Abstract:
The disclosed embodiments relate to exploiting circuitry that exists in a typical Orthogonal Frequency Division Multiplexing (OFDM) receiver to find the phase of a complex number corresponding to an input signal without implementing additional costly circuitry or employing a relatively slow inverse tangent look-up table. The magnitude of the complex number is normalized and processed through a closed loop to produce an output proportional to the phase of the complex number.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to processing orthogonal frequency division multiplexed (OFDM) signals.  
       BACKGROUND OF THE INVENTION  
       [0002]     This section is intended to introduce the reader to various aspects of art which may be related to various aspects of the present invention which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.  
         [0003]     A wireless LAN (WLAN) is a flexible data communications system implemented as an alternative or extension to a wired LAN within a building or campus. Using electromagnetic waves, WLANs transmit and receive data over the air, minimizing the need for wired connections.  
         [0004]     Thus, WLANs combine data connectivity with user mobility, and, through simplified configuration, enable movable LANs. Some industries that have benefited from the productivity gains of using portable terminals (e.g., notebook computers) to transmit and receive real-time information are the digital home networking, health are, retail, manufacturing, and warehousing industries. Manufacturers of WLANs have a range of transmission technologies to choose from when designing a WLAN. Some exemplary technologies are multicarrier systems, spread spectrum systems, narrowband systems, and infrared systems. Although each system has its own benefits and detriments, one particular type of multicarrier transmission system, orthogonal frequency division multiplexing (OFDM), has proven to be exceptionally useful for WLAN communications.  
         [0005]     OFDM is a robust technique for efficiently transmitting data over a channel. The technique uses a plurality of sub-carrier frequencies (sub-carriers) within a channel bandwidth to transmit data. These sub-carriers are arranged for optimal bandwidth efficiency compared to conventional frequency division multiplexing (FDM) which can waste portions of the channel bandwidth in order to separate and isolate the sub-carrier frequency spectra and thereby avoid inter-carrier interference (ICI). By contrast, although the frequency spectra of OFDM sub-carriers overlap significantly within the OFDM channel bandwidth, OFDM nonetheless allows resolution and recovery of the information that has been modulated onto each sub-carrier.  
         [0006]     The transmission of data through a channel via OFDM signals also provides several other advantages over more conventional transmission techniques. Some of these advantages are a tolerance to multipath delay spread and frequency selective fading, efficient spectrum usage, simplified sub-channel equalization, and good interference properties.  
         [0007]     In processing OFDM signals, it is frequently desirable to determine the phase of a given complex number corresponding to an input signal. One example of such a complex number is a frequency domain subcarrier value. The ability to determine the phase of complex numbers representing an input signal is useful for many purposes, such as synchronizing the received data signal to ensure the maximum amount of integrity in the received data compared to the transmitted data. Traditionally, determining the phase of a complex number would require first finding the tangent of the phase of the complex number: 
 
tangent=imaginary/real 
 
 After determination of the tangent of the complex number, an inverse tangent look-up table could be used to determine the phase angle of the complex number corresponding to the input signal. Depending on the accuracy required, such an inverse tangent look-up table could be very large and expensive to implement in hardware. A method and apparatus capable of determining the phase of a complex number corresponding to an input signal without accessing an inverse tangent look-up table is desirable. 
