf. The transmitted signal vector Xfmay be transmitted to the transmitting mobile terminal302via the communications medium344. The signal vector Xfmay be altered while traveling through the communications medium344. The communications direction from the receiving mobile terminal322to the transmitting mobile terminal302may be referred to as an uplink direction. The signal vector Xfmay be altered based on the transfer function H. In the uplink direction, the transfer function H may be referred to as Hup. The altered signal vector Xfmay be represented as the signal Yf. The transmitting mobile terminal302may receive the signal Yf.

The transmitting mobile terminal302may determine one or more values associated with the transfer function Hupbased on the signal Yfreceived via the communications medium344. The transmitting mobile terminal302may utilize the received feedback information (Hdown) to beamform subsequent signal vectors X, which may be transmitted in the downlink direction from the transmitting mobile terminal302to the receiving mobile terminal322.

Various embodiments of the invention may reduce the quantity of feedback information that may be communicated from the receiver322to the transmitter302via the uplink RF channel. In one aspect of the invention, the computed metric {tilde under (V)}{tilde under (D)}P may be represented based on a product of Givens matrices:
V=G1(ψ1)G2(ψ2)D1(φ1,φ2, . . . , φN)  equation[8]
where Gj(ψj) may represent a Givens matrix associated with a rotation angle ψj, and D1(φk) may represent a diagonal matrix with phase shift angles φk.

The feedback information communicated by the receiver322may comprise encoded rotation angles ψj. The transmitter302may utilize the encoded rotation angles to reconstruct the matrix V based on the feedback information.

FIG. 3Cis an exemplary diagram illustrating a system for GMD beamforming, in accordance with an embodiment of the invention. Referring toFIG. 3Cthere is shown a transmitting mobile terminal302, a receiving mobile terminal352, and a plurality of RF channels342. The transmitting mobile terminal302comprises a transmit filter coefficient block V304, a first source signal s1306, a second source signal s2308, a third source signal s3310, and a plurality of transmitting antenna312,314, and316. The receiving mobile terminal352comprises a receive filter coefficient block U*324, a plurality of receiving antenna332,334, and336, a scaled slicer block362, and a matrix subtraction block364.

The scaled slicer block362may enable detection of a received estimated signal ŝi, where the index i may represent an ithreceived signal among a plurality of signals received simultaneously from the transmitter302. The scale factor utilized by the scaled slicer block362may be based on a value associated with a diagonal matrix element from the upper triangular matrix R. The matrix R may be defined as in connection with equation[5]. The group of received signals ŝimay be represented as a received signal vector ŜR. The matrix subtraction block364may enable cancellation of a detected component signal ŝifrom the signal vector ŜR. The matrix subtraction block364may subtract a value corresponding to a diagonal matrix element riifrom the upper triangular matrix R. The value associated with each diagonal matrix element riimay be about equal.

An exemplary N×N upper triangular matrix R may be represented as follows:

In operation, the receiving mobile terminal352may compute estimates for the individual destination signals, ŝi, in the vector ŜRbased on a zero forcing (ZF) approach. The loop comprising the scaled slicer block362, matrix subtraction block364, and receive filter coefficient block U*324may implement a solution for the individual destination signals based on ZF as in the following equation:
Z=Ŷ−(R−diag(R))ŜRequation[10a]
where the N×1 column vector ŜR, may be represented as follows:

S^R=[s^1s^2⋮s^N]equation⁢[10⁢b]
and where Z is an N×1 column vector generated based on ZF, and diag(T) a version of the matrix T comprising the diagonal terms of the matrix T. The vector Ŷ may represent an N×1 column vector comprising a plurality of signals generated by the receive filter coefficient block U*324, which may be defined as in the following equation:
Ŷ=U*Yequation[11]
where Y may be as defined in equation[2a], and U* may be defined as in equation[7b], for example.

When solving for each of the individual destination signals, ŝi, the scaled slicer block362may compute estimated values for Q and I components associated with the individual destination signal. For an exemplary 3×3 matrix R, and 3×1 vectors Z, Ŷ, and ŜR:

By utilizing the scaled slicer block362, an estimated value for the individual destination signal, ŝ3, may be computed based on the value z3determined in equation[12b]. An estimated value for the individual destination signal, ŝ2, may be computed based on the value z2determined in equation[12c]. The value z2may be computed based on the estimated value for the individual destination signal, ŝ3. An estimated value for the individual destination signal, ŝ1, may be computed based on the value z1determined in equation[12d]. The value z1may be computed based on the estimated value for the individual destination signals, ŝ2and ŝ3.

