Abstract:
A method for reduced feedback for beamforming in a wireless communication begins by receiving a baseband signal. The method continues by digitally beamforming the baseband signal using a unitary matrix having polar coordinates.

Description:
CROSS REFERENCE TO RELATED PATENTS 
   This invention is claiming priority under 35 USC §119(e) to a provisionally filed patent application having the same title as the present patent application, a filing date of Apr. 21, 2005, and an application No. 60/673,451. 

   BACKGROUND OF THE INVENTION 
   1. Technical Field of the Invention 
   This invention relates generally to wireless communication systems and more particularly to wireless communications using beamforming. 
   2. Description of Related Art 
   Communication systems are known to support wireless and wire lined communications between wireless and/or wire lined communication devices. Such communication systems range from national and/or international cellular telephone systems to the Internet to point-to-point in-home wireless networks. Each type of communication system is constructed, and hence operates, in accordance with one or more communication standards. For instance, wireless communication systems may operate in accordance with one or more standards including, but not limited to, IEEE 802.11, Bluetooth, advanced mobile phone services (AMPS), digital AMPS, global system for mobile communications (GSM), code division multiple access (CDMA), local multi-point distribution systems (LMDS), multi-channel-multi-point distribution systems (MMDS), and/or variations thereof. 
   Depending on the type of wireless communication system, a wireless communication device, such as a cellular telephone, two-way radio, personal digital assistant (PDA), personal computer (PC), laptop computer, home entertainment equipment, et cetera communicates directly or indirectly with other wireless communication devices. For direct communications (also known as point-to-point communications), the participating wireless communication devices tune their receivers and transmitters to the same channel or channels (e.g., one of the plurality of radio frequency (RF) carriers of the wireless communication system) and communicate over that channel(s). For indirect wireless communications, each wireless communication device communicates directly with an associated base station (e.g., for cellular services) and/or an associated access point (e.g., for an in-home or in-building wireless network) via an assigned channel. To complete a communication connection between the wireless communication devices, the associated base stations and/or associated access points communicate with each other directly, via a system controller, via the public switch telephone network, via the Internet, and/or via some other wide area network. 
   For each wireless communication device to participate in wireless communications, it includes a built-in radio transceiver (i.e., receiver and transmitter) or is coupled to an associated radio transceiver (e.g., a station for in-home and/or in-building wireless communication networks, RF modem, etc.). As is known, the receiver is coupled to the antenna and includes a low noise amplifier, one or more intermediate frequency stages, a filtering stage, and a data recovery stage. The low noise amplifier receives inbound RF signals via the antenna and amplifies then. The one or more intermediate frequency stages mix the amplified RF signals with one or more local oscillations to convert the amplified RF signal into baseband signals or intermediate frequency (IF) signals. The filtering stage filters the baseband signals or the IF signals to attenuate unwanted out of band signals to produce filtered signals. The data recovery stage recovers raw data from the filtered signals in accordance with the particular wireless communication standard. 
   As is also known, the transmitter includes a data modulation stage, one or more intermediate frequency stages, and a power amplifier. The data modulation stage converts raw data into baseband signals in accordance with a particular wireless communication standard. The one or more intermediate frequency stages mix the baseband signals with one or more local oscillations to produce RF signals. The power amplifier amplifies the RF signals prior to transmission via an antenna. 
   In many systems, the transmitter will include one antenna for transmitting the RF signals, which are received by a single antenna, or multiple antennas, of a receiver. When the receiver includes two or more antennas, the receiver will select one of them to receive the incoming RF signals. In this instance, the wireless communication between the transmitter and receiver is a single-output-single-input (SISO) communication, even if the receiver includes multiple antennas that are used as diversity antennas (i.e., selecting one of them to receive the incoming RF signals). For SISO wireless communications, a transceiver includes one transmitter and one receiver. Currently, most wireless local area networks (WLAN) that are IEEE 802.11, 802.11a, 802.11b, or 802.11g employ SISO wireless communications. 
   Other types of wireless communications include single-input-multiple-output (SIMO), multiple-input-single-output (MISO), and multiple-input-multiple-output (MIMO). In a SIMO wireless communication, a single transmitter processes data into radio frequency signals that are transmitted to a receiver. The receiver includes two or more antennas and two or more receiver paths. Each of the antennas receives the RF signals and provides them to a corresponding receiver path (e.g., LNA, down conversion module, filters, and ADCs). Each of the receiver paths processes the received RF signals to produce digital signals, which are combined and then processed to recapture the transmitted data. 
   For a multiple-input-single-output (MISO) wireless communication, the transmitter includes two or more transmission paths (e.g., digital to analog converter, filters, up-conversion module, and a power amplifier) that each converts a corresponding portion of baseband signals into RF signals, which are transmitted via corresponding antennas to a receiver. The receiver includes a single receiver path that receives the multiple RF signals from the transmitter. In this instance, the receiver uses beam forming to combine the multiple RF signals into one signal for processing. 
   For a multiple-input-multiple-output (MIMO) wireless communication, the transmitter and receiver each include multiple paths. In such a communication, the transmitter parallel processes data using a spatial and time encoding function to produce two or more streams of data. The transmitter includes multiple transmission paths to convert each stream of data into multiple RF signals. The receiver receives the multiple RF signals via multiple receiver paths that recapture the streams of data utilizing a spatial and time decoding function. The recaptured streams of data are combined and subsequently processed to recover the original data. 
