Method and Apparatus for Cross-Talk Cancellation in Frequency Division Multiplexed Transmission Systems
A method and apparatus are disclosed for canceling cross-talk in a frequency-division multiplexed communication system. The disclosed frequency-division multiplexed communication system employs multiple carriers having overlapping channels and provides an improved cross-talk cancellation mechanism to address the resulting interference. Bandwidth compression is achieved using n level amplitude modulation in each frequency band. An FDM receiver is also disclosed that decomposes the received broadband signal into each of its respective frequency bands and returns the signal to baseband in the analog domain. Analog requirements are relaxed by removing cross-talk from adjacent RF channels, from image bands, and minimizing the performance degradation caused by In-phase and Quadrature-phase (I/Q) phase and gain mismatches in modulators and demodulators. The disclosed transmitter or receiver (or both) can be fabricated on a single integrated circuit.
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This application is a divisional of U.S. patent application Ser. No. 12/020,722, filed Jan. 28, 2008, which is continuation of U.S. patent application Ser. No. 10/219,906, filed Aug. 15, 2002, which claims the benefit of U.S. Provisional Application Ser. No. 60/366,923, filed Mar. 22, 2002, each incorporated by reference herein.
FIELD OF THE INVENTIONThe present invention relates generally to cross-talk cancellation techniques, and more particularly, to methods and apparatus for reducing cross-talk in frequency division multiplexed (FDM) communication systems.
BACKGROUND OF THE INVENTIONThe explosive growth of digital communications technology has resulted in an ever-increasing demand for bandwidth for communicating digital information, such as data, audio and/or video information. To keep pace with the increasing bandwidth demands, new or improved network components and technologies must constantly be developed to perform effectively at the ever-increasing data rates. In optical communication systems, however, the cost of deploying improved optical components becomes prohibitively expensive at such higher data rates. For example, it is estimated that the cost of deploying a 40 Gbps optical communication system would exceed the cost of existing 10 Gbps optical communication systems by a factor of ten. Meanwhile, the achievable throughput increases only by a factor of four.
Thus, much of the research in the area of optical communications has attempted to obtain higher throughput from existing optical technologies. For example, a number of techniques have been proposed or suggested to employ multi-carrier transmission techniques over fiber channels. Conventional multi-carrier transmission techniques, however, space the multiple carriers so that they do not interfere with one another. The required carrier spacing, however, leads to poor spectral efficiency and thus limits the throughput that can be achieved within the available frequencies. A further proposal has suggested the use of orthogonal carrier frequencies to minimize interference. A system employing orthogonal carrier frequencies, however, will require an all-digital implementation that is particularly challenging with existing analog-to-digital and digital-to-analog converters at optical rates (10 Gbps and higher).
A need therefore exists for a multi-carrier transmission technique that provides improved spectral efficiency and allows for an analog implementation. Among other benefits, improved spectral efficiency will allow greater tolerance to dispersion and the use of generic and available optical technologies.
SUMMARY OF THE INVENTIONGenerally, a method and apparatus are disclosed for canceling cross-talk in a frequency-division multiplexed communication system. The disclosed frequency-division multiplexing communication system employs multiple carriers having overlapping channels and provides an improved cross-talk cancellation mechanism to address the resulting interference.
Generally, the carrier spacing of the multiple carriers can approach the Nyquist limit. Another feature of the invention achieves bandwidth compression using n level amplitude modulation in each frequency band. The multi-level signaling improves spectral efficiency by a factor of log2n, at the expense of a higher signal-to-noise ratio (SNR) requirement.
According to another feature of the invention, an FDM receiver is disclosed where the received broadband signal is decomposed into each of its respective frequency bands and returned to baseband all in the analog domain. Duncdcrto relax the analog requirements, a digital cross-talk canceller is also disclosed that removes cross-talk from adjacent RF chaimels, from image bands, and minimizes the performance degradation caused by In-phase and Quadrature-phase (I/Q) phase and gain mismatches in modulators and demodulators. The disclosed transmitter or receiver (or both) can be fabricated on a single integrated circuit.