FIG. 3Dis an exemplary diagram illustrating a system for GMD beamforming with decoding, in accordance with an embodiment of the invention. Referring toFIG. 3Dthere is shown a transmitting mobile terminal302, a receiving mobile terminal372, and a plurality of RF channels342. The transmitting mobile terminal302comprises a transmit filter coefficient block V304, a first source signal s1306, a second source signal s2308, a third source signal s3310, and a plurality of transmitting antenna312,314, and316. The receiving mobile terminal352comprises a receive filter coefficient block U*324, a plurality of receiving antenna332,334, and336, a scaled slicer block362, and a matrix subtraction block364. The transmitting mobile terminal302, and the plurality of RF channels342may be substantially as described inFIG. 3C. The transmit filter coefficient block V304, the first source signal s1306, the second source signal s2308, the third source signal s3310, and the plurality of transmitting antenna312,314, and316may be substantially as described inFIG. 3C. The receive filter coefficient block U*324, the plurality of receiving antenna332,334, and336, the scaled slicer block362, and the matrix subtraction block364may be substantially as described inFIG. 3C.FIG. 3Dalso shows a demapper block374, a decoder block376, an encoder block378, and a mapper block380.

The demapper block374may enable transformation of a signal comprising Q and I components to a point within a constellation map. The point within the constellation map may correspond to a binary representation of the transformed signal. The transformation may be based on a demodulation technique. The binary representation may comprise encoded information.

The decoder block376may enable decoding of encoded information and subsequent generation of binary information. The decoding may enable the detection and/or correction of bit errors in the encoded information when generating the binary information.

The encoder block378may enable encoding of binary information and subsequent generation of encoded information.

The mapper block380may enable transformation of encoded information into a signal comprising Q and I components. The encoded information may be transformed into a representation comprising one or more symbols, wherein each symbol may correspond, or map, to a point within a constellation map. The symbols may be utilized to generate corresponding Q and I components. The transformation may be based on a modulation technique.

In operation, the receiving mobile terminal372may compute estimates for the individual destination signals, ŝi, in the vector ŜRbased on a zero forcing (ZF) approach. The loop comprising the scaled slicer block362, demapper block374, decoder block376, encoder block378, mapper block380, matrix subtraction block364, and receive filter coefficient block U*324may implement a solution for the individual destination signals based on ZF as in equation[10a]. The mapper block may be utilized to generate a corresponding vector ŜR′ based on the vector ŜR. The vector ŜR′ may comprise individual signals ŝi′, for example. The individual signals ŝi′ may correspond to the individual destination signals ŝi.

By utilizing the scaled slicer block362, an estimated value for Q and I components associated with the individual destination signal, ŝ3, may be computed based on the value z3determined in equation[12b]. The demapper block374may determine a constellation point that corresponds to the Q and I components. Based on the constellation point, a binary representation may be generated. The binary representation may comprise a binary estimated value for the individual destination signal, ŝ3. The decoder block376may decode the binary representation to generate binary information. The demapper block374and/or decoder block376may utilize statistical techniques, for example maximum likelihood estimation. The encoder block378may encode the binary information decoded by the decoder block376. The mapper block380may generate Q and I components associated with the constellation point determined by the demapper block374. The signal generated by the mapper block380may be referred to as ŝ3′.

An estimated value for the individual destination signal, ŝ2, may be computed based on the value a2determined in equation[12c]. The value a2may be computed based on the estimated value for the individual destination signal ŝ3′. The estimated value for the individual destination signal ŝ3′, utilized in equation[12c], may be based on Q and I components generated by the mapper block380. An estimated value for the individual destination signal, ŝ1, may be computed based on the value z1determined in equation[12d]. The value z1may be computed based on the estimated value for the individual destination signals ŝ2′ and ŝ3′. The estimated values for the individual destination signals ŝ2′ and ŝ3′, utilized in equation[12c], may be based on Q and I components generated by the mapper block380for the signals ŝ2′ and ŝ3′, respectively.