   To further improve wireless communications, transceivers may incorporate beamforming. In general, beamforming is a processing technique to create a focused antenna beam by shifting a signal in time or in phase to provide gain of the signal in a desired direction and to attenuate the signal in other directions. Prior art papers (1) Digital beamforming basics (antennas) by Steyskal, Hans, Journal of Electronic Defense, Jul. 1, 1996; (2) Utilizing Digital Downconverters for Efficient Digital Beamforming, by Clint Schreiner, Red River Engineering, no publication date; and (3) Interpolation Based Transmit Beamforming for MIMO-OFMD with Partial Feedback, by Jihoon Choi and Robert W. Heath, University of Texas, Department of Electrical and Computer Engineering, Wireless Networking and Communications Group, Sep. 13, 2003 discuss beamforming concepts. 
   In order for a transmitter to properly implement beamforming (i.e., determine the beamforming matrix[V]), it needs to know properties of the channel over which the wireless communication is conveyed. Accordingly, the receiver must provide feedback information for the transmitter to determine the properties of the channel. One approach for sending feedback from the receiver to the transmitter is for the receiver to determine the channel response (H) and to provide it as the feedback information. An issue with this approach is the size of the feedback packet, which may be so large that, during the time it takes to send it to the transmitter, the response of the channel has changed. 
   To reduce the size of the feedback, the receiver may decompose the channel using singular value decomposition (SVD) and send information relating only to a calculated value of the transmitter&#39;s beamforming matrix (V) as the feedback information. In this approach, the receiver calculates (V) based on H=UDV*, where H is the channel response, D is a diagonal matrix, and U is a receiver unitary matrix. While this approach reduces the size of the feedback information, its size is still an issue for a MIMO wireless communication. For instance, in a 2×2 MIMO wireless communication, the feedback needs four elements that are all complex Cartesian coordinate values[V11 V12; V21 V22]. In general, Vik=aik+j*bik, where aik and bik are values between [−1, 1]. Thus, with 1 bit express per each element for each of the real and imaginary components, aik and bik can be either −½ or ½, which requires 4×2×1=8 bits per tone. With 4 bit expressions per each element of V(f) in an orthogonal frequency division multiplexing (OFDM) 2×2 MIMO wireless communication, the number of bits required is 1728 per tone (e.g., 4*2*54*4=1728, 4 elements per tone, 2 bits for real and imaginary components per tone, 54 data tones per frame, and 4 bits per element), which requires overhead for a packet exchange that is too large for practical applications. 
   Therefore, a need exists for a method and apparatus for reducing beamforming feedback information for wireless communications. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention is directed to apparatus and methods of operation that are further described in the following Brief Description of the Drawings, the Detailed Description of the Invention, and the claims. Other features and advantages of the present invention will become apparent from the following detailed description of the invention made with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       FIG. 1  is a schematic block diagram of a wireless communication system in accordance with the present invention; 
       FIG. 2  is a schematic block diagram of a wireless communication device in accordance with the present invention; 
       FIG. 3  is a schematic block diagram of another wireless communication device in accordance with the present invention; 
       FIG. 4  is a schematic block diagram of baseband transmit processing in accordance with the present invention; 
       FIG. 5  is a schematic block diagram of baseband receive processing in accordance with the present invention; and 
       FIG. 6  is a schematic block diagram of a beamforming wireless communication in accordance with the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1  is a schematic block diagram illustrating a communication system  10  that includes a plurality of base stations and/or access points  12 ,  16 , a plurality of wireless communication devices  18 - 32  and a network hardware component  34 . Note that the network hardware  34 , which may be a router, switch, bridge, modem, system controller, et cetera provides a wide area network connection  42  for the communication system  10 . Further note that the wireless communication devices  18 - 32  may be laptop host computers  18  and  26 , personal digital assistant hosts  20  and  30 , personal computer hosts  24  and  32  and/or cellular telephone hosts  22  and  28 . The details of the wireless communication devices will be described in greater detail with reference to  FIG. 2 . 
   Wireless communication devices  22 ,  23 , and  24  are located within an independent basic service set (IBSS) area and communicate directly (i.e., point to point). In this configuration, these devices  22 ,  23 , and  24  may only communicate with each other. To communicate with other wireless communication devices within the system  10  or to communicate outside of the system  10 , the devices  22 ,  23 , and/or  24  need to affiliate with one of the base stations or access points  12  or  16 . 
   The base stations or access points  12 ,  16  are located within basic service set (BSS) areas  11  and  13 , respectively, and are operably coupled to the network hardware  34  via local area network connections  36 ,  38 . Such a connection provides the base station or access point  12   16  with connectivity to other devices within the system  10  and provides connectivity to other networks via the WAN connection  42 . To communicate with the wireless communication devices within its BSS  11  or  13 , each of the base stations or access points  12 - 16  has an associated antenna or antenna array. For instance, base station or access point  12  wirelessly communicates with wireless communication devices  18  and  20  while base station or access point  16  wirelessly communicates with wireless communication devices  26 - 32 . Typically, the wireless communication devices register with a particular base station or access point  12 ,  16  to receive services from the communication system  10 . 
   Typically, base stations are used for cellular telephone systems and like-type systems, while access points are used for in-home or in-building wireless networks (e.g., IEEE 802.11 and versions thereof, Bluetooth, and/or any other type of radio frequency based network protocol). Regardless of the particular type of communication system, each wireless communication device includes a built-in radio and/or is coupled to a radio. 
     FIG. 2  is a schematic block diagram illustrating a wireless communication device that includes the host device  18 - 32  and an associated radio  60 . For cellular telephone hosts, the radio  60  is a built-in component. For personal digital assistants hosts, laptop hosts, and/or personal computer hosts, the radio  60  may be built-in or an externally coupled component. 