 
       SUMMARY OF THE INVENTION  
       [0008]     The disclosed embodiments relate to exploiting circuitry that exists in a typical Orthogonal Frequency Division Multiplexing (OFDM) receiver to find the phase of a complex number corresponding to an input signal without implementing additional costly circuitry or employing a relatively slow inverse tangent look-up table. The magnitude of a complex number corresponding to an input signal is normalized, which has the effect of extracting the exponent of the complex portion of the sample. The exponent may be passed through a closed loop that includes a numerically controlled oscillator (NCO). The input value to the dosed loop may stay constant for a predetermined number of clock cycles sufficiently long to allow the loop to converge for any phase of input sample. After convergence, the output of the NCO will be a signal that is proportional to the phase of the complex number corresponding to the input signal. Additional mathematical processing may be needed to convert the NCO output to the desired phase value. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]     In the drawings:  
         [0010]      FIG. 1  is a block diagram of an exemplary OFDM receiver;  
         [0011]      FIG. 2  is a diagram illustrating the placement of a training sequence, user data, and pilot signals within an OFDM symbol frame;  
         [0012]      FIG. 3  is a block diagram of a circuit for extracting the phase of a complex number corresponding to an input signal;  
         [0013]      FIG. 4  is an alternative embodiment of a circuit for normalizing a complex number corresponding to an input signal; and  
         [0014]      FIG. 5  is a process flow diagram illustrating the operation of an exemplary embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0015]     The characteristics and advantages of the present invention will become more apparent from the following description, given by way of example.  
         [0016]     Referring to  FIG. 1 , the first element of a typical OFDM receiver  10  is an RF receiver  12 . Many variations of the RF receiver  12  exist and are well known in the art, but typically, the RF receiver  12  includes an antenna  14 , a low noise amplifier (LNA)  16 , an RF band pass filter  18 , an automatic gain control (AGC) circuit  20 , an RF mixer  22 , an RF carrier frequency local oscillator  24 , and an IF band pass filter  26 .  
         [0017]     Through the antenna  14 , the RF receiver  12  couples in the RF OFDM-modulated carrier after it passes through the channel. Then, by mixing it with a receiver carrier of frequency f cr  generated by the RF local oscillator  24 , the RF receiver  12  downconverts the RF OFDM-modulated carrier to obtain a received IF OFDM signal. The frequency difference between the receiver carrier and the transmitter carrier contributes to the carrier frequency offset, delta f c .  
         [0018]     This received IF OFDM signal is coupled to a mixer  28  and a mixer  30  to be mixed with an in-phase IF signal and a 90° phase-shifted (quadrature) IF signal, respectively, to produce in-phase and quadrature OFDM signals, respectively. The in-phase IF signal that feeds into the mixer  28  is produced by an IF local oscillator  32 . The 90° phase-shifted IF signal that feeds into mixer  30  is derived from the in-phase IF signal of the IF local oscillator  32  by passing the in-phase IF signal through a 90° phase shifter  34  before providing it to the mixer  30 .  
         [0019]     The in-phase and quadrature OFDM signals then pass into analog-to-digital converters (ADCs)  36  and  38 , respectively, where they are digitized at a sampling rate f ck     —     r as determined by a clock circuit 40. The ADCs 36 and 38 produce digital samples that form an in-phase and a quadrature discrete-time OFDM signal, respectively. The difference between the sampling rates of the receiver and that of the transmitter is the sampling rate offset, delta f   ck =f ck     —     r −f ck     —     t .  
         [0020]     The unfiltered in-phase and quadrature discrete-time OFDM signals from the ADCs  36  and  38  then pass through digital low-pass filters  42  and  44 , respectively. The output of the low pass digital filters  42  and  44  are filtered in-phase and quadrature samples, respectively, of the received OFDM signal. In this way, the received OFDM signal is converted into in-phase (qi) and quadrature (pi) samples that represent the real and imaginary-valued components, respectively, of the complex-valued OFDM signal, r i =q i +jp i . These in-phase and quadrature (real-valued and imaginary-valued) samples of the received OFDM signal are then delivered to an FFT  46 . Note that in some conventional implementations of the receiver  10 , the analog-to-digital conversion is done before the IF mixing process. In such an implementation, the mixing process involves the use of digital mixers and a digital frequency synthesizer. Also note that in many conventional implementations of receiver  10 , the digital-to-analog conversion is performed after the filtering.  