In various embodiments of the invention, the utilization of GMD may enable the computation of the matrix R wherein each of the matrix elements contained therein may be represented as a real number. This may reduce the number of computations required at the receiver352when detecting individual signals ŝirepresented by the signal vector Ŝ. When detecting the signals, matrix multiplications may utilize the matrix R and a matrix that comprises one or more matrix elements that may be represented as complex numbers. The multiplication of a real number and a complex number may involve two multiplication operations. By contrast, for a matrix R that comprises one or more complex elements, multiplication of two complex numbers may involve four multiplication operations.

In another aspect of the invention, the values associated with each of the diagonal elements in the matrix R may be equal. This may imply that the transmitter302may utilize equal signal gain when transmitting the spatial streams306,308, and310, for example. This may further imply that the signal strength and/or signal to noise ratio (SNR) measurements associated with the transmitted spatial streams may be about equal across the plurality of transmitted spatial streams. Thus, various embodiments of the invention that utilize a GMD method may achieve higher information transfer rates, as measured in bits/second, and lower packet error rates (PER) for weaker coding rates when compared to systems that utilize an SVD method. For example, a 5/6 BCC rate may represent a weak coding rate in comparison to a 1/2 BCC rate. The 5/6 BCC method may comprise 1 redundant bit for error detection and/or correction and 5 information bits in each group of 6 transmitted bits, for example. By comparison, the 1/2 BCC method may comprise 1 redundant bit and 1 information bit in each group of 2 transmitted bits, for example.

FIG. 4is an exemplary functional block diagram of transceiver comprising a transmitter and a receiver in a MIMO system, which may be utilized in accordance with an embodiment of the invention.FIG. 4shows a transceiver comprising a transmitter400, a receiver401, a processor440, a baseband processor442, a plurality of transmitter antennas415a. . .415n, and a plurality of receiver antennas417a. . .417n. The transmitter400may comprise a coding block402, a puncture block404, an interleaver block406, a plurality of mapper blocks408a. . .408n, a plurality of inverse fast Fourier transform (IFFT) blocks410a. . .410n, a beamforming V matrix block412, and a plurality of digital to analog (D to A) conversion and antenna front end blocks414a. . .414n. The receiver401may comprise a plurality of antenna front end and analog to digital (A to D) conversion blocks416a. . .416n, a beamforming U matrix block418, a plurality of fast Fourier transform (FFT) blocks420a. . .420n, a channel estimates block422, an equalizer block424, a plurality of demapper blocks426a. . .426n, a deinterleaver block428, a depuncture block430, and a Viterbi decoder block432.

The variables V and U* in beamforming blocks412and418respectively refer to matrices utilized in the beamforming technique. U.S. application Ser. No. 11/052,389 filed Feb. 7, 2005, provides a detailed description of Eigenbeamforming, which is hereby incorporated herein by reference in its entirety.

The processor440may perform digital receiver and/or transmitter functions in accordance with applicable communications standards. These functions may comprise, but are not limited to, tasks performed at lower layers in a relevant protocol reference model. These tasks may further comprise the physical layer convergence procedure (PLCP), physical medium dependent (PMD) functions, and associated layer management functions. The baseband processor442may similarly perform functions in accordance with applicable communications standards. These functions may comprise, but are not limited to, tasks related to analysis of data received via the receiver401, and tasks related to generating data to be transmitted via the transmitter400. These tasks may further comprise medium access control (MAC) layer functions as specified by pertinent standards.

In the transmitter400, the coding block402may transform received binary input data blocks by applying a forward error correction (FEC) technique, for example, binary convolutional coding (BCC). The application of FEC techniques, also known as “channel coding”, may improve the ability to successfully recover transmitted data at a receiver by appending redundant information to the input data prior to transmission via an RF channel. The ratio of the number of bits in the binary input data block to the number of bits in the transformed data block may be known as the “coding rate”. The coding rate may be specified using the notation ib/tb, where tbrepresents the total number of bits that comprise a coding group of bits, while ibrepresents the number of information bits that are contained in the group of bits tb. Any number of bits tb−ibmay represent redundant bits that may enable the receiver401to detect and correct errors introduced during transmission. Increasing the number of redundant bits may enable greater capabilities at the receiver to detect and correct errors in information bits. The penalty for this additional error detection and correction capability may result in a reduction in the information transfer rates between the transmitter400and the receiver401. The invention is not limited to BCC, and any one of a plurality of coding techniques, for example, Turbo coding or low density parity check (LDPC) coding, may also be utilized.