   As illustrated, the host device  18 - 32  includes a processing module  50 , memory  52 , a radio interface  54 , an input interface  58 , and an output interface  56 . The processing module  50  and memory  52  execute the corresponding instructions that are typically done by the host device. For example, for a cellular telephone host device, the processing module  50  performs the corresponding communication functions in accordance with a particular cellular telephone standard. 
   The radio interface  54  allows data to be received from and sent to the radio  60 . For data received from the radio  60  (e.g., inbound data), the radio interface  54  provides the data to the processing module  50  for further processing and/or routing to the output interface  56 . The output interface  56  provides connectivity to an output display device such as a display, monitor, speakers, et cetera such that the received data may be displayed. The radio interface  54  also provides data from the processing module  50  to the radio  60 . The processing module  50  may receive the outbound data from an input device such as a keyboard, keypad, microphone, et cetera via the input interface  58  or generate the data itself. For data received via the input interface  58 , the processing module  50  may perform a corresponding host function on the data and/or route it to the radio  60  via the radio interface  54 . 
   Radio  60  includes a host interface  62 , digital receiver processing module  64 , an analog-to-digital converter  66 , a high pass and low pass filter module  68 , an IF mixing down conversion stage  70 , a receiver filter  71 , a low noise amplifier  72 , a transmitter/receiver switch  73 , a local oscillation module  74 , memory  75 , a digital transmitter processing module  76 , a digital-to-analog converter  78 , a filtering/gain module  80 , an IF mixing up conversion stage  82 , a power amplifier  84 , a transmitter filter module  85 , a channel bandwidth adjust module  87 , and an antenna  86 . The antenna  86  may be a single antenna that is shared by the transmit and receive paths as regulated by the Tx/Rx switch  73 , or may include separate antennas for the transmit path and receive path. The antenna implementation will depend on the particular standard to which the wireless communication device is compliant. 
   The digital receiver processing module  64  and the digital transmitter processing module  76 , in combination with operational instructions stored in memory  75 , execute digital receiver functions and digital transmitter functions, respectively. The digital receiver functions include, but are not limited to, digital intermediate frequency to baseband conversion, demodulation, constellation demapping, decoding, and/or descrambling. The digital transmitter functions include, but are not limited to, scrambling, encoding, constellation mapping, modulation, and/or digital baseband to IF conversion. The digital receiver and transmitter processing modules  64  and  76  may be implemented using a shared processing device, individual processing devices, or a plurality of processing devices. Such a processing device may be a microprocessor, micro-controller, digital signal processor, microcomputer, central processing unit, field programmable gate array, programmable logic device, state machine, logic circuitry, analog circuitry, digital circuitry, and/or any device that manipulates signals (analog and/or digital) based on operational instructions. The memory  75  may be a single memory device or a plurality of memory devices. Such a memory device may be a read-only memory, random access memory, volatile memory, non-volatile memory, static memory, dynamic memory, flash memory, and/or any device that stores digital information. Note that when the processing module  64  and/or  76  implements one or more of its functions via a state machine, analog circuitry, digital circuitry, and/or logic circuitry, the memory storing the corresponding operational instructions is embedded with the circuitry comprising the state machine, analog circuitry, digital circuitry, and/or logic circuitry. 
   In operation, the radio  60  receives outbound data  94  from the host device via the host interface  62 . The host interface  62  routes the outbound data  94  to the digital transmitter processing module  76 , which processes the outbound data  94  in accordance with a particular wireless communication standard (e.g., IEEE 802.11, Bluetooth, et cetera) to produce outbound baseband signals  96 . The outbound baseband signals  96  will be digital base-band signals (e.g., have a zero IF) or a digital low IF signals, where the low IF typically will be in the frequency range of one hundred kilohertz to a few megahertz. 
   The digital-to-analog converter  78  converts the outbound baseband signals  96  from the digital domain to the analog domain. The filtering/gain module  80  filters and/or adjusts the gain of the analog signals prior to providing it to the IF mixing stage  82 . The IF mixing stage  82  converts the analog baseband or low IF signals into RF signals based on a transmitter local oscillation  83  provided by local oscillation module  74 . The power amplifier  84  amplifies the RF signals to produce outbound RF signals  98 , which are filtered by the transmitter filter module  85 . The antenna  86  transmits the outbound RF signals  98  to a targeted device such as a base station, an access point and/or another wireless communication device. 
   The radio  60  also receives inbound RF signals  88  via the antenna  86 , which were transmitted by a base station, an access point, or another wireless communication device. The antenna  86  provides the inbound RF signals  88  to the receiver filter module  71  via the Tx/Rx switch  73 , where the Rx filter  71  bandpass filters the inbound RF signals  88 . The Rx filter  71  provides the filtered RF signals to low noise amplifier  72 , which amplifies the signals  88  to produce an amplified inbound RF signals. The low noise amplifier  72  provides the amplified inbound RF signals to the IF mixing module  70 , which directly converts the amplified inbound RF signals into an inbound low IF signals or baseband signals based on a receiver local oscillation  81  provided by local oscillation module  74 . The down conversion module  70  provides the inbound low IF signals or baseband signals to the filtering/gain module  68 . The high pass and low pass filter module  68  filters, based on settings provided by the channel bandwidth adjust module  87 , the inbound low IF signals or the inbound baseband signals to produce filtered inbound signals. 
   The analog-to-digital converter  66  converts the filtered inbound signals from the analog domain to the digital domain to produce inbound baseband signals  90 , where the inbound baseband signals  90  will be digital base-band signals or digital low IF signals, where the low IF typically will be in the frequency range of one hundred kilohertz to a few megahertz. The digital receiver processing module  64 , based on settings provided by the channel bandwidth adjust module  87 , decodes, descrambles, demaps, and/or demodulates the inbound baseband signals  90  to recapture inbound data  92  in accordance with the particular wireless communication standard being implemented by radio  60 . The host interface  62  provides the recaptured inbound data  92  to the host device  18 - 32  via the radio interface  54 . 
