Abstract:
A method including downconverting an analog radio frequency signal into an analog baseband signal; recovering an analog in-phase signal and an analog quadrature signal from the analog baseband signal; converting the analog in-phase signal into a corresponding digital in-phase signal; converting the analog quadrature signal into a corresponding digital quadrature signal; compensating the digital in-phase signal and the digital quadrature signal; converting the compensated digital in-phase signal and the compensated digital quadrature signal into a frequency domain digital Orthogonal Frequency Division Multiplexing (OFDM) symbol; generating a plurality of channel estimates, wherein each channel estimate corresponds to an estimate of the channel for a corresponding sub-carrier of the frequency domain digital OFDM symbol; and generating (i) a most likely estimate of the imbalance between the digital in-phase signal and the digital quadrature signal and (ii) a most likely estimate of a common phase error in the plurality of channel estimates.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/645,678 (now U.S. Pat. No. 7,881,237), filed Dec. 23, 2009, which is a continuation of U.S. patent application Ser. No. 12/287,199 (now U.S. Pat. No. 7,643,405), filed Oct. 7, 2008, which is a continuation of U.S. patent application Ser. No. 10/316,806 (now U.S. Pat. No. 7,433,298), filed Dec. 10, 2002, which claims priority benefit under 35 U.S.C. §119(e)(1) to U.S. Provisional Application No. 60/404,655, filed Aug. 19, 2002. The disclosures of the above applications are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The invention generally relates to symbol modulated communication techniques, and more particularly, to a method and apparatus which improves reception performance of OFDM modulated signals through compensating for at least one of residual frequency offset, phase noise and I/Q imbalance in the received baseband signal. 
     BACKGROUND 
     The past few years has witnessed the ever-increasing availability of relatively cheap, low power wireless data communication services, networks and devices, promising near wire speed transmission and reliability. One technology in particular, described in the IEEE Standard 802.11a (1999) and Draft IEEE Standard 802.11g (2002) High Rate PHY Supplements to the ANSI/IEEE Standard 802.11, 1999 edition, collectively incorporated herein fully by reference, has recently been commercialized with the promise of 54 Mbps effective bandwidth, making it a strong competitor to traditional wired Ethernet and the more ubiquitous “802.11b” or “WiFi” 11 Mbps mobile wireless transmission standard. 
     IEEE 802.11a and 802.11g or “802.11a/g” compliant transmission systems achieve their high data transmission rates through using Orthogonal Frequency Division Modulation or OFDM encoded symbols mapped up to 64 QAM multicarrier constellation and beyond. Generally, OFDM works generally by dividing one high-speed data carrier into multiple low speed sub-carriers which are used for transmission of data in parallel. Put another way, the data stream of interest is divided into multiple parallel bit streams, each transmitted over a different sub-carrier having a lower effective bit rate. Before final power amplification and transmission, the multicarrier OFDM symbol encoded symbols are converted into the time domain using Inverse Fast Fourier Transform techniques resulting in a relatively high-speed time domain signal with a large peak-to-average ratio (PAR). OFDM is also used in fixed broadband wireless access systems such as proposed in IEEE Standard 802.16a: Air Interface for Fixed Broadband Wireless Access Systems Part A: Systems between 2 and 1 GHz, Draft working document, February 2002, (“802.16a”) which is incorporated herein fully by reference. 
     In the case of 802.11a and 802.11g, there are up to 52 defined subcarriers, of which 48 are available to carry data (4 remaining are pilot sub-carriers or tones, which bear predetermined data). These sub-carriers are substantially orthogonal to each other, so they can be spaced closer together than in conventional frequency division multiplexing. Mathematically, the integral of the product of any two orthogonal sub-carriers is zero. This property allows the separating of sub-carriers at the receiver without interference from other sub-carriers. 
     In wireless OFDM communications systems, residual frequency offset and phase noise can impact Bit Error Rate performance, and ultimately reception performance in OFDM compliant wireless communications due to a loss of sub-carrier orthogonality. Reception performance, and ultimately throughput and range of an OFDM system is further limited by imbalance of the I and Q components of the analog baseband signal recovered from the inbound RF signals bearing the OFDM modulated data of interest. It is, therefore, advantageous if an OFDM compliant receiver and receiving techniques could be provided to account and compensate for such effects and improve overall reception performance, including range and effective throughput in less than ideal conditions. 