The puncture block404may receive transformed binary input data blocks from the coding block402and alter the coding rate by removing redundant bits from the received transformed binary input data blocks. For example, if the coding block402implemented a 1/2 coding rate, 4 bits of data received from the coding block402may comprise 2 information bits, and 2 redundant bits. By eliminating1of the redundant bits in the group of 4 bits, the puncture block404may adapt the coding rate from 1/2 to 2/3. The interleaver block406may rearrange bits received in a coding rate-adapted data block from the puncture block404prior to transmission via an RF channel to reduce the probability of uncorrectable corruption of data due to burst of errors, impacting contiguous bits, during transmission via an RF channel. The output from the interleaver block406may also be divided into a plurality of streams where each stream may comprise a non-overlapping portion of the bits from the received coding rate-adapted data block. Therefore, for a given number of bits in the coding rate-adapted data block, bdb, a given number of streams from the interleaver block406, nst, and a given number of bits assigned to an individual stream i by the interleaver block406, bst(i), the number of bits, bdb, may equal the number of bits, bst(i), summed across the nststreams.

The plurality of mapper blocks408a. . .408nmay comprise a number of individual mapper blocks that is equal to the number of individual streams generated by the interleaver block406. Each individual mapper block408a. . .408nmay receive a plurality of bits from a corresponding individual stream, mapping those bits into a “symbol” by applying a modulation technique based on a “constellation” utilized to transform the plurality of bits into a signal level representing the symbol. The representation of the symbol may be a complex quantity comprising in-phase (I) and quadrature (Q) components. The mapper block408a. . .408nfor stream i may utilize a modulation technique to map a plurality of bits, bst(i), into a symbol.

The beamforming V matrix block412may apply the beamforming technique to the plurality of symbols, or “spatial modes”, generated from the plurality of mapper blocks408a. . .408n. The beamforming V matrix block412may generate a plurality of signals where the number of signals generated may be equal to the number of transmitting antenna at the transmitter400. Each signal in the plurality of signals generated by the beamforming V block412may comprise a weighted sum of at least one of the received symbols from the mapper blocks408a. . .408n.

The plurality of IFFT blocks410a. . .410nmay receive a plurality of signals from the beamforming block412. Each IFFT block410a. . .410nmay subdivide the bandwidth of the RF channel into a plurality of n sub-band frequencies to implement orthogonal frequency division multiplexing (OFDM), buffering a plurality of received signals equal to the number of sub-bands. Each buffered signal may be modulated by a carrier signal whose frequency is based on that of one of the sub-bands. Each of the IFFT blocks410a. . .410nmay then independently sum their respective buffered and modulated signals across the frequency sub-bands to perform an n-point IFFT thereby generating a composite OFDM signal.

The plurality of digital (D) to analog (A) conversion and antenna front end blocks414a. . .414nmay receive the plurality of signals generated by the plurality of IFFT blocks410a. . .410n. The digital signal representation received from each of the plurality of IFFT blocks410a. . .410nmay be converted to an analog RF signal that may be amplified and transmitted via an antenna. The plurality of D to A conversion and antenna front end blocks414a. . .414nmay be equal to the number of transmitting antenna415a. . .415n. Each D to A conversion and antenna front end block414a. . .414nmay receive one of the plurality of signals from the beamforming V matrix block412and may utilize an antenna415a. . .415nto transmit one RF signal via an RF channel.

In the receiver401, the plurality of antenna front end and A to D conversion blocks416a. . .416nmay receive analog RF signals via an antenna, converting the RF signal to baseband and generating a digital equivalent of the received analog baseband signal. The digital representation may be a complex quantity comprising I and Q components. The number of antenna front end and A to D conversion blocks416a. . .416nmay be equal to the number of receiving antenna417a. . .417n.

The plurality of FFT blocks420a. . .420nmay receive a plurality of signals from the plurality of antenna front end and A to D conversion blocks416a. . .416n. The plurality of FFT blocks420a. . .420nmay be equal to the number of antenna front end and A to D conversion blocks416a. . . .416n. Each FFT block420a. . .420nmay receive a signal from an antenna front end and A to D conversion block416a. . .416n, independently applying an n-point FFT technique, and demodulating the signal by a utilizing a plurality of carrier signals based on the n sub-band frequencies utilized in the transmitter400. The demodulated signals may be mathematically integrated over one sub band frequency period by each of the plurality of FFT blocks420a. . .420nto extract n symbols contained in each of the plurality of OFDM signals received by the receiver401.