   As one of average skill in the art will appreciate, the wireless communication device of  FIG. 2  may be implemented using one or more integrated circuits. For example, the host device may be implemented on one integrated circuit, the digital receiver processing module  64 , the digital transmitter processing module  76  and memory  75  may be implemented on a second integrated circuit, and the remaining components of the radio  60 , less the antenna  86 , may be implemented on a third integrated circuit. As an alternate example, the radio  60  may be implemented on a single integrated circuit. As yet another example, the processing module  50  of the host device and the digital receiver and transmitter processing modules  64  and  76  may be a common processing device implemented on a single integrated circuit. Further, the memory  52  and memory  75  may be implemented on a single integrated circuit and/or on the same integrated circuit as the common processing modules of processing module  50  and the digital receiver and transmitter processing module  64  and  76 . 
     FIG. 3  is a schematic block diagram illustrating a wireless communication device that includes the host device  18 - 32  and an associated radio  60 . For cellular telephone hosts, the radio  60  is a built-in component. For personal digital assistants hosts, laptop hosts, and/or personal computer hosts, the radio  60  may be built-in or an externally coupled component. 
   As illustrated, the host device  18 - 32  includes a processing module  50 , memory  52 , radio interface  54 , input interface  58  and output interface  56 . The processing module  50  and memory  52  execute the corresponding instructions that are typically done by the host device. For example, for a cellular telephone host device, the processing module  50  performs the corresponding communication functions in accordance with a particular cellular telephone standard. 
   The radio interface  54  allows data to be received from and sent to the radio  60 . For data received from the radio  60  (e.g., inbound data), the radio interface  54  provides the data to the processing module  50  for further processing and/or routing to the output interface  56 . The output interface  56  provides connectivity to an output display device such as a display, monitor, speakers, et cetera such that the received data may be displayed. The radio interface  54  also provides data from the processing module  50  to the radio  60 . The processing module  50  may receive the outbound data from an input device such as a keyboard, keypad, microphone, et cetera via the input interface  58  or generate the data itself For data received via the input interface  58 , the processing module  50  may perform a corresponding host function on the data and/or route it to the radio  60  via the radio interface  54 . 
   Radio  60  includes a host interface  62 , a baseband processing module  100 , memory  65 , a plurality of radio frequency (RF) transmitters  106 - 110 , a transmit/receive (T/R) module  114 , a plurality of antennas  81 - 85 , a plurality of RF receivers  118 - 120 , a channel bandwidth adjust module  87 , and a local oscillation module  74 . The baseband processing module  100 , in combination with operational instructions stored in memory  65 , executes digital receiver functions and digital transmitter functions, respectively. The digital receiver functions include, but are not limited to, digital intermediate frequency to baseband conversion, demodulation, constellation demapping, decoding, de-interleaving, fast Fourier transform, cyclic prefix removal, space and time decoding, and/or descrambling. The digital transmitter functions include, but are not limited to, scrambling, encoding, interleaving, constellation mapping, modulation, inverse fast Fourier transform, cyclic prefix addition, space and time encoding, and digital baseband to IF conversion. The baseband processing modules  100  may be implemented using one or more processing devices. Such a processing device may be a microprocessor, micro-controller, digital signal processor, microcomputer, central processing unit, field programmable gate array, programmable logic device, state machine, logic circuitry, analog circuitry, digital circuitry, and/or any device that manipulates signals (analog and/or digital) based on operational instructions. The memory  65  may be a single memory device or a plurality of memory devices. Such a memory device may be a read-only memory, random access memory, volatile memory, non-volatile memory, static memory, dynamic memory, flash memory, and/or any device that stores digital information. Note that when the processing module  100  implements one or more of its functions via a state machine, analog circuitry, digital circuitry, and/or logic circuitry, the memory storing the corresponding operational instructions is embedded with the circuitry comprising the state machine, analog circuitry, digital circuitry, and/or logic circuitry. 
   In operation, the radio  60  receives outbound data  94  from the host device via the host interface  62 . The baseband processing module  64  receives the outbound data  88  and, based on a mode selection signal  102 , produces one or more outbound symbol streams  90 . The mode selection signal  102  will indicate a particular mode of operation that is compliant with one or more specific modes of the various IEEE 802.11 standards. For example, the mode selection signal  102  may indicate a frequency band of 2.4 GHz, a channel bandwidth of 20 or 22 MHz and a maximum bit rate of 54 megabits-per-second. In this general category, the mode selection signal will further indicate a particular rate ranging from 1 megabit-per-second to 54 megabits-per-second. In addition, the mode selection signal will indicate a particular type of modulation, which includes, but is not limited to, Barker Code Modulation, BPSK, QPSK, CCK, 16 QAM and/or 64 QAM. The mode select signal  102  may also include a code rate, a number of coded bits per subcarrier (NBPSC), coded bits per OFDM symbol (NCBPS), and/or data bits per OFDM symbol (NDBPS). The mode selection signal  102  may also indicate a particular channelization for the corresponding mode that provides a channel number and corresponding center frequency. The mode select signal  102  may further indicate a power spectral density mask value and a number of antennas to be initially used for a MIMO communication. 
   The baseband processing module  100 , based on the mode selection signal  102  produces one or more outbound symbol streams  104  from the outbound data  94 . For example, if the mode selection signal  102  indicates that a single transmit antenna is being utilized for the particular mode that has been selected, the baseband processing module  100  will produce a single outbound symbol stream  104 . Alternatively, if the mode select signal  102  indicates 2, 3 or 4 antennas, the baseband processing module  100  will produce 2, 3 or 4 outbound symbol streams  104  from the outbound data  94 . 