     SUMMARY OF THE INVENTION 
     To address these and other perceived shortcomings, the present invention is directed to baseband signal processing methods and apparatus which incorporate I/Q imbalance compensation based on most likely estimates of the I/Q imbalance between the I and Q components of the baseband signal. Further, in accordance with at least one disclosed embodiment of the invention, most likely estimates of the common phase error (CPE) may be used to compensate the initial channel estimates to further improve symbol demodulation rates and overall receiver performance. 
     Though applicable to any multicarrier OFDM communications system, methods and apparatus consistent with the present invention may be conveniently implemented in IEEE 802.11a, IEEE 802.11g, or 802.16a compliant wireless communications systems to reduce the effects of imbalanced I/Q components of baseband signals bearing packets or frames of OFDM symbols of data recovered from inbound RF signals, as well as counter residual frequency offset and phase noise potentially present in such baseband signals 
     Additional aspect features and advantages of this invention will become apparent from the following detailed description of embodiments thereof, which proceeds with reference to the accompanying drawings, in which like reference numerals indicate like parts or features. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a simplified functional block diagram of a transceiver according to an embodiment of the present invention. 
         FIG. 2  is a functional block diagram of the receive baseband processing unit shown in  FIG. 1 . 
         FIG. 3  is a calculation flow diagram for obtaining maximum likelihood estimates of the common phase error and I/Q imbalance consistent with the baseband processing unit shown in  FIG. 2 . 
         FIG. 4  is a more detailed block diagram of the transmitter shown in  FIG. 1 . 
         FIG. 5  is a diagram of an OFDM PPDU frame. 
         FIG. 6  is a flowchart illustrating I/Q imbalance compensation and adaptive channel estimate refinement according to another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       FIG. 1  illustrates a wireless communications transceiver  100  according to an embodiment of the present invention, including the receiver baseband processing unit shown in  FIG. 2 . In this embodiment, inbound RF signals conveying a 802.11a/g or 802.16a compliant frame of OFDM encoded symbols are picked up by the duplex antenna  110  and routed to the RF receiver unit  115  of a receiver  150  arranged in a manner consistent with the present invention. The RF receiver unit  115  performs routine downconversion and automatic gain control of the inbound RF signals, and presents an analog baseband signal containing at least one frame of 802.11a/g OFDM symbols to the receive baseband processing unit or processor  120 . Generally speaking, the receive baseband processing unit or processor  120  performs symbol demodulation of the each inbound 802.11a/g compliant frame to recover bitstream data for receiver synchronization (preamble), frame or packet definition (header), or the actual inbound data of interest (payload). Consistent with the present invention, this processor  120  includes I/Q imbalance and common phase error compensation consistent with the present invention, as will be described in more detail below. 
     Once recovered by the receive baseband processor  120 , the inbound data contained in each received 802.11a/g formatted frame is delivered to a network interface such as the MAC layer interface  125  and then on to higher layer applications and devices being serviced by the transceiver  100 . Outbound data intended for wireless transmission originating from the device(s) or application(s) being serviced by the transceiver  100  are delivered to the transmit baseband processor  135  of the transmitter  160  from the MAC interface  125 . The transmit baseband processor  135  formulates appropriate 802.11a/g frame preamble and header information, and OFDM symbol encodes the outbound data to generate one or more complete outbound 802.11a/g frames. As the frame or packet is being developed, it is converted into analog form suitable for upconversion and RF transmission by the RF transmitter unit  140  consistent with well-known 802.11a/g physical layer requirements. 
     Though only a single duplex antenna arrangement is shown in  FIG. 1 , the transceiver  100  can be easily adapted to incorporate multiple receive pathways or chains to take advantage of selection diversity or MRC diversity techniques. Likewise, though not shown in  FIG. 1 , transmit diversity techniques may be employed in addition or in the alternative as would be understood by those skilled in the art. 
