1. Field of the Invention
The present invention relates to the use of a time-domain equalizer (TEQ) algorithm in a discrete multi-tone transceiver (DMT) and, more particularly, to a time-domain equalizer algorithm which operates as both a channel shortening filter and a noise whitening filter.
2. Related Art
The fast, efficient and error-free transmission of digital information from one point to another has become increasingly important. Many communications systems exist which permit digital information to be transmitted over various types of communication channels, such as wireless channels, fiber-optic channels, and wire line channels.
The present invention will be described in the context of a wire line communications channel, such as a telephone line which utilizes a twisted pair of copper wires. It is noted that the use of the present invention is not limited to wire line systems as those skilled in the art will appreciate from the discussion hereinbelow.
A modem is typically used to transmit and receive digital data over a telephone line. Modems employ a modulator to transmit the digital data over the telephone line and a demodulator to receive digital data from the telephone line. One common modulation technique is known as digital multi-tone modulation which requires a discrete multi-tone transmitter and a discrete multi-tone receiver at each modem in a communication system. Often, those skilled in the art refer to such modems as employing a DMT physical layer modulation technique.
Reference is now made to FIG. 1 which is a block diagram of a conventional DMT communications system 1. The system 1 includes a DMT transmitter 10, a transmission channel 20, and a DMT receiver 30. The DMT transmitter 10 includes a symbol generator 12, an inverse fast fourier transform (IFFT) modulator 14, and a cyclic prefix generator 16. The DMT transmitter 10 receives an input bit stream b(n) which is fed into the symbol generator 12. The symbol generator 12 produces a signal X(k) which is fed into the IFFT modulator 14. X(k) is a complex signal (i.e., a signal understood by those skilled in the art to comprise both a real and an imaginary component) formed by mapping pairs of bits of the input bit stream b(n) into a complex data space such that the complex signal X(k) has a length of N/2 samples. Symbol generator 12 also augments the signal X(k) with a complex conjugate to obtain a conjugate symmetric signal of N samples.
The IFFT modulator 14 performs an N-point inverse fast fourier transform on the conjugate complex signal X(k) to obtain the sampled real signal x(n). Since X(k) is a symmetric signal, the output of the IFFT modulator 16 is a real signal x(n). The real signal x(n) may be thought of as the summation of a plurality of cosine functions each having a finite length and a different frequency, phase, and amplitude, where these frequencies are multiples of a fundamental frequency. Since each of the cosine functions has a finite duration, x(n) is a varying amplitude discrete signal having a finite duration spanning N samples.
For the purpose of simplifying equations which will be discussed below, the transmission channel 20 is modeled as including a D/A converter 22, transmit filter (not shown), a receive filter (not shown), and an A/D converter 26 on either end of a wire loop 24. Those skilled in the art will appreciate that a practical system will employ the D/A converter 22 (and the transmit filter) in the DMT transmitter 10 and will employ the A/D converter 26 (and the receive filter) in the DMT receiver 30.
Those skilled in the art will appreciate that the frequency spectrum of x(n) may be thought of as a plurality of orthogonal (SIN X)/(X) functions, each centered at a respective one of the frequencies of the cosine functions of x(n).
x(n) is transmitted over the channel 20 to the DMT receiver 30. Since the transmission channel 20 has a non-ideal impulse response h(n), the received signal y(n) will not exactly match x(n). Instead, y(n) will be a function of the convolution of x(n) and h(n). Typically, h(n) will look substantially like the curve shown in FIG. 2. The non-ideal characteristic of h(n) introduces an amount of interference (specifically intersymbol and interchannel interference) which should be compensated for in both the DMT transmitter 10 and the DMT receiver 30.
A common technique in compensating for the non-ideal impulse response of the transmission channel 20 is to introduce a so-called guard band at the beginning of each finite duration signal x(n) to produce xxe2x80x2(n). The cyclic prefix generator 16 performs this function. The guard band is typically formed of the last V samples of x(n) for each DMT symbol. If the length of the impulse response h(n) of the transmission channel 20 is less than or equal to V+1, then the guard band of length V will be sufficient to eliminate the interference cause by the impulse response h(n). The guard band is commonly referred to in the art as a xe2x80x9ccyclic prefixxe2x80x9d (CP).
Unfortunately, the impulse response h(n) of a typical transmission channel 20 may be excessively long, requiring cyclic prefix lengths which substantially reduce the rate at which digital bits are transmitted across the transmission channel 20. The DMT receiver 30, therefore, employs signal processing techniques which effectively shorten the impulse response h(n) of the transmission channel 20, thereby permitting a corresponding reduction in the length of the cyclic prefix required at the DMT transmitter 10.