A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings.
In one exemplary implementation of a 40 Gbps system, there are 16 quadrature amplitude modulated (QAM) constellations (four levels each for in-phase and quadrature-phase bands) having 2.5 Gbps per carrier frequency. In this system, each channel requires a bandwidth greater than 622 MHz (the baud rate per channel is 622 Mbaud). Therefore, the total bandwidth must be slightly greater than 10 GHz (16×622 MHz). Thus, the multi-channel QAM transmission scheme can provide a 40 Gbps throughput using only 10 Gbps optical components. The present invention recognizes that while the close spacing of each carrier exhibits excellent spectral efficiency, cross-talk will be introduced in the received signal. Thus, another aspect of the invention provides an improved cross-talk cancellation mechanism.
As shown in
The transmitted signal is received by a receiver 150. As shown in
Let tx(t) be the transmit signal:
where sn,k is the nth symbol transmitted on the carrier k:
Thus, as shown in
rxj(t)=∫tx(u)·e−iw
The values a(t) and b(t) are defined as follows:
aj,k(t)=∫p(v)p(v−t)e−i(ω
bj,k(t)=∫p(v)p(v−t)e−i(ω
The receive signal rxj(t) is then written in a more compact form:
where the first term represents the main signal and cross-talk with other carriers and the second term represents the image bands after demodulation. The second term may be negligible if receive filters are very selective, or for particular choices of the carrier frequencies coj.
The sampled receive signal rxj(mT) is given by:
A convenient simplification is obtained when assuming that the shaping filter's impulse response p(t) has a finite duration T (T=baud-period):
aj,k((m−n)T)=0 if m≠n
aj,k((m−n)T)=aj,k if m=n
bj,k((m−n)T)=0 if m≠n
bj,k((m−n)T)=bj,k if m=n
rxj(mT) is therefore expressed in the simplified form:
where:
aj,k=∫p2(v)e−i(ω
bj,k=∫p2(v)e−i(ω
The pulse shaping filters p(t) in the transmitter 110 and the corresponding matched filters p(−t) in the receiver may be embodied as rectangular functions of duration T′ (where T′≦T) or as square root raised cosine filters of period T, and excess bandwidth α. When the pulse shaping filters p(t) and corresponding matched filters p(−t) are embodied as rectangular functions of duration T′ (where T′≦T), in an exemplary return-to-zero (RZ) transmitter and an “integrate and dump” receiver, the filter p(t), shown in
p(t)=ΠT′(t)T′≦T
where:
The value of a can be computed (and similarly b) as follows:
aj,k(mT)=∫ΠT′(v)ΠT′(v−mT)e−i(ω
If a is 0 and m is non zero, the following is true:
Thus, if ωk equals kωT′ (where ωT′=2π/T′), then:
aj,k(nT)=δj,k·δm
bj,k(mT)=0
In this case, the basis functions are orthogonal, and the transmission is referred to as orthogonal frequency division multiplexing (OFDM). Please note that this is due to the particular choice of T′ and ωk, the quantity ωT′/ωT can be considered as “excess bandwidth” of the shaping filter p(t):
ωk+1−ωk=ωT′=(1+α)ωT
It was observed that coarse filters, such as the transmit pulse shaping filter p(t) being embodied as a continuous-time third order Butterworth filter, and the receive matched filter being embodied as a continuous-time fifth order Butterworth, demonstrated degraded performance at the correct sampling time due to intersymbol interference, but the greater selectivity of the coarse filters provided a much wider eye opening making the receiver 150 more tolerant to random timing jitter.