         [0021]     The FFT  46  performs the Fast Fourier Transform (FFT) of the received OFDM signal in order to recover the sequences of frequency-domain sub-symbols that were used to modulate the sub-carriers during each OFDM symbol interval. The FFT  46  then delivers these sequences of sub-symbols to a decoder  48 .  
         [0022]     The decoder  48  recovers the transmitted data bits from the sequences of frequency-domain sub-symbols that are delivered to it from the FFT  46 . This recovery is performed by decoding the frequency domain sub-symbols to obtain a stream of data bits which should ideally match the stream of data bits that were fed into the OFDM transmitter.  
         [0023]     This decoding process can include soft Viterbi decoding and/or Reed-Solomon decoding, for example, to recover the data from the block and/or convolutionally encoded sub-symbols.  
         [0024]     Turning to  FIG. 2 , an exemplary OFDM symbol frame  50  of the present invention is shown. The symbol frame  50  includes a training sequence or symbol  52  containing known transmission values for each subcarrier in the OFDM symbol, and a predetermined number of a cyclic prefix  54  and user data  56  pairs. For example, the proposed ETSI-BRAN HIPERLAN/2 (Europe) and IEEE 802.11a (USA) wireless LAN standards, herein incorporated by reference, assign  64  known values or subsymbols (i.e., 52 non-zero values and 12 zero values) to selected training symbols of a training sequence (e.g., “training symbol C” of the proposed ETSI standard and “long OFDM training symbol” of the proposed IEEE standard). The user data  56  has a predetermined number of pilots  58 , also containing known transmission values, embedded on predetermined subcarriers. For example, the proposed ETSI and IEEE standards have four pilots located at bins or subcarriers ±7 and ±21. Although the present invention is described as operating in a receiver that conforms to the proposed ETSI-BRAN HIPERLAN/2 (Europe) and IEEE 802.11a (USA) wireless LAN standards, it is considered within the skill of one skilled in the art to implement the teachings of the present invention in other OFDM systems.  
         [0025]      FIG. 3  is a block diagram of a circuit for extracting the phase of a complex number corresponding to an input signal. In processing OFDM signals, it is frequently desirable to determine the phase of complex numbers, such as the output from the BPF  26  ( FIG. 1 ). The complex numbers of which the phase is desired to be known is identified by reference numeral  60  in  FIG. 3 . The complex number may be generally represented as follows: 
 |a|e j*phi    
 In this representation, |a| is the magnitude of the complex number and phi is the phase angle of the complex number in radians. 
 
         [0026]     To extract this phase angle, the complex number representation must be manipulated mathematically to determine the angle phi. The first step in this mathematical manipulation is to extract the exponent from the complex representation of the sample. Extraction of the exponent may be accomplished by normalizing the magnitude of the sample to one. Normalizing the magnitude of the complex number ensures a constant gain closed-loop operation, which in turn assures loop convergence over a fixed number of dock cycles. The step of normalizing the magnitude of the complex number allows sampling of the loop output after a predetermined number of clocks (i.e. after the loop is known to have converged), thus eliminating the need to implement a relatively expensive and potentially unreliable loop-lock indicator.  
         [0027]     To normalize the complex number, the magnitude of the complex number |a| is squared by a squaring circuit  62 , which typically exists in most OFDM receivers (i.e. it does not have to be specially included). A squaring circuit  64  squares the entire value of the complex number (both the real and imaginary components). If no additional squaring circuit is present in the OFDM receiver in which the invention is implemented, the squaring circuit  62  may be used to square the complex number as well as to determine the square of the magnitude of the complex number. An inversion circuit  66  (also typically present in most OFDM receivers) is used to invert the output of the squaring circuit  62 . The output of the squaring circuit  64  and the inversion circuit  66  are combined by multiplier  68 . The output of the multiplier  68  equates to the normalized value of the square of the complex number, which may be expressed as e 2j*phi .  