The DMT receiver 30 includes a time-domain equalizer (TEQ) 32, a window circuit 34, a fast fourier transform (FFT) demodulator 36, and a bit generator 38. The time-domain equalizer 32 is a finite impulse response (FIR) filter designed to compensate for the non-ideal impulse response h(n) of the transmission channel 20. In particular, the time-domain equalizer 32 employs a finite number of coefficients (T) which are calculated to compensate for the non-ideal impulse response of the transmission channel 20. As will be discussed in more detail below, the time domain equalizer 32 operates on the impulse response h(n) of the channel 20 such that the combined impulse response heff(n) of the channel 20 and the time domain equalizer 32 has maximum energy within a limited band of samples. This may be thought of as xe2x80x9cshorteningxe2x80x9d the effective impulse response of the channel 20. The output of the time domain equalizer is zxe2x80x2(n).
A window circuit 34 is employed to remove the cyclic prefix from zxe2x80x2(n) to obtain z(n). The signal z(n) is input into the FFT demodulator 36 (which is understood to include a frequency domain equalizer function) to produce the complex symmetric signal X(k). After the complex conjugate portion of the signal X(k) is removed, the bit generator 38 maps the complex signal X(k) into an output bit stream b(n), which theoretically matches the input bit stream b(n).
Several algorithms exist for calculating the T coefficients of the time-domain equalizer 32. One such algorithm is referred to as the least squares based pole zero cancellation algorithm (hereinafter xe2x80x9cPROCESS #1xe2x80x9d), which is discussed in detail in P. J. Melsa, R. Y. Younce and C. E. Rohrs, xe2x80x9cImpulse Response Shortening for Discrete Multitone Transceivers,xe2x80x9d IEEE Trans. On Comm. Vol. 44, No. 12, pp. 1662-71, December 1996, the entire disclosure of which is hereby incorporated by reference. Another such algorithm is referred to as the optimal shortening algorithm (hereinafter xe2x80x9cPROCESS #2xe2x80x9d), which is also discussed in detail in the above referenced IEEE publication. Still another algorithm is referred to as the eigenvector approach using the power method (hereinafter xe2x80x9cPROCESS #3xe2x80x9d), which is discussed in detail in M. Nafie and A. Gatherer, xe2x80x9cTime-Domain Equalizer Training for ADSL,xe2x80x9d Proc. ICC, pp. 1085-1089 (1997), the entire disclosure of which is hereby incorporated by reference.
Although the above techniques for calculating the coefficients of the time-domain equalizer 32 address the issue of xe2x80x9cshorteningxe2x80x9d the effective impulse response of the transmission channel 20, they do not adequately address the problem of interference caused by noise. The system 1 is susceptible to injected white noise and colored noise. Colored noise exhibits concentrated spectral energy at some frequencies and relatively little spectral energy at other frequencies. White noise exhibits a substantially constant amount of spectral energy at all frequencies.
While the conventional DMT receiver 30 of FIG. 1 operates optimally when white noise is present at the output of the time domain equalizer 32, it is susceptible to interchannel interference when colored noise is present. This is a particularly difficult problem when the colored noise exhibits spectral nulls.
Colored noise may be present at the output of the time domain equalizer 32 because (i) additive colored noise was injected into the signal xxe2x80x2(n) as it was transmitted over the transmission channel 20; and/or (ii) the time domain equalizer 32 itself introduces spectral shaping (especially spectral nulls) into the signal zxe2x80x2(n). Thus, even if the transmission channel 20 does not introduce additive colored noise into the received signal y(n), the time domain equalizer 32 may itself introduce spectral coloration into the additive noise of signal zxe2x80x2(n). Consequently, although the time domain equalizer 32 may produce a xe2x80x9cshorterxe2x80x9d effective impulse response heff(n), it may degrade system performance by introducing colored noise (especially spectral nulls) into zxe2x80x2(n). In particular, the rate at which data bits b(n) are transmitted over the transmission channel 20 and the error rate of such transmission may be adversely affected by colored noise at the output of the time domain equalizer 32.
Accordingly, there is a need in the art for an improved DMT communication system which is capable of (i) compensating for the non-ideal impulse response of a transmission channel; (ii) compensating for additive colored noise introduced by the transmission channel; and/or (iii) mitigating against the spectral coloration of additive noise by the time domain equalizer.
In order to overcome the disadvantages of the prior art, an apparatus for receiving a discrete multi-tone signal over a communications channel having an impulse response h(n), energy of the impulse response being substantially concentrated in a first band of samples, the apparatus comprising:
a receiver for receiving the discrete multi-tone signal; and
a T coefficient finite impulse response time-domain equalizer included in the receiver, the time-domain equalizer having an output additive noise signal, the T coefficients of the time-domain equalizer being provided such that:
(a) energy of an effective impulse response heff(n) of at least the communications channel combined with the time-domain equalizer is substantially concentrated in a second band of V+1 samples, whereby the second band of samples is shorter than the first band of samples; and
(b) a variance in a frequency spectrum of the output additive noise signal of the time-domain equalizer is controlled.