When the pulse shaping filters p(t) and the corresponding matched filters p(−t) are embodied as square root raised cosine filters of period T, and excess bandwidth α, each carrier frequency is better isolated, as shown in
αj,k(t)=∫p(v)p(v−t)e−i(ω
By setting f(u) equal to p(u) and g(u) equal to p(u-t), the following is obtained:
aj,k(t)=∫f(v)g(v)e−i(ω
In the above expression, the Fourier transform of the product function (f·g) is recognized. This Fourier transform can also be expressed as the convolution of the individual Fourier transforms of F and G, respectively:
aj,k(t)=∫F(ω−Ω)G(Ω)dΩ
where F and G are given by:
F(ω−Ω)=P(ω−Ω)
G(Ω)=∫p(v−t)e−iΩvdv=e−iΩt·∫p(u)e−iΩudu=e−iΩt·P(Ω)
Therefore,
aj,k(t)=∫P((ωj−ωk)−Ω)P(Ω)e−iΩtdΩ
The raised-cosine pulse is defined as follows:
and its Fourier transform is expressed as:
If p(t) is embodied as the square root raised cosine then:
P(ω)=√{square root over (C(ω))}
If the following is assumed for all j and k:
|ωj−ωk|>2(1+α)π/T, if j≠k
then using the above frequency domain expression of a, the following is obtained:
aj,k(t)=∫P((ωj−ωk)−Ω)P(Ω)e−iΩtdΩ=0 if ωj≠ωk
Similarly, (assuming that all carrier frequencies are non-zero):
∀(j,k)bj,k(t)=0
and:
aj,j(t)=∫P2(Ω)e−iΩtdΩ=∫C(Ω)e−iΩtdΩ=∫C(Ω)e+iΩtdΩ=c(t)
and therefore:
aj,j(mT)=c(mT)
It is noted that:
aj,j(mT)=0 if m≠0
Again, under these assumptions of the pulse shaping filter, p(t), the transmission is orthogonal (OFDM). However in practice, the pulse shape is realized in the sampled domain, and due to speed limitations, it is desirable to limit oversampling to 2-4×. For instance, if the baudrate equals 666 MBaud, the minimum D/A sampling rate required with T/2 fractional spacing would be 1.3 GS/s which is already quite high. The example shown in
A rotator 840 in the receiver 800 removes the rotation introduced in the sampled signal elements, rxn,0 through rxn,K−1, by the multipliers 810 in the receiver 800. A time-frequency analyzer 850 cancels the cross-talk and equalizes the channel 140, in a manner discussed further below in conjunction with
Θn,j,k=δj,k−iω
Each time domain filter in the array 920, represented as Λj,k,1:N, is an N-tap filter with the following z-transform:
Λj,k,1:N(z)=λj,k,0·z0+δj,k,l·z−1+ . . . +λj,k,N−1·z−(N−1)
In a discrete-time system, the modulator and Λ can be permutated following the rule shown in
Λ(z)=λ0·z0+λ1·z−1+ . . . +λN−1·z−(N−1)
Thus,
yn=λ0·eiωnTxn+λ1·eiω(n−1)Txn−1+ . . . +λN−1·eiω(n−N+1)Txn−N+1
yn=eiωnT·(λ0·eiω0Txn+λ1·e−iω1·Txn−1+ . . . +λN−1·e−iω(N−1)Txn−
Λ′(z)=λ0·e−iω0·T·z0+λ1·e−iω1·T·z−1+ . . . +λN−1·e−ω(N−1)·T·z−(N−
Equivalent forms of the structure of
Λ′j,k,1:N(z)=λj,k,0·ei
Λ″j,k,1:N(z)=λj,k,0·e+i
A rotator 1440 in the receiver 1400 removes the rotation introduced in the sampled signal elements, rxn,0 through rxn,K−1, by the multipliers 1410 in the receiver 1400. A time-frequency equalizer 1450 cancels the cross-talk and equalizes the channel 140, in a similar manner to the time-frequency equalizer 850 discussed above in conjunction with
Θn,j,k=δj,ke−iω
As shown in
It is noted that the architecture of
Λ(x+jy)+Γ(x−jy)=(Λ+Γ)x+j(Λ−Γ)y=Λtx+jΓty
It is noted that the right side of the above expression comprises two multiplications of complex and real numbers, thus equaling four real multiplications.