   Depending on the number of outbound streams  104  produced by the baseband module  10 , a corresponding number of the RF transmitters  106 - 110  will be enabled to convert the outbound symbol streams  104  into outbound RF signals  112 . In general, each of the RF transmitters  106 - 110  includes a digital filter and upsampling module, a digital to analog conversion module, an analog filter module, a frequency up conversion module, a power amplifier, and a radio frequency bandpass filter. The RF transmitters  106 - 110  provide the outbound RF signals  112  to the transmit/receive module  114 , which provides each outbound RF signal to a corresponding antenna  81 - 85 . 
   When the radio  60  is in the receive mode, the transmit/receive module  114  receives one or more inbound RF signals  116  via the antennas  81 - 85  and provides them to one or more RF receivers  118 - 122 . The RF receiver  118 - 122 , based on settings provided by the channel bandwidth adjust module  87 , converts the inbound RF signals  116  into a corresponding number of inbound symbol streams  124 . The number of inbound symbol streams  124  will correspond to the particular mode in which the data was received. The baseband processing module  100  converts the inbound symbol streams  124  into inbound data  92 , which is provided to the host device  18 - 32  via the host interface  62 . 
   As one of average skill in the art will appreciate, the wireless communication device of  FIG. 3  may be implemented using one or more integrated circuits. For example, the host device may be implemented on one integrated circuit, the baseband processing module  100  and memory  65  may be implemented on a second integrated circuit, and the remaining components of the radio  60 , less the antennas  81 - 85 , may be implemented on a third integrated circuit. As an alternate example, the radio  60  may be implemented on a single integrated circuit. As yet another example, the processing module  50  of the host device and the baseband processing module  100  may be a common processing device implemented on a single integrated circuit. Further, the memory  52  and memory  65  may be implemented on a single integrated circuit and/or on the same integrated circuit as the common processing modules of processing module  50  and the baseband processing module  100 . 
     FIG. 4  is a schematic block diagram of baseband transmit processing 100-TX within the baseband processing module  100 , which includes an encoding module  121 , a puncture module  123 , a switch, a plurality of interleaving modules  125 ,  126 , a plurality of constellation encoding modules  128 ,  130 , a beamforming module (V)  132 , and a plurality of inverse fast Fourier transform (IFFT) modules  134 ,  136  for converting the outbound data  94  into the outbound symbol stream  104 . As one of ordinary skill in the art will appreciate, the baseband transmit processing may include two or more of each of the interleaving modules  125 ,  126 , the constellation mapping modules  128 ,  130 , and the IFFT modules  134 ,  136 . In addition, one of ordinary skill in art will further appreciate that the encoding module  121 , puncture module  123 , the interleaving modules  124 ,  126 , the constellation mapping modules  128 ,  130 , and the IFFT modules  134 ,  136  may be function in accordance with one or more wireless communication standards including, but not limited to, IEEE 802.11a, b, g, n. 
   In one embodiment, the encoding module  121  is operably coupled to convert outbound data  94  into encoded data in accordance with one or more wireless communication standards. The puncture module  123  punctures the encoded data to produce punctured encoded data. The plurality of interleaving modules  125 ,  126  is operably coupled to interleave the punctured encoded data into a plurality of interleaved streams of data. The plurality of constellation mapping modules  128 ,  130  is operably coupled to map the plurality of interleaved streams of data into a plurality of streams of data symbols. The beamforming module  132  is operably coupled to beamform, using a unitary matrix having polar coordinates, the plurality of streams of data symbols into a plurality of streams of beamformed symbols. The plurality of IFFT modules  134 ,  136  is operably coupled to convert the plurality of streams of beamformed symbols into a plurality of outbound symbol streams. 
   The beamforming module  132  is operably coupled to multiply a beamforming unitary matrix (V) with baseband signals provided by the plurality of constellation mapping modules  128 ,  130 . The beamforming module  132  determines the beamforming unitary matrix V from feedback information from the receiver, wherein the feedback information includes a calculated expression of the beamforming matrix V having polar coordinates. The beamforming module  132  generates the beamforming unitary matrix V to satisfy the conditions of “V*V=VV*=“I”, where “I” is an identity matrix of [1 0; 0 1] for 2×2 MIMO wireless communication, is [1 0 0; 0 1 0; 0 0 1] for 3×3 MIMO wireless communication, or is [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1] for 4×4 MIMO wireless communication. In this equation, V*V means “conjugate (V) times V” and VV* means “V times conjugate (V)”. Note that V may be a 2×2 unitary matrix for a 2×2 MIMO wireless communication, a 3×3 unitary matrix for a 3×3 MIMO wireless communication, and a 4×4 unitary matrix for a 4×4 MIMO wireless communication. Further note that for each column of V, a first row of polar coordinates including real values as references and a second row of polar coordinates including phase shift values. 
   In one embodiment, the constellation mapping modules  128 ,  130  function in accordance with one of the IEEE 802.11x standards to provide an OFDM (Orthogonal Frequency Domain Multiplexing) frequency domain baseband signals that includes a plurality of tones, or subcarriers, for carrying data. Each of the data carrying tones represents a symbol mapped to a point on a modulation dependent constellation map. For instance, a 16 QAM (Quadrature Amplitude Modulation) includes 16 constellation points, each corresponding to a different symbol. For an OFDM signal, the beamforming module  132  may regenerate the beamforming unitary matrix V for each tone from each constellation mapping module  128 ,  130 , use the same beamforming unitary matrix for each tone from each constellation mapping module  128 ,  130 , or a combination thereof. 
   The beamforming unitary matrix varies depending on the number of transmit paths (i.e., transmit antennas−M) and the number of receive paths (i.e., receiver antennas−N) for an M×N MIMO communication. For instance, for a 2×2 MIMO communication, the beamforming unitary matrix may be: 
           V   =     [           cos   ⁢           ⁢     ψ   1             cos   ⁢           ⁢     ψ   2                 sin   ⁢           ⁢     ψ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   1                 sin   ⁢           ⁢     ψ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   2                 ]           
In order to satisfy V*V=I, it needs to satisfy followings.
 cos ψ 1  cos ψ 2 +sin ψ 1  sin ψ 2   e   j(φ     1     −φ     2     ) =0 cos ψ 1  cos ψ 2 +sin ψ 1  sin ψ 2   e   j(φ     2     −φ     1     ) =0 
where i, j=1, 2; ψ 1 , Φ 1 , ψ 2 , and Φ 2  represent angles of the unit circle, wherein absolute value of ψ 1 −ψ 2 =π/2 and Φ 1 =Φ 2  or Φ 1 =ψ 2 +π and ψ 1 +ψ 2 =π/2.
 
