Abstract:
A method and a receiver are provided for demodulating a received multi-carrier modulated signal. The demodulation procedure includes (a) multiplying the received multi-carrier modulated signal with its complex conjugate to obtain a squared signal; (b) multiplying the squared signal with a carrier demodulating signal to obtain a product signal, and integrating the product signal over the duration T. A bit decision may then be performed on the integration result using analog components without the need for high-speed analog-to-digital conversion.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     The present application is related to and claims priority of U.S. provisional patent application, Ser. No. 61/146,254, entitled “Method and System of Differential Complex and Real Multi-Carrier Demodulation,” filed on Jan. 21, 2009. The Provisional Application is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to wireless communications; in particular, the present invention relates to multi-carrier modulation and demodulation techniques suitable for use in wireless healthcare, wireless body area networks, and wireless sensor networks. 
     2. Discussion of the Related Art 
     Multi-carrier modulation and demodulation techniques are used in broadband wireless communications. For example, orthogonal frequency division multiplexing (OFDM) has been extensively used. Early descriptions of OFDM may be found, for example, in (a) U.S. Pat. No. 3,488,445 (“Chang”), in “Orthogonal frequency multiplex data transmission system,” by R. W. Chang, which was filed on Nov. 14, 1966 and issued on Jan. 6, 1970; and (b) the article “Data transmission by frequency division multiplexing using the discrete Fourier transform” (“Weinstein”), by S. B. Weinstein and P. M. Ebert, published in  IEEE Trans. Corn. Tech ., vol. 19, no. 5, pp. 628-634, October 1971. 
     OFDM modulates information samples on a set of narrowband carriers at the transmitter. At the receiver, after analog-to-digital conversion (ADC), the OFDM signal may be demodulated using a fast Fourier transform (FFT). OFDM using narrowband carriers requires only relatively simple channel equalization. However, the high-speed ADC and the digital processing that follows incur high hardware cost and high power consumption. Such costs are not economical for simple, low cost, and low data rate products, such as those found in wireless healthcare applications. 
     The article “Slightly frequency-shifted reference ultra-wideband (UWB) radio” (“Goeckel”), by D. Goeckel and Q. Zhang, published in  IEEE Trans. Commun ., vol. 55, no. 3,: pp. 508-519, March 2007, discloses a dual-carrier differential modulation and demodulation scheme. Goeckel transmits one information symbol in each symbol period using a differential relationship between two carriers. At the receiver, the information symbol is demodulated and recovered using simple analog processing; Goeckel&#39;s system therefore avoids ADC and digital signal processing, thus significantly reducing system complexity and power consumption. However, because only two carriers are used, Goeckel&#39;s system takes advantage of very limited frequency resources. Goeckel&#39;s system therefore does not take advantage of frequency diversity inherent in multipath channels. Such frequency diversity represents significant efficiency in, for example, wireless body area network (WBAN) applications. 
     Complex multi-carrier modulation and demodulation techniques are used in a wide range of systems, such as the downlink of the long term evolution (LTE) system. Complex multi-carrier modulation and demodulation techniques in an LTE system is described, for example, in the article “Technical solutions for the 3G Long-Term Evolution” (“Ekström”), by H. Ekström et al., published in  IEEE Commun. Mag ., vol. 44, no. 3, March 2006, pp. 38-45. Real multi-carrier modulation and demodulation techniques are also used for wireless communication systems (e.g., the impulse radio). For example, the article “Impulse radio: how it works,” by M. Z. Win and R. A. Scholtz,  IEEE Commun. Lett ., vol. 2, no. 2, February 1998, pp. 36-38, discloses real multiple-carrier modulation and demodulation. 
     SUMMARY 
     The present invention provides a method that incorporates both complex multi-carrier modulation and demodulation for complex channels and real multi-carrier modulation and demodulation for real channels. 
     In one embodiment, a transmitter according to the present invention may have a conventional multi-carrier transmitter structure, which uses inverse fast Fourier transform (IFFT) and discrete Cosine transform (DCT) techniques to provide multi-carrier modulation. In such a transmitter, one information sample is modulated in each symbol duration on all carriers in a differential manner. The present invention provides a simple receiver structure, which avoids expensive complex digital components, such as ADC, a high accuracy sampling clock and a high-speed digital signal processer (DSP). At the receiver, the information sample is demodulated using a simple two-step analog processing technique. In one embodiment, the received signal is squared and the resultant waveform is then carrier-demodulated. 
     According to one embodiment of the present invention, the information sample may be demodulated using an analog receiver. As compared to OFDM modulation/demodulation schemes (e.g., those disclosed in Chang and Weinstein, discussed above), the modulation/demodulation scheme of the present invention avoids both high cost digital components and high power consumption. Such cost savings are important for wireless healthcare applications, e.g., WBANs, and wireless home control applications e.g., such as home automation, and wireless sensor networks, etc. 
     Unlike Goekel (discussed above), the techniques of the present invention are applicable broadly to use any arbitrary number of carriers to support different data rates, depending on the needs of the specific application. Therefore, the present invention efficiently exploits frequency resources more efficiently, taking advantage of frequency diversity provided by a multipath channel. The present invention is applicable to narrowband, wideband and ultra-wideband systems, depending on the number of carriers used. 
     The present invention is better understood upon consideration of the detailed description below in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of complex differential multi-carrier system  100 , in accordance with one embodiment of the present invention. 
         FIG. 2  is a block diagram of real differential multi-carrier modulation and demodulation system  200 , in accordance with one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     According to one embodiment of the present invention, complex multi-carrier differential modulation and demodulation techniques may be used in a complex channel.  FIG. 1  is a block diagram of complex differential multi-carrier system  100 , in accordance with one embodiment of the present invention. As shown in  FIG. 1 , a M-ary phase shift keying (MPSK) signal s is transmitted during symbol duration T by transmitter  100   a , which may be a conventional OFDM transmitter. (Of course, MPSK is used in  FIG. 1  merely as an example; other signal modulation scheme may also be used to provide signal s.) Differential modulation module  101  constructs data samples α k , k=0, . . . K−1 from amplitude-normalized MPSK signal s according to the following equations:
 