         [0028]     Now that the magnitude of the complex number has been normalized, the second step in determining the phase angle of the complex number comprises sending the output of the multiplier  68  through a closed loop. The second order carrier tracking loop, which is typically implemented in an OFDM receiver (i.e. does not have to be specifically added), is useful for this purpose.  
         [0029]     Those of ordinary skill in the art will appreciate that the output of the multiplier  68  must be provided to the tracking loop (beginning with a derotator  70 ) for a predetermined number of dock cydes to ensure stabilization of the loop. The exact number of dock cycles needed to ensure loop stabilization in a given OFDM receiver configuration may be readily determined by those of ordinary skill in the art. Moreover, the determination of the number of clock cycles required for loop stabilization is not a crucial aspect of the present invention. To continue with the description of the processing of the complex number by a closed loop such as the carrier tracking loop of a typical OFDM receiver, the output from the multiplier  68  is fed into the derotator  70  and the output of the derotator  70  is passed on to a phase detector  72 . The output of the phase detector  72  is passed on to an integral gain amplifier  74  and a proportional gain amplifier  76 . The output of the integral gain amplifier  74  is fed into an integrator  78 . The output of the integrator  78  is combined with the output of the proportional gain amplifier  76  by a summing circuit  80 . The output of the summing circuit  80  is fed into a numerically controlled oscillator (NCO)  82 , which feeds into a sine/cosine look-up table  84 . The output of the sine/cosine look-up table  84  is provided as feedback to the derotator  70 .  
         [0030]     In the illustrated embodiment, the output of the NCO  82  is equal to twice the phase of the complex number corresponding to the input signal. Division of the output of the NCO  82  by two with a divider circuit  84  results in a signal  86  that is equivalent to the phase angle phi of the complex number. Thus, the present invention determines the phase angle of a complex number corresponding to an input signal without the need of a cumbersome and costly inverse tangent look-up table.  
         [0031]      FIG. 4  is an alternative embodiment of a circuit for normalizing a complex number. In the embodiment shown in  FIG. 4 , the complex number  60  is inverted by an inversion circuit  90 . The complex conjugate of the inverse of the sample is determined by a complex conjugation circuit  92 . A multiplier  94  multiplies the output of the complex conjugation circuit  92  by the complex number  60  (both the real and imaginary parts). The output of the multiplier  94 , which is the normalized value of the complex number  60 , may be fed into the closed loop circuit shown in  FIG. 3  beginning with the rotator  70 . Processing of the signal may then continue as described with reference to  FIG. 3 .  
         [0032]      FIG. 5  is a process flow diagram illustrating the operation of an exemplary embodiment of the present invention. The overall process is referred to by the reference numeral  100 . The process begins at  102 . At  104 , a complex number corresponding to an input signal is obtained. This complex number may be representative of a portion of an OFDM signal that has been received by an OFDM receiver. At  106 , the complex number is normalized. Normalization may be performed using any known method, including hardware methods, software methods and combined hardware and software methods. Examples of circuits that may be used for normalization of a complex number are shown and described with reference to  FIG. 3  (the circuitry that feeds into the derotator  70 ) and FIG.  4 . As described above, normalization of a complex number corresponding to an input signal ensures that loop convergence can be guaranteed within a predetermined number of receiver dock cycles.  
         [0033]     Next, the normalized complex number is fed into dosed loop at  108 . An example of such a loop is the carrier tracking loop typically present in OFDM receivers. At  110 , the input to the dosed loop is maintained for a predetermined number of clock cydes. As described above, the purpose of waiting for a predetermined number of clock cycles is to allow loop convergence around a value that is proportional to the phase of the complex number. At  112 , the loop output is divided by 2 to yield the phase of the complex. The method of the present invention eliminates the need to implement a costly and time consuming inverse tangent look-up table to determine the phase of a complex number corresponding to an input signal. At  114 , the process of  FIG. 5  ends.  
         [0034]     While the invention may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and will be described in detail herein. However, it should be understood that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the invention as defined by the following appended claims.