   Therefore, with Φ 1  and ψ 1 , the beamforming module  132  may regenerate V per each tone. For example, With 4-bits expression for angle Φ 1  and 3-bits for angle ψ 1 , and 1-bit for the index for # 1  or # 2  in 54 tones, (i.e., 8-bits per tone) total feedback information may be 8×54/8=54 bytes. (ψ in [0, π], Φ in [−π, π]). 
   For a 3×3 MIMO communication, the beamforming unitary matrix may be: 
           V   =         (   V   )     ⁢   ij     =     [           cos   ⁢           ⁢     ψ   1             cos   ⁢           ⁢     ψ   2             cos   ⁢           ⁢     ψ   3                 sin   ⁢           ⁢     ψ   1     ⁢   cos   ⁢           ⁢     θ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   21                 sin   ⁢           ⁢     ψ   2     ⁢   cos   ⁢           ⁢     θ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   22                 sin   ⁢           ⁢     ψ   3     ⁢   cos   ⁢           ⁢     θ   3     ⁢     ⅇ     j   ⁢           ⁢     ϕ   23                     sin   ⁢           ⁢     ψ   1     ⁢   sin   ⁢           ⁢     θ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   31                 sin   ⁢           ⁢     ψ   2     ⁢   sin   ⁢           ⁢     θ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   32                 sin   ⁢           ⁢     ψ   3     ⁢   sin   ⁢           ⁢     θ   3     ⁢     ⅇ     j   ⁢           ⁢     ϕ   33                 ]             
where i, j=1, 2, 3; ψ 1 , ψ 2 , ψ 3 , θ 1 , θ 2 , θ 3 , Φ 21 , Φ 22 , Φ 23 , Φ 31 , Φ 32 , Φ 33  represent angles of the unit circle, wherein Diagonal (V*V)=1 s, and wherein:
 