The beamforming U* block418may apply the beamforming technique to the plurality of signals received from the plurality of FFT blocks420a. . .420n. The beamforming U* block418may generate a plurality of signals where the number of signals generated may be equal to the number of spatial streams utilized in generating the signals at the transmitter400. Each of the plurality of signals generated by the beamforming U* block418may comprise a weighted sum of at least one of the signals received from the FFT blocks420a. . .420n.

The channel estimates block422may utilize preamble information, contained in a received RF signal, to compute channel estimates. The equalizer block424may receive signals generated by the beamforming U* block418. The equalizer block424may process the received signals based on input from the channel estimates block422to recover the symbol originally generated by the transmitter400. The equalizer block424may comprise suitable logic, circuitry, and/or code that may enable transformation of symbols received from the beamforming U* block418to compensate for fading in the RF channel.

The plurality of demapper blocks426a. . .426nmay receive symbols from the equalizer block424, reverse mapping each symbol to one or more binary bits by applying a demodulation technique, based on the modulation technique utilized in generating the symbol at the transmitter400. The plurality of demapper blocks426a. . .426nmay be equal to the number of streams in the transmitter400.

The deinterleaver block428may receive a plurality of bits from each of the demapper blocks426a. . .426n, rearranging the order of bits among the received plurality of bits. The deinterleaver block428may rearrange the order of bits from the plurality of demapper blocks426a. . .426nin, for example, the reverse order of that utilized by the interleaver406in the transmitter400. The depuncture block430may insert “null” bits into the output data block received from the deinterleaver block428that were removed by the puncture block404. The Viterbi decoder block432may decode a depunctured output data block, applying a decoding technique that may recover the binary data blocks that were input to the coding block402.

In operation, the processor440may receive decoded data from the Viterbi decoder432. The processor440may communicate received data to the baseband processor442for analysis and further processing. The processor440may also communicate data received via the RF channel, by the receiver401, to the channel estimates block422. This information may be utilized by the channel estimates block422, in the receiver401, to compute channel estimates for a received RF channel. The baseband processor442may generate data to be transmitted via an RF channel by the transmitter400. The baseband processor442may communicate the data to the processor440. The processor440may generate a plurality of bits that are communicated to the coding block402.

The elements shown inFIG. 4may comprise components that may be present in an exemplary embodiment of a wireless communications terminal. One exemplary embodiment of a may be a wireless communications transmitter comprising a transmitter400, a processor440, and a baseband processor442. Another exemplary embodiment of a may be a wireless communications receiver comprising a receiver401, a processor440, and a baseband processor442. Another exemplary embodiment of a may be a wireless communications transceiver comprising a transmitter400, a receiver401, a processor440, and a baseband processor442.

U.S. application Ser. No. 11/372,752 provides further details about RF channels utilized in MIMO communications and the construction of the feedback matrix V and is hereby incorporation in its entirety.

The Givens rotation may be represented as an N×N Givens rotation matrix, Gli(ψ), in the following expression:

A steering matrix may be utilized to rotate elements in a matrix such that at least a portion of the rotated elements are represented as real numbers. A matrix, {tilde under (V)}, may comprise elements that may be represented as complex numbers. The matrix {tilde under (V)} may be multiplied by an M×M column-wise steering matrix {tilde under (D)} which may be represented as follows:

D~=[ⅇjθ10…00ⅇjθ20⋮⋮0⋱00…0ⅇjθM]equation⁢[14]
where θimay represent a phase shift associated with column i, e may represent a value about equal to 2.718, and j may represent the complex value equal to the square root of −1.

In an exemplary embodiment of the invention, the values for the phase shifts θiin equation[14] may be selected such that the matrix elements in the last row in a matrix representing the matrix multiplication product {tilde under (V)}×{tilde under (D)} may each be represented as a real number. The matrix V may be computed based on the matrix multiplication product {tilde under (V)}×{tilde under (D)} and the matrix P, as shown in equation[7a]

The matrix V may be multiplied by an N×N phase rotation matrix, Di, which may be represented as follows:

Di=[Ii-10…00ⅇjφi,i0⋮0⋱⋮ⅇjφN-1,i0…1]equation⁢[15⁢a]
where φa,bmay represent a phase shift associated with a matrix element located at row a and column b in the matrix V. For example a phase rotation D1matrix may be represented as follows:

The result of the matrix multiplication of the matrix V by the phase rotation matrix Di* may result in a phase shifted version of the matrix V, where Di* may represent an Hermitian transpose of the phase shift matrix Di. For example, the matrix product D1*V may be represented as a matrix in which the values associated with elements in the first column may each be represented as a real number.