The time-domain equalizer of the present invention preferably has an input additive noise signal, the T coefficients of the time-domain equalizer being provided as a function of both the input additive noise signal and an estimate of the impulse response h(n).
The receiver is preferably operable to compute the T coefficients of the time-domain equalizer as a function of balancing (i) a degree to which the energy of the effective impulse response heff(n) is concentrated: in the second band of V+1 samples; and (ii) a degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced.
The receiver is preferably operable to vary the degree to which the energy of the effective impulse response heff(n) is concentrated in the second band of V+1 samples; and the degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced.
The receiver is preferably operable to compute the T coefficients of the time-domain equalizer by evaluating the following system of equations:
xe2x80x83min¦wwT(HoutTHout+xcex2outR)w, subject to wT(HinTHin+xcex2inR)w=1, where
w is a Txc3x971 matrix representing the T coefficients of the time-domain equalizer,
Hout is an (M+Txe2x88x92Vxe2x88x922)xc3x97T matrix representing samples of the estimated impulse response h(n) of the communications channel which produce M+Txe2x88x92Vxe2x88x922 samples of the effective impulse response heff(n) not containing concentrated energy when matrix w is multiplied by Hout,
Hin is a (V+1)xc3x97T matrix representing samples of the estimated impulse response h(n) of the communications channel which produce the V+1 samples of the effective impulse response heff(n) having concentrated energy when matrix w is multiplied by Hin,
R is a Txc3x97T additive noise correlation matrix constructed from the input additive noise signal, and
xcex2out and xcex2in are scalars which vary the degree to which the energy of the effective impulse response heff(n) is concentrated in the second band of V+1 samples; and the degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced.
The receiver is preferably operable to obtain w by solving w=(GT)xe2x88x921emin, where G=HinTHin+xcex2inR, and emin is an eigenvector corresponding to the smallest eigenvalue of (G)xe2x88x921(HoutTHout+xcex2outR)(GT)xe2x88x921.
The present invention also provides a method of determining T coefficients of a finite impulse response time-domain equalizer having input and output additive noise signals, the time-domain equalizer being employed in a receiver for receiving a discrete multi-tone signal over a communications channel having an impulse response h(n), energy of the impulse response being substantially concentrated in a first band of samples, the method comprising the step of:
computing the T coefficients of the time-domain equalizer such that:
(a) energy of an effective impulse response heff(n) of at least the communications channel combined with the time-domain equalizer is substantially concentrated in a second band of V+1 samples, whereby the second band of samples is shorter than the first band of samples; and
(b) a variance in a frequency spectrum of the output additive noise signal of the time-domain equalizer is controlled.
The method of the present invention also preferably comprises the step of balancing (i) a degree to which the energy of the effective impulse response heff(n) is concentrated in the second band of V+1 samples; and (ii) a degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced.
The method of the present invention also preferably comprises the step of varying the degree to which the energy of the effective impulse response heff(n) is concentrated in the second band of V+1 samples; and the degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced.
It is preferred that the method of the present invention also include the steps of:
estimating the impulse response h(n) of the communication channel;
estimating the input additive noise signal to the time-domain equalizer;
providing a Txc3x971 matrix w representing the T coefficients of the time-domain equalizer;
providing a (V+1)xc3x97T matrix Hin representing samples of the estimated impulse response h(n) of the communications channel which produce the V+1 samples of the effective impulse response heff(n) having concentrated, energy when matrix w is multiplied by Hin; and
providing an (M+Txe2x88x92Vxe2x88x922)xc3x97T matrix Hout representing samples of the estimated impulse response h(n) of the communications channel which produce M+Txe2x88x92Vxe2x88x922 samples of the effective impulse response heff(n) not containing concentrated energy when matrix w is multiplied by Hout.
It is also preferred that the method of the present invention include the steps of:
providing a Txc3x97T additive noise correlation matrix R from the input additive noise signal, and
determining scalars xcex2out and xcex2in which control a degree to which the energy of the effective impulse response heff(n) is concentrated in the second band of V+1 samples; and a degree to which the variance in the frequency spectrum of the output additive noise of the time-domain equalizer is reduced
It is also preferred that the step of computing the T coefficients of the time-domain equalizer is obtained by solving the following system of equations:
min¦wwT(HoutTHout+xcex2outR)w, subject to wT(HinTHin+xcex2inR)w=1.
In the method of the present invention, it is also preferred that w is obtained by solving w=(GT)xe2x88x921emin, where G=HinTHin+xcex2inR and emin is an eigenvector corresponding to the smallest eigenvalue of: (G)xe2x88x921(HoutTHout+xcex2outR) (GT)xe2x88x921.
Other features and advantages of the present invention will become apparent from the following description of the invention which refers to the accompanying drawing.