     Also, though not shown in  FIG. 1 , the transceiver  100  may form an operational part of a network interface apparatus such as a PC card or network interface card capable of interfacing with the CPU or information processor of an information processing apparatus such as a desktop or laptop computer, and may be integrated within and constitute a part of such information processing apparatus. This network interface apparatus may alternatively fowl an operational component of a wireless communications access point such as a base station as will be appreciated by these ordinarily skilled in the art. 
       FIG. 4  is a more detailed block diagram of the transmitter  140 , which includes an OFDM PMD compliant with the IEEE 802.11a/g standards. In  FIG. 4 , an outbound PPDU  400 , i.e. a data unit is provided to the input of the transmit baseband processor  135  from the MAC interface  125  ( FIG. 1 ). This data unit, described in greater detail below, has a preamble, a header, data portion, tail, pad bits etc. The data unit bit stream is input to a convolutional encoder  402 . The information preferably is encoded using convolutional encoding rate R=1/2, 2/3, or 3/4 depending on the specified data rate, and using known polynomials. 
     Next the encoded data is input to bit interleaving and mapping block  404 . Bit interleaving is accomplished by a block interleaver with a block size corresponding to the number of bits in a single OFDM symbol, NCBPS, as detailed in e.g. the IEEE 802.11a standard (1999) at section 17.3.5.6. The first permutation ensures that adjacent coded bits are mapped onto nonadjacent sub-carriers. The second permutation step ensures that adjacent coded bits are mapped alternately onto less and more significant bits of the constellation and, thereby, long runs of low reliability (LSB) bits are avoided. 
     Block  404  in  FIG. 1  also represents mapping or symbol modulating the data. The encoded and interleaved binary serial input data is divided into groups of bits, each group sized according to the selected modulation (1, 2, 4 or 6 bits). For example, 64-QAM modulation maps 6-bit quantities onto the constellation. The same procedures can be extended to higher rate encoding, beyond the 802.11a/g standards, such as 256-QAM as proposed in e.g. IEEE 802.16a, in which case each group of 8 bits of the serial data is mapped onto one complex number (I+jQ) corresponding to a location on the 256-QAM constellation. The output values are multiplied by a normalization factor, depending on the base modulation mode (for 64-QAM, it is 1/√{square root over (42)}) to achieve the same average power for all mappings. 
     Each group of 48 complex numbers is associated with one OFDM symbol. Thus 48×6=288 data bits are encoded per OFDM symbol in the case of 64-QAM constellation bit encoding. The symbol duration is 4.0 μsec. Each group of 48 numbers is mapped to a corresponding one of 48 useful sub-carriers, frequency offset index numbers − 26  to +26. Accordingly each sub-carrier (except the pilot sub-carriers) will be modulated by one complex number for each OFDM symbol in the current data unit. 
     In each symbol, four of the sub-carriers are dedicated to pilot signals to assist in coherent detection. They are also used in the accordance with the present invention in compensating for I/Q imbalance in the digital I and Q components of the inbound baseband signal and as well as in compensating for common phase error in the initial channel estimates. The pilot signals are put in sub-carriers −21, −7, 7 and 21 according to the IEEE 802.11a/g standards. The pilots are BPSK modulated by a pseudo binary sequence to prevent the generation of spectral lines. 
     The inverse FFT  406  receives all 52 sub-carrier signals and combines them to form a time domain digital signal. Next, a guard interval (not shown) is inserted. The guard interval is to increase immunity to multipath by extending the length of the transmitted symbol. (It is also known as CP or cyclic prefix.) The window length used in the baseband processor in the receiver to decode the symbol is that of the active symbol length, in other words excluding the guard interval period. Symbol wave shaping follows in block  408 . Then modulation onto in-phase I and quadrature-phase Q carriers is performed and the combined signal is modulated onto the radio frequency carrier fc for transmission (via RF transmitter  140 ). To summarize mathematically, as noted above, the transmitted time-domain signal x(t) (after D/A conversion at rate 1/T) is represented by 
                     x   ⁡     (   t   )       =       1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢       X   k     ⁢           ⁢     ⅇ     j   ⁢       2   ⁢   nkt     NT                       (   1   )               
where X k  are the frequency-domain data symbols. In other words, the N values X k  represent the respective values of the discretely-varying (e.g. QPSK or QAM) signals modulating the OFDM carriers.
 