α 0 =1
 
α k =α K−1   s, k= 1, . . .  K− 1  (1)
 
     In complex differential multi-carrier system  100 , in order to avoid interference with other wireless systems, transmitter  100   a  selects carrier frequency f 0  in carrier selection module  108  from a portion of the spectrum that is not currently used by another system, after scanning the spectrum with spectrum sensing module  107 . 
     The symbols α k , k=0, . . . K−1, are modulated on to K orthogonal complex carriers exp(j2π(k/T+f c )t), k=0, . . . K−1, in the duration tε[0,T] in transmitter  100   a . As shown in  FIG. 1 , the serially created K data samples in differential modulation module  101  are provided to serial-to-parallel conversion  102  to create a K-dimensional vector. The K parallel samples in the vector are then subject to an inverse Fourier Transform (IFFT) at IFFT module  103 . The resulting K time-domain samples are then summed in parallel-to-serial conversion  104 , a cyclic prefix (CP) is then inserted by CP module  105  and the resulting signal is made a baseband analog signal in digital-to-analog conversion (DAC) and low-pass filter  106 . The baseband signal is modulated onto carrier in up-conversion module  109  and transmitted from a transmit antenna. The resultant transmitted waveform (not including the CP term) is represented by 
                       x   ⁡     (   t   )       =       ∑     k   =   0       K   -   1       ⁢       a   k     ⁢     exp   ⁡     (     j   ⁢           ⁢   2   ⁢     π   ⁡     (       k   T     +     f   c       )       ⁢     (     t   -     T   cp       )       )             ,     t   ∈     [     0   ,     T   +     T   cp         ]       ,           (   2   )               
where T cp  is the length of the CP.
 
     After propagating through channel  110 , the transmitted signal is received into receiver  100   b  over a receive antenna. The CP may be removed from the waveform using any suitable conventional technique in cyclic prefix removal module  111 . The received waveform may be represented by: 
                       r   ⁡     (   t   )       =         ∑     k   =   0       K   -   1       ⁢       H   k     ⁢     a   k     ⁢     exp   ⁡     (     j   ⁢           ⁢   2   ⁢     π   ⁡     (       k   T     +     f   c       )       ⁢   t     )           +     n   ⁡     (   t   )           ,     t   ∈     [     0   ,   T     ]       ,           (   3   )               
where H k  is the channel frequency response on the k th carrier and n(t) is a noise term. In receiver  100   b , demodulation may be carried out by steps carried out in module  130 . The square (of the modulus) of the received waveform r(t) is obtained in squaring module  112  by multiplying r(t) with its complex conjugate r′(t), which is obtained in a complex conjugate operation:
 