   
     
       
         
           
             
               ψ 
               i 
             
             = 
             
               
                 cos 
                 
                   - 
                   1 
                 
               
               ⁢ 
               
                 V 
                 
                   1 
                   ⁢ 
                   i 
                 
               
             
           
           , 
           
             
               θ 
               i 
             
             = 
             
               
                 cos 
                 
                   - 
                   1 
                 
               
               ⁢ 
               
                  
                 
                   
                     V 
                     
                       2 
                       ⁢ 
                       i 
                     
                   
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ψ 
                       i 
                     
                   
                 
                  
               
             
           
         
       
     
     
       
         
           
             
               ϕ 
               
                 2 
                 ⁢ 
                 i 
               
             
             = 
             
               ∠ 
               ⁡ 
               
                 ( 
                 
                   V 
                   
                     2 
                     ⁢ 
                     i 
                   
                 
                 ) 
               
             
           
           , 
           
             
               ϕ 
               
                 3 
                 ⁢ 
                 i 
               
             
             = 
             
               ∠ 
               ⁡ 
               
                 ( 
                 
                   V 
                   
                     3 
                     ⁢ 
                     i 
                   
                 
                 ) 
               
             
           
         
       
     
   
   In this example, with 12 angles, the beamforming module  132  may regenerate V as a 3×3 matrix per tone. With 4-bits for expression for the angles, a 54 tone signal may have feedback information of 324 bytes (e.g., 4×12×54/8). 
   For a 4×4 MIMO communication, the beamforming unitary matrix may be: 
           V   =         (   V   )     ⁢   ij     =     [           cos   ⁢           ⁢     ψ   1     ⁢   cos   ⁢           ⁢     φ   1             cos   ⁢           ⁢     ψ   2     ⁢   cos   ⁢           ⁢     φ   2             cos   ⁢           ⁢     ψ   3     ⁢   cos   ⁢           ⁢     φ   3             cos   ⁢           ⁢     ψ   4     ⁢   cos   ⁢           ⁢     φ   4                 cos   ⁢           ⁢     ψ   1     ⁢   sin   ⁢           ⁢     φ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   11                 cos   ⁢           ⁢     ψ   2     ⁢   sin   ⁢           ⁢     φ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   12                 cos   ⁢           ⁢     ψ   3     ⁢   sin   ⁢           ⁢     φ   3     ⁢     ⅇ     j   ⁢           ⁢     ϕ   13                 cos   ⁢           ⁢     ψ   4     ⁢   sin   ⁢           ⁢     φ   4     ⁢     ⅇ     j   ⁢           ⁢     ϕ   14                     sin   ⁢           ⁢     ψ   1     ⁢   cos   ⁢           ⁢     θ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   21                 sin   ⁢           ⁢     ψ   2     ⁢   cos   ⁢           ⁢     θ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   22                 sin   ⁢           ⁢     ψ   3     ⁢   cos   ⁢           ⁢     θ   3     ⁢     ⅇ     j   ⁢           ⁢     ϕ   23                 sin   ⁢           ⁢     ψ   4     ⁢   cos   ⁢           ⁢     θ   4     ⁢     ⅇ     j   ⁢           ⁢     ϕ   24                     sin   ⁢           ⁢     ψ   1     ⁢   sin   ⁢           ⁢     θ   1     ⁢     ⅇ     j   ⁢           ⁢     ϕ   31                 sin   ⁢           ⁢     ψ   2     ⁢   sin   ⁢           ⁢     θ   2     ⁢     ⅇ     j   ⁢           ⁢     ϕ   32                 sin   ⁢           ⁢     ψ   3     ⁢   sin   ⁢           ⁢     θ   3     ⁢     ⅇ     j   ⁢           ⁢     ϕ   33                 sin   ⁢           ⁢     ψ   4     ⁢   sin   ⁢           ⁢     θ   4     ⁢     ⅇ     j   ⁢           ⁢     ϕ   34                 ]             
=[cos(ψ 1 ) cos(ψ 2 ); sin(ψ 1 )*e jΦ1  sin(ψ 2 )*e jΦ2 ], where i, j=1, 2, 3, 4; wherein ψ 1 , ψ 2 , ψ 3 , ψ 4 , θ 1 , θ 2 , θ 3 , θ 4 , Φ 1 , Φ 2 , Φ 3 , Φ 4 , Φ 21 , Φ 22 , Φ 23 , Φ 24 , Φ 31 , Φ 32 , Φ 33 , Φ 33 , Φ 41 , Φ 42 , Φ 43 , Φ 43  represent angles of the unit circle, wherein Diagonal (V*V)=1 s, and wherein:
 
   
     
       
         
           
             
               ψ 
               i 
             
             = 
             
               
                 cos 
                 
                   - 
                   1 
                 
               
               ⁡ 
               
                 ( 
                 
                   
                     
                       
                          
                         
                           V 
                           
                             1 
                             ⁢ 
                             i 
                           
                         
                          
                       
                       2 
                     
                     + 
                     
                       
                          
                         
                           V 
                           
                             2 
                             ⁢ 
                             i 
                           
                         
                          
                       
                       2 
                     
                   
                 
                 ) 
               
             
           
           , 
           
             
               φ 
               i 
             
             = 
             
               
                 cos 
                 
                   - 
                   1 
                 
               
               ⁡ 
               
                 ( 
                 
                   
                     V 
                     
                       1 
                       ⁢ 
                       i 
                     
                   
                   
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ψ 
                       i 
                     
                   
                 
                 ) 
               
             
           
           , 
           
             
               θ 
               i 
             
             = 
             
               
                 cos 
                 
                   - 
                   1 
                 
               
               ⁢ 
               
                  
                 
                   
                     V 
                     
                       3 
                       ⁢ 
                       i 
                     
                   
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ψ 
                       i 
                     
                   
                 
                  
               
             
           
         
       
     
     
       
         
           
             
               ϕ 
               
                 1 
                 ⁢ 
                 i 
               
             
             = 
             
               ∠ 
               ⁡ 
               
                 ( 
                 
                   V 
                   
                     2 
                     ⁢ 
                     i 
                   
                 
                 ) 
               
             
           
           , 
           
             
               ϕ 
               
                 2 
                 ⁢ 
                 i 
               
             
             = 
             
               ∠ 
               ⁡ 
               
                 ( 
                 
                   V 
                   
                     3 
                     ⁢ 
                     i 
                   
                 
                 ) 
               
             
           
           , 
           
             
               ϕ 
               
                 3 
                 ⁢ 
                 i 
               
             
             = 
             
               ∠ 
               ⁡ 
               
                 ( 
                 
                   V 
                   
                     4 
                     ⁢ 
                     i 
                   
                 
                 ) 
               
             
           
         
       
     
   