     Before describing the receiver  150  of the transceiver  100 , we examine more closely the structure of the data unit frame and how it is designed to assist the receiver  150  in perceiving and decoding inbound OFDM packets or frames.  FIG. 5  is a block diagram illustrating the structure of a PLCP protocol data unit (PPDU) frame, in accordance with the IEEE 802.11a standard, and is similar to the 20 Mbps+ rate PPDU frame format for IEEE 802.11g. In particular, this frame structure is a part of the IEEE 802.11a physical layer extension to the basic 802.11 protocol. The 802.11a extension defines requirements for a PHY operating in the 5.0 GHz unlicensed frequency bands and data rates ranging from 6 Mbps to 54 Mbps. 
     Under this protocol, the PPDU (PLCP protocol data unit) frame consists of a PLCP preamble and signal and data fields as illustrated in  FIG. 5 . The receiver  150  uses the PLCP preamble to acquire the incoming OFDM signal and synchronize the baseband processor  120 . The PLCP header contains information about the PSDU (PLCP service data unit containing data of interest) from the sending OFDM PHY. The PLCP preamble and the signal field are always transmitted at 6 Mbps, binary phase shift keying (BPSK), modulated using convolutional encoding rate R=½. 
     The PLCP preamble  502  is used to acquire the incoming signal and train and synchronize the receiver  150 . The PLCP preamble consists of 12 symbols, 10 of which are short symbols, and 2 long symbols. The short symbols are used to train the receiver&#39;s AGC (not shown) and obtain a coarse estimate of the carrier frequency and the channel. The long symbols are used to fine-tune the frequency and channel estimates. Twelve sub-carriers are used for the short symbols and 52 for the long symbols. The training of an 802.11a compliant OFDM receiver, such as receiver  150 , is accomplished in 16 μsec. This is calculated as 10 short symbols times 0.8 μsec each, plus 2 long training symbols at 3.2 μsec each, plus the guard interval. See e.g. IEEE standard 802.11a (1999) section 17.3.3. These training symbols, as noted above, provide for initial channel and frequency offset estimation, but do not compensate for other factors such as sampling frequency jitter. 
     Referring still to  FIG. 5 , the preamble field  502  is followed by a signal field  504  which consists of one OFDM symbol. This contains the rate and length fields as requested by the MAC interface  125 . The rate field conveys information about the type of modulation and the coding rate as used in the rest of the packet. The encoding of the SIGNAL single OFDM symbol is performed with BPSK modulation of the sub-carriers and again using convolutional coding at R=½. The SIGNAL field is composed of 24 bits, with bits  0  to  3  encoding the rate, bit  4  reserved, and bits  5 - 16  encoding the length of the packet, with the LSB being transmitted first. A single parity bit and 6-bit tail field complete the SIGNAL symbol. Finally, the SIGNAL field  504  is followed by the data  506  comprising a variable number of OFDM symbols including the SERVICE field still forming part of the PLCP Header, consistent with the length specified in the SIGNAL field  504 . 
     As mentioned previously in discussing  FIG. 1 , the receiver  150  includes an RF receiver unit  115  to receive, downconvert and gain condition inbound RF signals to present an analog baseband signal to the receive baseband processor  120 . A more detailed view of the receive baseband processor  120  in accordance with an embodiment of the invention is illustrated in  FIG. 2 . Here, the recovered analog baseband signal z(t) is provided to the input of the I/Q detector  205  to recover analog in-phase (i) and quadrature-phase (q) signals, which are then fed to the analog to digital converter  210 . The i and q signals are converted into their respective digital counterpart signal components I and Q, each bearing digital data in the time domain. Next, the I and Q components are sent to the I/Q imbalance compensation unit  220 , where they undergo I/Q imbalance compensation using maximum likelihood estimates of the gain εML and phase θML imbalance calculated by the common phase error and I/Q imbalance calculation unit  240  for, e.g., the