The matrix product Gli(ψli)Di*V may represent a Givens rotated version of the matrix that represents the matrix product Di*V. If a nonzero value is associated with an element located in the Ithrow and ithcolumn of the matrix that represents the matrix product Di*V, represented as the (l,i) element, the corresponding value of the (l,i) element of the matrix that represents the matrix product Gli(ψli)Di*V may be about equal to 0.

One characteristic of Givens rotations is that rotations may be applied iteratively to select matrix elements for which corresponding values are to be set to about 0 as a result of successive rotations. For example, based on a current Givens rotation matrix, Gli(ψli), and a subsequent Givens matrix Gki(ψki), a subsequent matrix product Gli(ψli)Gki(ψki)Di*V may be computed. The value of the (l,i) element of the matrix that represents the subsequent matrix product may be equal to about 0. The value of the (k,i) element of the matrix that represents the subsequent matrix product may also be about equal to 0.

In various embodiments of the invention, the process may be repeated until a subsequent rotated matrix is computed such that the value associated with each element I in column i is about equal to 0. The range of values for the row indicator I may be subject to the following condition:
N≧1>i  equation[16]
where N may represent the number of rows in the matrix V.

After repeating the process for each element I in column i=1, for example, a subsequent rotated matrix may be represented as follows:

For i=2, a submatrix V3may be computed as follows:

For an ithcolumn, equation[17a] may be generalized and represented as follows:

GN,1⁡(ψN⁢⁢1)⁢…⁢⁢Gi+2,i⁡(ψ31)Gi+1,i⁡(ψ21)⁢Di*⁢Ri=[Ii0…00⋮Vi+10]equation⁢[18]
where Rimay represent an intermediate rotated matrix that corresponds to an identity matrix Ii-1, and a submatrix Vi. The submatrix Vi+1may represent an (N−i)×(M−i) submatrix. For example, in equation[17b] the intermediate rotated matrix R2may be represented by the matrix product (GN1(ψN2) . . . G31(ψ31) G21(ψ21)D1*)V.

In various embodiments of the invention, the process shown in equation[18] may be repeated for a subsequent column wherein the range of values for the column indicator i may be subject to the following condition:
min(M,N−1)≧i≧1  equation[19]
where N may represent the number of rows in the matrix V, M may represent the number of columns in the matrix V, and min(a,b) may represent an expression, the value of which may be the minimum value among arguments a and b.

Based on equations [13], [15a], [18], [19], and the unitary matrix property, the matrix V may be expressed based the Givens rotations according to the following equation:

V=∏i=1min⁡(M,N-1)⁢[Di⁢∏l=i+1N⁢Gli*⁡(ψli)]×I~equation⁢[20]
where Ĩ may represent an N×M matrix comprising an identity matrix Imin(N,M)and either a block of max(0,N−M) rows of elements, or a block of max(0,M−N) columns of elements, with each element of a value about 0, max(a,b) may represent an expression, the value of which may be the maximum value among arguments a and b, and the operator π[Xi] may represent a right-side matrix multiplication product among a set of matrices Xi. Gli(ψli)* may represent an Hermitian transpose of the Givens rotation matrix Gli(ψli). The Givens rotation matrix Gli(ψli) is as defined in equation[13] and the phase shift matrix Diis as defined in equation[15a].

In various embodiments of the invention, feedback information may comprise values for one or more rotation angle parameters comprising one or more phase shift angles ψliand one or more Givens rotation angles ψli. The following table represents the number of parameters that may be utilized in feedback information to represent an N×M beamforming matrix V, for exemplary values of N rows and M columns:

The feedback angles represented in Table 1 may be reported for each of the Nscplurality of frequency subcarriers associated with the corresponding downlink RF channel. The order of angles represented in Table 1 may be determined based on the order of multiplications that may be performed when reconstructing the V matrix for each subcarrier at the WLAN106that receives the feedback information. For example, for given feedback angles, φliand ψli, the angles may be represented as a vectors of angles, φli[−Nsc/2, −Nsc/2+1, . . . , −2, −1, 1, 2, . . . , Nsc/2−1, Nsc/2] and ψli[−Nsc/2, −Nsc/2+1, . . . , −2, −1, 1, 2, . . . , Nsc/2−1, Nsc/2], where Nscmay represent the number of subcarriers associated with the downlink RF channel.