The least mean square (LMS) update algorithm for the generalized adaptive filters of
Λn+1t=Λtn+μenreal(Xn)
Γn+1t=δnt+μenimag(Xn)
In a more detailed form:
real(Λn+1t)=real(Λnt)+μ·real(en)·real(xn)
imag(Λn+1t)=imag(Λnt)+μ·imag(en)·real(Xn)
real(Γn+1t)=real(Γnt)+μ·real(en)·imag(Xn)
imag(Γn+1t)=imag(Γnt)+μ·imag(en)·imag(xn)
This modified LMS update algorithm has the added feature that it provides compensation for a fairly large I/Q phase and gain mismatch in the analog component. This is possible because of the added two degrees of freedom.
It is to be understood that the embodiments and variations shown and described herein are merely illustrative of the principles of this invention and that various modifications may be implemented by those skilled in the art without departing from the scope and spirit of the invention. For example, additional filters can be employed in the transmitter to provide additional resilience to cross-talk, in a known manner. In addition, while the exemplary embodiment shown in
Claims
1. A method for receiving a frequency division multiplexed signal, said method comprising the steps of:
- decomposing said frequency division multiplexed signal into a plurality of frequency bands;
- returning said decomposed frequency bands to baseband signals; and
- removing far-end cross-talk from one or more of said baseband signals, wherein said far-end crosstalk is caused by one or more of said frequency bands.
2. The method of claim 1, wherein said plurality of frequency bands are overlapping.
3. The method of claim 1, wherein said removing step further comprises the step of removing said far-end cross-talk from a given baseband signal using said given baseband signal and at least one additional baseband signal.
4. A method for receiving a frequency division multiplexed signal, said method comprising the steps of:
- decomposing said frequency division multiplexed signal into a plurality of frequency bands;
- returning said decomposed frequency bands to baseband signals;
- removing far-end cross-talk from one or more of said baseband signals, wherein said far-end crosstalk is caused by one or more of said frequency bands; and
- removing image bands from said baseband signal.
5. An integrated circuit, comprising:
- RF carrier demodulators to decompose a frequency division multiplexed signal into a plurality of frequency bands and return said decomposed frequency bands to baseband signals; and
- a cross-talk canceller for removing far-end cross-talk in one or more of said baseband signals, wherein said far-end crosstalk is caused by one or more of said frequency bands.
6. The integrated circuit of claim 5, wherein said cross-talk canceller is a digital signal processor.
7. A system for receiving a frequency division multiplexed signal, said system comprising:
- a demodulator for decomposing said frequency division multiplexed signal into a plurality of frequency bands and returning said decomposed frequency bands to baseband signals; and
- a cross-talk canceller for removing far-end cross-talk from one or more of said baseband signals, wherein said far-end crosstalk is caused by one or more of said frequency bands.
8. The system of claim 7, wherein said plurality of frequency bands are overlapping.
9. The system of claim 7, wherein said cross-talk canceller removes said far-end cross-talk from a given baseband signal using said given baseband signal and at least one additional baseband signal.
10. The system of claim 7, further comprising an image band canceller for removing image bands from said baseband signal.
11. The system of claim 10, wherein said image band canceller is at a receiver.
12. The system of claim 10, wherein said image band canceller is at a transmitter.
Type: Application
Filed: Jan 12, 2012
Publication Date: May 3, 2012
Applicant: AGERE SYSTEMS INC. (Allentown, PA)
Inventor: Kameran Azadet (Morganville, NJ)
Application Number: 13/348,851
International Classification: H04J 1/12 (20060101);