previously received OFDM symbol. Imbalance compensation according to this embodiment, including calculation of εML and θML will be described in more detail below with reference to equations 13-16. Imbalance compensated counterparts Ĩ and {tilde over (Q)} are obtained by the I/Q imbalance compensation unit  220  and sent to the FFT  230  for conversion into the frequency domain and recovery of the OFDM symbols present therein. In fact, the FFT  230  recovers the 52 subcarrier signals Yk 1  . . . Yk 52  forming each OFDM symbol borne by the time domain Ĩ and {tilde over (Q)} signals. At block  235 , the guard interval subcarriers are discarded and the remaining subcarriers are then input to demapping block  255  and Viterbi decoder  260  for bit de-interleaving and de-mapping (from the e.g. 64 QAM constellation), as well as most likely sequence determination consistent with known Viterbi algorithms. The resulting serial binary stream then undergoes descrambling (not shown) to recover the inbound data of interest in proper sequence, as is known in the art. 
     It should be noted that, unlike conventional OFDM baseband processors, the baseband processor  120  utilizes common phase error compensated channel estimates in the OFDM demodulation and decoding process. In particular, a common phase error and I/Q imbalance calculation unit  240  is provided after the guard subcarrier discard block  235  to calculate the most likely estimate of the I/Q imbalance αML and the most likely estimate of the common phase error Λ0,ML using the initial channel estimates {tilde over (H)} k1  . . . {tilde over (H)} k52  derived from the pilot subcarriers by the channel estimator  265  as well as the OFDM symbol bearing subcarriers Yk 1  . . . Yk 52  themselves on a per symbol basis. In turn, the imbalance estimate αML is used to derive εML and θML for use in the I/Q imbalance compensation performed by the I/Q imbalance compensation unit  220 , and the common phase error Λ0,ML estimate is multiplicatively applied to the channel estimates {tilde over (H)} k1  . . . {tilde over (H)} k52  by the channel estimate compensation unit  245 . The resulting compensated channel estimates, {tilde over (H)} k1  . . . {tilde over (H)} k52  minus those specified for the pilot subcarriers which are unneeded for demodulation and Viterbi decoding, are provided to the Viterbi decoder  260  to provide more accurate recovery of the most likely sequence of transmitted data from the received OFDM symbol(s). These compensated channel estimates {tilde over (H)} k1  . . . {tilde over (H)} k52  are also provided to the channel estimator  265  to refine the channel estimates for subsequent OFDM symbol(s), if any, in the frame (adaptive channel estimation using common phase error compensation). Details as to calculating αML and Λ0,ML will be discussed below with reference to equations (6)-(11), as will performance of common phase error compensation of the channel estimates with reference to e.g. equation (12) discussed below. 
     Obtaining the most likely estimates of the common phase error and I/Q imbalance, as well as channel estimate and I/Q imbalance compensation consistent with the present invention will now be discussed. Recalling equation (1), the transmitted signal x(t) is convolved with a multi-path channel with impulse response h(t). At the receiver (such as receiver  160  of the transceiver  100  shown in  FIG. 1 ), residual frequency offset and phase noise contribute to a multiplicative distortion ejΦ(t). Let y(t)=ejΦ(t) [h(t)*x(t)], where * denotes convolution. The in-phase (I) and quadrature-phase (Q) components of y(t) are distorted by a gain imbalance of c and a phase imbalance of θ. Finally, white Gaussian noise v(t) is added to form the received baseband signal z(t): 
                     z   ⁡     (   t   )       =         y   ⁡     (   t   )       ⁡     [       cos   ⁡     (     θ   /   2     )       +     j   ⁢     ɛ   2     ⁢     sin   ⁡     (     θ   /   2     )           ]       +     y   *       (   t   )     ⁡     [         ɛ   2     ⁢     cos   ⁡     (     θ   /   2     )         +     jsin   ⁡     (     θ   /   2     )         ]         +     v   ⁡     (   t   )                 (   2   )               
For |θ|&lt;&lt;1 and |ε|&lt;&lt;1,
 