In various embodiments of the invention, the order in which feedback angles φliand ψlimay be reported as shown in Table 1 is exemplary, the feedback angles may be reported based on other orderings. In an exemplary embodiment of the invention, which utilizes a 4×2 beamforming matrix V, the order in which feedback angles may be reported may be represented φ11, φ21, ψ21, φ22, φ31, ψ31, φ41, ψ41, φ32, ψ32, and ψ42.

Actual values for angles reported in feedback information may be determined based on a codebook. For example, a range of true values for Givens rotation angles may comprise 0≦ψli≦π/2. A range of true values for phase rotation angles may comprise 0≦φli≦2π, for example. Values for the Givens rotation angles may be approximated based on a binary encoding comprising a plurality of bψbits. Values for Givens rotation angles that are represented by a binary encoding of bits may be referred to as quantized values. In one embodiment of the invention, the range of values for binary quantized values for the Givens rotation angles may comprise kπ/2bψ+1+π/2bψ+2, where k may be equal to one of a range of values comprising 0, 1, . . . , 2bψ−1, for example. Values for the phase rotation angles may be approximated based on a binary encoding comprising a plurality of bφbits. In an embodiment of the invention, the range of values for binary quantized values for the phase rotation angles may comprise kπ/2bφ−1, where k may be equal to one of a range of values comprising 0, 1, . . . , 2bφ−1, for example. Differences in value between a true value and a corresponding quantized value may be referred to as a quantization error. The potential size of a given quantization error may be based on the number of bits utilized during binary encoding.

The number of bits utilized during binary encoding of ψliand during binary encoding of φlirespectively may be represented as a (bψ, bφ) tuple. A tuple utilized in an exemplary codebook may comprise (1,3) to represent the combination bψ=1 and bφ=3. Other tuples in the exemplary codebook may comprise (2,4), (3,5), or (4,6).

Table 2A presents an exemplary mapping between bits contained in feedback information, and the corresponding angle that may be reported. In Table 2A, N=2, M=2, the downlink channel may be a 20 MHz RF channel, and the bits utilized may be represented by (3,5). The range bj. . . bkmay represent a range of bit positions in the feedback information where in bjmay represent the least significant bit (LSB) in the range and bkmay represent the most significant bit (MSB) in the range, for example. The notation fpmay represent a frequency subcarrier associated with the RF channel. Values for the index p may represent a range of integer values as determined in equations [15a] and [16]. The notation ψli(fp) may refer to a Givens rotation angle associated with frequency subcarrier fp. The notation φli(fp) may refer to a phase rotation angle associated with frequency subcarrier fp.

The exemplary feedback information shown in Table 2A contains 448 bits: 168 bits may be utilized to communicate Givens rotation angles, and 280 bits may be utilized to communicate phase rotation angles.

Various embodiments of the invention may also be utilized with tone grouping methods. U.S. application Ser. No. 11/372,752 describes tone grouping methods and is hereby incorporated herein in its entirety.

The order in which feedback angles φliand φlimay be encoded as shown in Table 2A is exemplary, the feedback angles may be reported based on other orderings. Table 2B presents an exemplary mapping between bits contained in feedback information, in which the feedback angles may be grouped by frequency for a 20 MHz RF channel, and for a 4×2 beamforming matrix V.

Table 3A presents an exemplary mapping between bits contained in feedback information, and the corresponding angle that may be reported. In Table 3A, N=2, M=4, the downlink channel may be a 40 MHz RF channel, and the bits utilized may be represented by (2,4). The tone grouping size may be represented by ε=4. The range bj. . . bkmay represent a range of bit positions in the feedback information where in bjmay represent the least significant bit (LSB) in the range and bkmay represent the most significant bit (MSB) in the range, for example. The notation fpmay represent a frequency subcarrier associated with the RF channel. The notation ψli(fp) may refer to a Givens rotation angle associated with frequency subcarrier fp. The notation φli(fp) may refer to a phase rotation angle associated with frequency subcarrier fp.

The exemplary feedback information shown in Table 3A contains 840 bits: 280 bits may be utilized to communicate Givens rotation angles, and 560 bits may be utilized to communicate phase rotation angles.