   In this example, with 24 angles, the beamforming module  132  may regenerate V as a 4×4 matrix per tone. With 4-bits for expression for the angles, a 54 tone signal may have feedback information of 648 bytes (e.g., 4×24×54/8). 
   The baseband transmit processing 100-TX receives the polar coordinates Φ and ψ from the receiver as feedback information as will described in greater detail with reference to  FIG. 6 . 
     FIG. 5  is a schematic block diagram of baseband receive processing 100-RX that includes a plurality of fast Fourier transform (FFT) modules  140 ,  142 , a beamforming (U) module  144 , a plurality of constellation demapping modules  146 ,  148 , a plurality of deinterleaving modules  150 ,  152 , a switch, a depuncture module  154 , and a decoding module  156  for converting a plurality of inbound symbol streams  124  into inbound data  92 . As one of ordinary skill in the art will appreciate, the baseband receive processing 100-RX may include two or more of each of the deinterleaving modules  150 ,  152 , the constellation demapping modules  146 ,  148 , and the FFT modules  140 ,  142 . In addition, one of ordinary skill in art will further appreciate that the decoding module  156 , depuncture module  154 , the deinterleaving modules  150 ,  152 , the constellation decoding modules  146 ,  148 , and the FFT modules  140 ,  142  may be function in accordance with one or more wireless communication standards including, but not limited to, IEEE 802.11a, b, g, n. 
   In one embodiment, a plurality of FFT modules  140 ,  142  is operably coupled to convert a plurality of inbound symbol streams  124  into a plurality of streams of beamformed symbols. The inverse beamforming module  144  is operably coupled to inverse beamform, using a unitary matrix having polar coordinates, the plurality of streams of beamformed symbols into a plurality of streams of data symbols. The plurality of constellation demapping modules is operably coupled to demap the plurality of streams of data symbols into a plurality of interleaved streams of data. The plurality of deinterleaving modules is operably coupled to deinterleave the plurality of interleaved streams of data into encoded data. The decoding module is operably coupled to convert the encoded data into inbound data  92 . 
   The beamforming module  144  is operably coupled to multiply a beamforming unitary matrix (U) with baseband signals provided by the plurality of FFT modules  140 ,  142 . The FFT modules  140 ,  142  function in accordance with one of the IEEE 802.11x standards to provide an OFDM (Orthogonal Frequency Domain Multiplexing) frequency domain baseband signals that includes a plurality of tones, or subcarriers, for carrying data. Each of the data carrying tones represents a symbol mapped to a point on a modulation dependent constellation map. The baseband receive processing 100-RX is further functional to produce feedback information for the transmitter as further described with reference to  FIG. 6 . 
     FIG. 6  is a schematic block diagram of a beamforming wireless communication where H=UDV* (H—represents the channel, U is the receiver beamforming unitary matrix, and V* is the conjugate of the transmitter beamforming unitary matrix. With H=UDV*, y (the received signal)=Hx+N, where x represents the transmitted signals and N represents noise. If z=Vx, then U*y=U*UDV*VZ+U*n=Dz+N. 
   From this expression, the baseband receive processing 100-RX may readily determine the feedback of V, where V includes polar coordinates. For instance, the receiver may decompose the channel using singular value decomposition (SVD) and send information relating only to a calculated value of the transmitter&#39;s beamforming matrix (V) as the feedback information. In this approach, the receiver calculates (V) based on H=UDV*, where H is the channel response, D is a diagonal matrix, and U is a receiver unitary matrix. This approach reduces the size of the feedback information with respect to SVD using Cartesian coordinates. For example, in a 2×2 MIMO wireless communication, the feedback needs four elements that are all complex values [V11 V12; V21 V22] with two angles (ψ and Φ). In general, Vik=aik+j*bik, where aik and bik are values between [−1, 1]. To cover [−1, 1], ψ is in [0, π] and Φ is in [0, 2π]. With π/2 resolutions for angles, ψ needs to be π/4 or 3π/4, i.e., cos(ψ)=0.707 or −0.707, which requires 1 bit, where Φ needs to be either π/4, 3π/4, 5π/4, 7π/4, i.e., exp(jΦ)=0.707(1+j), 0.707(1−j), 0.707(−1+j) or 0.707(−1−j), which requires 2 bits. With π/4 resolutions for angles, ψ needs to be π/8, 3π/8, 5π/8 or 7π/8, which requires 2 bits, where Φ needs to be either π/8, 3π/8, 5π/8, 7π/8, 9π/8, 11π/8, 13π/8 or 15π/8, which requires 4 bits. So, for an example of 2×2 system to use 4 bits per tone, it may have 1 bit for ψ, 2 bits for Φ and 1 index bit to determine the relationship between ψ and Φ, such as either ψ 1 =ψ 2 +π and Φ 1 +Φ 2 =π/2, or ψ 1 =ψ 2  and Φ 1 −ψ 2 =π/2. 
   For the same resolution in Cartesian expression of 4 bits per each element for each of the real and imaginary components, aik and bik, can be within [−½, ½], it requires 4*2*4=32 bits per tone. For OFDM MIMO wireless communications, the number of bits required is 1728 bits for the Cartesian expression. While an angle expression in accordance with the present invention requires 8 bits per tone, which for the same OFDM MIMO wireless communications would require 432 bits. This represents a significant reduction in the overhead needed for packet exchange. 
   The preceding discussion has presented a method and apparatus for reducing feedback information for beamforming in a wireless communication by using polar coordinates. As one of average skill in the art will appreciate, other embodiments may be derived from the present teachings without deviating from the scope of the claims.