[ CAP modulation is gaining acceptance]
By Burton R. Saltzberg
Several years ago, Discrete Multitone modulation, or DMT, was adopted as the standard for the Asymmetric Digital Subscriber Line. Nevertheless, more than 90 percent of the modems provided for ADSL today use Carrierless AM-PM (CAP) modulation. Around the world, numerous trials of CAP-based ADSL of various services are going on, with excellent performance reported.
It may seem unusual that in spite of the presence of a modulation standard, another modulation format has gained nearly universal acceptance. Part of the reason is availability: low-cost, production-grade CAP chips have been available for over two years, while similar DMT chips have not yet been produced, although they are expected this year.
But that's not the whole story. In addition to availability, a closer look at performance and implementation issues since the adoption of the standard has led to a much more favorable view of CAP techniques. The adoption of DMT as a modulation standard for ADSL occurred before the contending systems were optimized, before implementation issues were fully understood and before any realistic tests under true field conditions were undertaken. Since then, a better understanding of the relative merits of the modulation alternatives has evolved in terms of performance, cost and power drain.
The ins and outs of CAP
CAP may be considered a variation of Quadrature Amplitude Modulation (QAM), in which the explicit modulation and demodulation of QAM is eliminated. Complexity is reduced, particularly for the subscriber line, which does not introduce frequency offset or phase variation. Performance of CAP is fully equivalent to that of QAM, which has been used for decades in voiceband and other modems.
The essence of DMT is to effectively use many narrowband subchannels to carry the digital information. It is possible to allow these subchannels to overlap without interference under ideal conditions. As usually implemented, input data is first blocked and then converted to a set of N multibit complex symbols. The number of bits assigned per symbol (or constellation size) may vary over the block. An inverse discrete Fourier transform (DFT) is then applied to form a new set of N complex symbols, which are then transmitted. The spectrum of the line signal, sampled at N equally spaced frequencies, thus corresponds to the input data. For ADSL, N is in the order of a few hundred. At the receiver, data symbols are recovered by performing a DFT on each block of received samples. DFTs and their inverses can be performed by Fast Fourier Transform (FFT) techniques.
The DMT system achieves good performance over the subscriber line by assigning a larger constellation to those subchannels where the signal-to-noise ratio (SNR) is high; in the frequency regions where the loss is high or the noise is high, fewer bits are assigned per subchannel. In practice, a bit-allocation procedure may be used in which the receiver continually measures the SNR across the band and sends messages back to the transmitter to alter constellation sizes. This procedure must be carefully designed to keep the transmitter and receiver constellations in synchronism and to avoid instability in a rapidly changing noise environment.
It is highly desirable to confine all processing to a single block to avoid excessive complexity and latency. This requires inserting a guard interval between transmitted blocks to minimize interference between blocks. Because of the mechanics of the DFT, the guard interval is typically filled with a "cyclic prefix"-that is. a repetition of the other end of the block, which is discarded at the receiver. To the extent that any overlap between blocks still occurs at the receiver, some conventional equalization is needed.
The primary determination of the distance over which a particular bit rate can be satisfactorily carried is the loss of the line plus noise due to crosstalk of other signals in the same cable. The crosstalk, which depends on the other services on the cable, varies highly with frequency and is usually modeled as Gaussian. Near-end crosstalk is more severe than far-end because of its higher level and is more severe at the central-office end. In addition, various implementation imperfections can be modeled as an added white-noise floor.
In pursuit of performance
It has been shown theoretically that for any loss and noise vs. frequency shapes, a single-channel system such as CAP with an ideal DFE provides the same performance as a DMT system with ideal bit allocation. However, practical implementation issues cause both systems to deviate from ideal. The single-carrier system requires a well-designed DFE with more than 100 taps. The DMT requires extremely high constellation sizes, in the order of thousands of points, in the high SNR region. Also, a practical DMT system is restricted to an integral number of bits per subchannel, further reducing bit rate from the theoretical ideal. For these reasons, recently developed DFE techniques have caused CAP performance, in terms of transmission distance for a given rate, to exceed that of DMT.