The order in which feedback angles φliand ψlimay be encoded as shown in Table 3A is exemplary, the feedback angles may be reported based on other orderings. Table 3B presents an exemplary mapping between bits contained in feedback information, in which the feedback angles may be grouped by frequency for a 40 MHz channel.

U.S. application Ser. No. 11/372,752 further details exemplary numbers of bytes contained in feedback information in accordance with various embodiments of the invention and is hereby incorporation in its entirety.

FIG. 5is a flowchart illustrating exemplary steps for computing quantization for a general beamforming matrix in feedback information, in accordance with an embodiment of the invention. Referring toFIG. 5, in step502, a signal Y may be received at a receiving mobile terminal322. In step504, a channel estimate matrix H may be computed. In step506, the computed channel estimate matrix may be decomposed into a matrix multiplication representation, H=URV*. In step508, the matrix V may be computed such that the matrix R is a real valued upper diagonal matrix. A matrix may be referred to as being real valued when each of the matrix elements contained within the matrix may be represented as a real number. The values of each of the diagonal matrix elements in the matrix R, rii, may be about equal. In step510, the receiving mobile terminal322may send feedback information based on the computed matrix V to the transmitting mobile terminal302via an uplink channel.

FIG. 6is a flowchart illustrating exemplary steps for utilizing quantization for a general beamforming matrix in feedback information, in accordance with an embodiment of the invention. Referring toFIG. 6, in step602, a transmitting mobile terminal302may receive feedback information. In step604, beamforming parameters may be adjusted based on the feedback information. In step606, the transmitting mobile terminal302may transmit spatial streams. Each spatial stream may be transmitted with approximately equal signal gain based on the feedback information. Each transmitted spatial stream may be characterized by approximately equal signal strength and/or signal to noise ratio (SNR) measurements. The signal strength and/or SNR may be measured in decibels (dB), for example.

Various embodiments of the invention may not be limited to geometric mean decomposition (GMD) but may comprise other methods that may be utilized at a receiving mobile terminal322to compute feedback information based on a signal Y, received via a downlink channel. The received signal may be utilized to compute a channel estimate matrix H. The channel estimate matrix H may be decomposed into a matrix multiplication representation H=URV*. The matrix V may be computed such that the matrix R is an upper diagonal real valued matrix with equal valued diagonal matrix elements. The receiving mobile terminal322may send feedback information, based on the computed matrix V, to a transmitting mobile terminal302via an uplink channel. The receiving mobile terminal may utilize the feedback information to beamform a subsequent transmitted signal vector X. The signal vector X may comprise a plurality of transmitted spatial streams. For each transmitted spatial stream in the beamformed subsequent signal vector X, a signal strength and/or SNR measurement may be about equal to corresponding measurements associated with each of the other transmitted spatial streams.

Aspects of a system for processing signals in a communication system may comprise a processor282that enables receipt of a matrix for a wireless medium, which comprises a multiplicative product of at least one rotation matrix and at least one diagonal phase rotation matrix. Each of the rotation matrices comprises at least one matrix element whose value is based on a Givens rotation angle. The system may also comprise a transmitter286that enables transmission of a plurality of signals via the wireless medium based on feedback information. A signal strength and/or signal to noise ratio (SNR) measurement associated with each of the plurality of signals may be about equal.

A value associated with each matrix element in a last row of the received matrix may be represented as a real number. The processor282may enable computation of a phase rotated matrix by multiplying the received matrix by a diagonal phase rotation matrix. A value associated with each matrix element in a first column of the phase rotated matrix may be represented as a real number. The processor282may enable computation of a product matrix based on a multiplicative product of the phase rotated matrix and at least one phase rotation matrix. Each of the one or more phase rotation matrices may comprise at least one matrix element the value of which may be based on a Givens rotation angle. The product matrix may comprise an identity matrix and a second matrix. The second matrix may comprise one row and one column less than the received matrix.

The processor282may enable computation of a subsequent product matrix based on a multiplicative product of the received matrix, at least one diagonal phase rotation matrix, and at least one phase rotation matrix. The processor282may enable computation of a phase rotated intermediate matrix by multiplying an intermediate matrix by a corresponding one of the one or more diagonal phase rotation matrices. A value associated with each matrix element in a corresponding column of the phase rotated intermediate matrix may be represented as a real number. The subsequent product matrix may comprise an identity matrix and a subsequent matrix. The subsequent matrix may comprise at least one row and at least one column less than the received matrix.