     
       
         
           
             
               
                 
                   
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     Let Φn, yn, zn, vn denote the discrete-time versions of Φ(t), y(t), z(t), v(t), respectively, sampled at the rate 1/Ts. Let Yk, Zk, Vk denote the N-point FFT&#39;s of yn, zn, vn, respectively. Also, let α=(ε−jθ)/2, which represents the I/Q imbalance in the frequency domain, and Λk, phase noise and residual frequency offset, denote the FFT of ejΦn (the residual frequency offset and phase noise in the frequency domain). The FFT output Zk is given by 
                       Z   k     ≈       Y   k     +       Y     -   k     *     ⁢   α     +     V   k         =         1   N     ⁢     Λ   0     ⁢     H   k     ⁢     X   k       +       1   N     ⁢     Λ   0   *     ⁢     H     -   k     *     ⁢     X     -   k     *     ⁢           ⁢   α     +     W   k               (   4   )               
where
 
               H   k     =     ∫       h   ⁡     (   τ   )       ⁢     ⅇ     -   j       ⁢       2   ⁢   nkτ     NTs     ⁢     ⅆ   τ               
is the FFT of the channel impulse response and W k  represents intercarrier interference and noise (also known as Additive White Gaussian Noise or AWGN). The common phase error (CPE) is given by Λ o . Let A k =H k X k /N. Therefore,
 
 Z   k ≈Λ 0   A   k +Λ 0   *αA   −k   *+W   k   (5)
 
     Suppose that there are 2M pilot subcarriers (with subcarrier indeces ±k1 . . . , ±kM) in every OFDM symbol. For example, in the IEEE 802.11a or draft 802.11g standards, there are 2M=4 pilot subcarriers symmetrically positioned in the constellation with indeces k=±7, ±21. These pilot subcarriers are used in this embodiment to estimate the common phase error Λo and the I/Q imbalance α. Thus, Ak can be estimated for these pilot subcarriers by Â k =Ĥ k X k |N where Ĥ k  are the estimates of Hk. The maximum likelihood estimates of Λo and α can be derived and are given by 
                     Λ     o   ,   ML       =             c   1     ⁢     r   2       -       c   2   *     ⁢     r   1             c   1   2     -            c   2          2         ⁢           ⁢   and             (   6   )                 α   ML     =           c   1     ⁢     r   1       -       c   2     ⁢     r   2               c   1     ⁢     c   2   *       -       c   2     ⁢     r   1   *                   (   7   )               
where
 
                       c   1     =       ∑     i   =   1     M     ⁢     (                A   ^       k   i            2     +              A   ^       -     k   i              2       )         ,           (   8   )                   c   ⁢           ⁢   2     =     2   ⁢       ∑     i   =   1     M     ⁢           ⁢         A   ^     ki     ⁢       A   ^       -   ki               ,           (   9   )                 r   1     =       ∑     i   =   1     M     ⁢     (           Z     k   i       ⁢       A   ^       -     k   i           +       Z     -     k   i         ⁢       A   ^       k   i           ,   and                 (   10   )                 r   2     =       ∑     i   =   1     M     ⁢       (         Z     k   i       ⁢       A   ^       k   i     *       +       Z     -     k   i         ⁢       A   ^       -     k   i       *         )     .               (   11   )               
The most likely estimates Λ 0,ML  and α ML  are in fact here derived from a maximum likelihood estimation expression:
 