Practical modems have limits on the extremes of signal amplitude that they can handle because of amplifier saturation and D/A and A/D range limits. The average power must be reduced to avoid clipping, thus limiting performance. The peak-to-average power ratio (PAR) is therefore a key factor in the performance of a modulation scheme. For a CAP system with sharp rolloff (15 percent) plus channel dispersion, the PAR is approximately 14 dB, with no peaks exceeding that. On the other hand, in a DMT system, the absolute PAR is extremely high, proportional to n, the number of subchannels. The PAR is approximately 28 dB when n = 256.
However, such extreme peaks are very rare and a clip rate which occurs with a probability that has low effect on the error rate can be tolerated. Such probability is given in the standards. The amplitude distribution of a DMT signal with high n can be approximated by a normal distribution. The effective PAR for an acceptable clipping probability is approximately 17 dB, 3 dB higher than the absolute PAR of CAP.
Impulse noise can be a severe problem on a subscriber line. The nature of impulse noise varies widely and, in spite of many studies, it remains not-well-understood. The simplest, but not very realistic, model of impulse noise consists of short-duration, widely spaced pulses of varying amplitude. Such impulses will cause errors in CAP at a lower amplitude than in DMT. However, when errors do occur, they will occur in longer bursts for DMT. This is due to the impulse's effect on an entire DMT block, whereas a CAP system will still suffer only a few symbol errors. When an error-correcting code is used, such as the Reed-Solomon code commonly used in ADSL, the relative performance of the systems is close. This is also true for long-duration impulses and for impulses that occur in bursts.
As the density of digital circuitry continually improves, cost and power drain in a modem tend to be dominated by the analog components, which include the D/A and A/D converters, transmitter line driver, receiver input amplifier and analog filters. The line driver is particularly critical since it must deliver approximately 100 mW (+20 dBm) of average signal power into a low impedance with high linearity and low probability of clipping. It is the largest consumer of power, which is of major importance in the central office and even more critical when remote terminals are deployed in the loop plant. The high PAR in DMT causes its line driver requirements to be more severe, thereby leading to higher cost and power drain.
Impact on cost, power
Other major contributors to cost and power drain are the D/A and A/D converters. For a given speed of operation, cost increases rapidly with the number of bits. The converters must handle the full signal-amplitude range with no (or negligible) clipping and also introduce quantization noise low enough to have negligible effect on error probability. DMT systems will require more bits of precision than CAP: first, because of the larger PAR; and second, because of the sensitivity of large constellations to quantization noise.
Although digital processing circuitry contributes less to the cost and power drain than analog components, computational complexity does translate into cost and power drain of that digital circuitry through the required number and size of processing devices and memory. Because of the efficiency of the FFT algorithm and the large number of taps required in a high-performance equalizer, the number of multiplies and additions per unit time will be lower in a DMT system than in a CAP system. This is at least partially compensated for by the smoother control flow in time-domain equalization. In addition, the inherent complexity of bit-allocation leads to the need for a large program store.
It is interesting to note that less transmitter digital processing is required in CAP. This may be significant in reducing the relative cost of the central office modem where the high-rate transmitter is located.
In Rate-Adaptive ADSL (RADSL), it is important to provide the maximum bit rate that the line can support.
Such rate adaptation is inherent in the bit-allocation process in DMT. For CAP, rate adaptation involves changing the size of the signal constellation, the symbol rate and filter coefficients. This process has long been used in voiceband modems and has proved not to be a difficult one in CAP ADSL modems.
Most current DMT versions of ADSL modems use echo cancellation, while current CAP modems do not. The principal reason is the phase distortion introduced by the analog filters required to implement frequency separation of the two directions of transmission when echo cancellation is not used. The CAP equalizer readily corrects for this, while DMT would have to use a sizable equalizer to avoid overlap of transmitted blocks with short guard intervals.
-Burton R. Saltzberg, a consultant in Middletown, NJ, was with Bell Laboratories from 1957 to 1996. His most recent position there was as technical manager of the Data Theory Group.
Copyright (c) 1997 CMP Media Inc.
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