                         r   ⁡     (   t   )       ⁢       r   ′     ⁡     (   t   )         =         ∑     n   =   0       K   -   1       ⁢       ∑     m   =   0       K   -   1       ⁢       H   n     ⁢     H   m   ′     ⁢     a   n     ⁢     a   m   ′     ⁢     exp   ⁡     (     j   ⁢           ⁢   2   ⁢   π   ⁢               ⁢     n   -   m       T     ⁢   t     )             +     η   ⁢           ⁢     (   t   )           ,           (   4   )               
where η(t) is the additive noise term. Then, at demodulation module  113 , the squared waveform r(t)r′(t) is carrier demodulated using the complex waveform exp(−j2πt/T). The demodulation procedure, represented by mixer  113  and integrator  114 , is represented by
 
                   d   =       1     T   ⁢               ⁢       ∫   0   T     ⁢       r   ⁡     (   t   )       ⁢       r   ′     ⁡     (   t   )       ⁢     exp   ⁡     (       -   j     ⁢           ⁢   2   ⁢   π   ⁢           ⁢     t   T       )       ⁢       ⅆ   t     .                   (   5   )               
The demodulation result, therefore, has the form:
 
                     d   =         ∑     k   =   0       K   -   2       ⁢       H     k   +   1       ⁢     H   k   ′     ⁢   s       +   η       ,           (   6   )               
where η is the noise term. Where the channel frequency response varies slowly in the frequency domain (i.e., H k ≈H k+1 ), the demodulation result d may be approximated by:
 
                     d   ≈         ∑     k   =   0       K   -   2       ⁢              H   k          2     ⁢   s       +   η       ,           (   7   )               
Signal s may be recovered from the demodulated signal d in decision circuit  115 .
 
       FIG. 2  is a block diagram of real differential multi-carrier modulation and demodulation system  200 , in accordance with one embodiment of the present invention. Real differential multi-carrier system  200  may be realized in real channels. As shown in  FIG. 2 , real differential multi-carrier system  200  transmits a binary phase shift keying (BPSK) signal in symbol duration T. (Of course, BPSK is used in  FIG. 2  merely as an example; other signal modulation scheme may also be used to provide signal s.) As in complex differential multi-carrier system  100 , the modulated signal of real differential multi-carrier system  200  may be transmitted by a conventional OFDM transmitter. 
     Transmitter  200   a  transmits a symbol of amplitude-normalized BPSK signal bε[−1,1] in each symbol duration of T. In order to avoid interference with another wireless system, carrier frequency f c  is selected, after scanning the spectrum. In the differential modulation module  201  in  FIG. 2 , data samples α k , k=0, . . . K−1, are constructed from b according to the following equations:
 
α 0 =1
 
αa k   =b   k   , k= 1, . . .  K− 1  (8)
 
Data samples α k , for k=0, . . . K−1 are then modulated on the set of K real carriers cos(2π(k/T+f c )t), k=0, . . . K−1, which are orthogonal in the duration tε[0, T]. This can be carried out with modules in  FIG. 2  including serial-to-parallel conversion  202 , discrete cosine transform (DCT)  203 , parallel-to-serial conversion  204 , CP insertion  205 , DAC and low pass filter  206 , and up-conversion module  209 . The resultant waveform (not including the CP), which may be transmitted over a conventional transmit antenna, is represented by:
 
                       x   ⁡     (   t   )       =       ∑     k   =   0       K   -   1       ⁢     2   ⁢     a   k     ⁢     cos   ⁡     (     2   ⁢     π   ⁡     (       k   T     +     f   c       )       ⁢     (     t   -     T   cp       )       )             ,     t   ∈     [     0   ,     T   +     T   cp         ]       ,           (   9   )               
which may be rewritten as:
 
     
       
         
           
             
               
                 
                   
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     After propagation over channel  210 , the CP may be removed from the received waveform in CP removal module  211 . The CP-removed, received waveform may be represented by: 
                       r   ⁡     (   t   )       =         ∑     k   =   0       K   -   1       ⁢       a   k     ⁢     H   k     ⁢     exp   ⁡     (     j   ⁢           ⁢   2   ⁢     π   ⁡     (       k   T     +     f   c       )       ⁢   t     )           +       ∑     k   =   0       K   -   1       ⁢       a   k     ⁢     H     -   k       ⁢     exp   ⁡     (       -   j     ⁢           ⁢   2   ⁢     π   ⁡     (       k   T     +     f   c       )       ⁢   t     )               ,     
     ⁢           ⁢     t   ∈     [     0   ,   T     ]       ,           (   11   )               
where H k  is the channel frequency response on the k th frequency component and n(t) is a noise term.
 