               Λ   0   min     ,     α   [       ∑     i   =   1     M     ⁢           ⁢     [              Z   ki     -       Λ   o     ⁢     A   ki       -       Λ   o   *     ⁢   α   ⁢           ⁢     A     -   ki     *     ⁢          2     ⁢     +              Z     -   ki       -       Λ   o     ⁢           ⁢     A     -   ki         ⁢     -     k   ⁢           ⁢   1       ⁢       Λ   o   *     ⁢   α   ⁢           ⁢     A   ki   *              2       ]         ]     ,                 
based on a likelihood function for equation (5) listed above for pilot subcarriers at ±k 1 , . . . , ±k M , distributed according to multi dimensional Gaussian distribution. To find Λ 0,ML  and α ML  from this expression, this expression is differentiated with respect to α and Λ 0 , the results are set to 0 and solved for these variables.
 
     With αML for the current OFDM symbol obtained, the I/Q gain and phase imbalance are estimated by the
 
ε ML =2           (α ML )  (13)
 
θ ML =2         (α ML )  (14)

     Let In, Qn denote the I and Q components of the output of the analog to digital converter, namely ADC  210  in  FIG. 2  which define the nth OFDM symbol in the inbound PLCP frame. The I/Q imbalance is compensated by the I/Q imbalance compensation unit  220  by forming Ĩ n , {tilde over (Q)} n  where 
                       I   ~     n     =         (     1   -       ɛ     ML   ,     n   -   1         2       )     ⁢     I   n       +         θ     ML   ,     n   -   1         2     ⁢     Q   n                 (   15   )                   Q   ~     n     =           θ     ML   ,     n   -   1         2     ⁢     I   n       +       (     1   +       ɛ     ML   ,     n   -   1         2       )     ⁢     Q   n                 (   16   )               
Thus, in this embodiment, the values for ε ML  and θ ML  for the previous symbol (n−1) are used to compensate the I/Q imbalance in the nth or succeeding OFDM symbol. In turn, the imbalance compensated signal components Ĩ n , {tilde over (Q)} n  are provided to the input of the FFT  230  to improve symbol demodulation performance, and ultimately OFDM receiver performance.
 
     Though not shown in  FIG. 2 , in an alternative embodiment, historical analysis of αML may be used to compensate the I/Q components, including use of averaged εML and θML values over a particular relative (e.g. within a current PLCP frame) or absolute (e.g. preceding 10 μsec) period of time. 
     In the embodiment shown in  FIG. 2 , the channel estimates Ĥ k  are compensated for the common phase error by the e.g. channel estimate compensation unit  245  ( FIG. 2 ) as follows:
 
 {tilde over (H)}   k =Λ 0,ML   Ĥ   k   ;Ĥ   k   ={tilde over (H)}   k   (12)
 
In other words, the channel estimate for demodulating next OFDM symbol is the CPE compensated version of the channel estimates for the present OFDM symbol, with H kINIT  (or the initial channel estimates) being used for the first OFDM symbol in the received PLCP frame. In an alternative embodiment, also not shown in  FIG. 2 , historical analysis of Λ 0,ML  may be employed for common phase error compensation, similarly to α ML  previously discussed.
 