     As shown in  FIG. 2 , the demodulation procedure is represented by the steps in demodulation module  203 . First, the received waveform is squared in squaring module  212 , where the received waveform is multiplied by itself. Then, the resultant squared waveform (r(t)) 2  is carrier demodulated using waveform cos(2πt/T), represented by mixer  213  and integrator  214 . The demodulation procedure may be represented by 
                         d   =       ⁢       1   T     ⁢       ∫   0   T     ⁢         (     r   ⁡     (   t   )       )     2     ⁢     cos   ⁡     (     2   ⁢   π   ⁢           ⁢     t   T       )       ⁢     ⅆ   t                       =       ⁢       1     2   ⁢   T       ⁢       ∫   0   T     ⁢         (     r   ⁡     (   t   )       )     2     ⁢     (       exp   ⁡     (       -   j     ⁢           ⁢   2   ⁢   π   ⁢           ⁢     t   T       )       +     exp   ⁡     (     j   ⁢           ⁢   2   ⁢   π   ⁢           ⁢     t   T       )         )     ⁢       ⅆ   t     .                         (   13   )               
The demodulation result is given by:
 
                     d   =         ∑     k   =   0       K   -   2       ⁢       a     k   +   1       ⁢     a   k     ⁢     H     k   +   1       ⁢     H     -   k           +       ∑     k   =   1       K   -   1       ⁢       a     k   -   1       ⁢     a   k     ⁢     H     k   -   1       ⁢     H     -   k           +   η       ,           (   14   )               
where η is the noise term. Using the relationship that α k =b k  and bε[−1,1], equation (14) may be rewritten as:
 
                   d   =         ∑     k   =   0       K   -   2       ⁢       H     k   +   1       ⁢     H     -   k       ⁢   b       +       ∑     k   =   1       K   -   1       ⁢       H     k   -   1       ⁢     H     -   k       ⁢   b       +     η   .               (   15   )               
For real channels, the channel frequency response satisfies H −k =H k ′. Thus,
 
                   d   =         ∑     k   =   0       K   -   2       ⁢       H     k   +   1       ⁢     H   k   ′     ⁢   b       +       ∑     k   =   1       K   -   1       ⁢       H     k   -   1       ⁢     H   k   ′     ⁢   b       +     η   .               (   16   )               
For a channel that varies slowly in the frequency domain (i.e., H k ≈H k+1 ), the demodulation result may be approximated by:
 
                   d   ≈         ∑     k   =   0       K   -   2       ⁢              H   k          2     ⁢   b       +       ∑     k   =   1       K   -   1       ⁢            H   k          2       +   b   +     η   .               (   17   )               
From equation (17), signal b may be recovered in decision circuit  215 .
 
     Thus the present invention may be implemented using a simple receiver structure including only analog processing elements. Consequently, there is no need for an ADC, a high-frequency oscillator, a high-accuracy sampling clock or a high-speed DSP. Accordingly, hardware-cost, form factor (e.g., device size) and power consumption can be significantly reduced, as compared to prior art devices that require complex digital reception techniques. Therefore, the present invention is especially suitable for use in low-cost, low-power consumption—hence, energy efficient—devices, such as sensors in wireless sensor networks, wireless home control/or home automation, WBANs or wireless healthcare networks. 
     Further, the present invention may be used with any number of frequency carriers. Consequently, the present invention has the advantage of high scalability and high adaptability in the required data rates, according to the requirements of the application under consideration. Because any number of frequency carriers may be used, the present invention allows frequency diversity of the multipath channel be exploited, resulting in high reliability to the wireless system. Such features are especially important for life critical applications common in wireless healthcare and WBANs. The invention is applicable extensively to narrow band, wide band and ultra wide band systems, depending on the number of carriers (thus spectrum) selected. 
     The above detailed description is provided to illustrate the specific embodiments and is not intended to be limiting. Numerous variations and modifications are possible within the scope of the present invention. The present invention is set forth in the following claims.