       FIG. 3  illustrates a calculation flow diagram for obtaining αML, Λ0,ML for the four pilot subcarriers in the IEEE 802.11a/g standards consistent with the embodiment shown in  FIG. 2 . In particular this calculation flow diagram represents the implementation of equations (6)-(11) undertaken by the common phase error and I/Q imbalance calculation unit  240  in terms of complex convolution  305 , multiplier  310 , adder  315 , subtractor  320 , and division 325 units. It should be understood that  FIG. 3  merely illustrates certain calculations and is not a particularized hardware schematic, in whole or in part, of the common phase error and I/Q imbalance calculation unit  240 . In fact, the illustrated calculations can be conveniently implemented in a variety of ways, as would be understood by those skilled in the art, including programmable hardware, e.g. a DSP or microprocessor core with appropriate embedded software, or dedicated custom hardware, such as provided by discrete logic and/or an ASIC, could be used in whole or in part to provide the desired functionality. As such, various arrangements consistent with the calculation flow diagram of  FIG. 3  or equations (6)-(11) may be used without departing from the scope of the present invention. 
       FIG. 6  illustrates I/Q imbalance and common phase error compensation according to an alternative embodiment of the invention. In this embodiment, processing begins at step  610  when the beginning of a new PLCP frame is recognized. During the preamble (result of query  610  is yes) of this frame, the initial channel estimates HkINIT are formed from the pilot subcarriers based on known preamble information consistent with 802.11a/g standards (step  615 ), and the channel estimates Ĥ k  and εML and θML are initialized. Then, until the end of the current frame is reached (step  625 ), the I/Q components for the current OFDM symbol in the frame are recovered (step ( 630 ), compensated for I/Q imbalance based on εML and θML calculated with reference to the previous symbol (or initial values if at the beginning symbol of the header or payload) (step  640 ) whilst the current Λ0,ML and αML, values are calculated (step  635 ), and the channel estimates are updated (step  638 ). Thereafter, as shown in  FIG. 6 , the I/Q imbalance compensated I and Q components obtained in step  640  are then converted into the frequency domain (step  642 ), demapped from the constellation (step  645 ), Viterbi decoded step  650 ), and descrambled (step  655 ) as is known in the art. Note that one or more of the illustrated processing steps shown in the flowchart of  FIG. 6  may be carried out by discrete or combinational logic, as well as through an information processor, such as a general perpose microprocessor or microcontroller, or a specific-purpose processor such as a digital signal processor programmed in accordance with the functions and general sequence so described. Of course, any variety and combination of logic and/or instruction programming consistent with  FIG. 6  may be used, such as the substitution of any functionally equivalent steps or inclusion of additional steps or operations, without departing from the scope of the present invention. 
     In a further alternative embodiment, maximum likelihood estimates for I/Q imbalance can be calculated without regard to phase noise or residual frequency offset effects, as was previously described. In such case, αML reduces to: 
                       α   ML     =         ∑     i   =   1     M     ⁢           ⁢     [         (       Z     k   i       -       A   ^       k   i         )     ⁢       A   ^       -     k   i           +       (       Z     -     k   i         -       A   ^       -     k   i           )     ⁢       A   ^       k   i           ]           ∑     i   =   1     M     ⁢           ⁢     [                A   ^       -     k   i              2     +           ⁢              A   ^       k   i            2       ]           ,           (   17   )               
where Â k =Ĥ k X k |N. Here, the common phase error □ o, ML  is deemed to be negligible and so no adaptive compensation of the channel estimates accounting for □ o, ML  need occur. In comparison to the previously described embodiments, this results in a less complex I/Q imbalance calculation unit (which only needs to calculate □ ML  per equation (17), as well as □ ML  and □ ML  in light thereof, as presented in equations (13) and (14) if, for example, an I/Q imbalance compensation unit such as unit  220  ( FIG. 2 ) is employed. However, this potentially result in reduced receiver performance in comparison with previously described embodiments, particularly where effective data throughput approaches 802.11a/g maximum rates or orthogonality of the sub-carriers is substantially comprised by ambient noise.
 
     It will be obvious to those having skill in the art that many changes may be made to the details of the above-described embodiments of this invention without departing from the underlying principles thereof. For example, although the above-described embodiments are directed to 802.11a/g transceiver-receiver implementations, the teachings of the present invention are not meant to be so limited. In fact, the above described I/Q imbalance, residual frequency offset and phase noise compensation techniques can be easily extended to other multicarrier OFDM systems, including those compliant with IEEE 802.16a. The scope of the present invention should, therefore, be determined only by the following claims.