2.5 Discrete Multichannel Transmission (DMT)
| The concept of multichannel transmission is one often used against a formidable adversary, following the old adage: "divide and conquer," where the adversary in this case is the difficult transmission characteristic of the DSL twisted pair. Multichannel methods transform the DSL transmission line into hundreds to thousands of tiny transmission lines, each of which is easy to transmit on. The overall data rate is the sum of the data rates over all the easy channels. The most common approach to the "division"is transmission in non-overlapping narrow bands. The "conquer" part is that a simple line code on each such channel achieves best performance without concern for the formidable difficulty of intersymbol interference, which only occurs when wide bandwidth signals are transmitted. Multichannel line codes have the highest performance and are fundamentally optimum for a channel with intersymbol interference. A key feature of multichannel transmission for DSLs is the adaption of the input signal to the individual characteristics of a particular phone line. This allows considerable improvement in range and reliability, two aspects of an overall system design that can dominate overall system cost. Thus, multichannel line codes have become increasingly used and popular for DSLs. Multichannel transmission methods achieve the highest levels of performance and are used in ADSL and VDSL. The equalizers of Section 2.4 only partially mitigate intersymbol interference and are used in suboptimum detection schemes. As the ISI becomes severe, the equalizer complexity rises rapidly and then performance loss usually widens with respect to theoretical optimums. The solution, as originally posed by Shannon in his famous mathematical theory of communication (see references in [1]) is to partition the transmission channel into a large number of narrowband AWGN subchannels . Usually, these channels correspond to contiguous disjoint frequency bands, and the transmission is called multicarrier or multitone transmission. If such multitone subchannels have sufficiently narrow bandwidth, then each has little or no ISI, and each independently approximates an AWGN. The need for complicated equalization is replaced by the simpler need to multiplex and demultiplex the incoming bit stream to/from the subchannels. Multicarrier transmission is now standardized and used because the generation of the subchannels can be easily achieved with digital signal processing. Equalization with a single wideband carrier may then be replaced by no or little equalization with a set of carriers or "multicarrier," following Shannon's optimum transmission suggestion, and can be implemented and understood more easily. The capacity of a set of such parallel independent channels is the sum of the individual capacities , making computation of theoretical maximum data rates or use of gaps for practical rates easy. The basic concept is illustrated in Figure 2.14. There, two DSL transmission line characteristics are posed, each of which would have severe ISI if a single wideband signal were transmitted. Instead, by partitioning the transmit spectrum into narrow bands, then those subchannels that pass through the channel can be loaded with the information to be transmitted. Note the receiver has a matched filter to each transmit bandpass filter, thus constituting an easily implemented maximum likelihood receiver (without need for Viterbi sequence detection, even on a channel with severe spectral filtering). Better subchannels get more information, whereas poor subchannels get little or no information. If the subchannels are sufficiently narrow, then no equalizer need be used. Figure 2.14. Basic multitone concept. The set of signal-to-noise ratios that characterize each of the subchannels is important to performance calculation. It is assumed that there are N subchannels each carrying where SNR geo is the geometric signal-to-noise ratio, or essentially the geometric mean of the 1 + SNR/ G terms, The entire set of parallel independent channels then behaves as one additive white Gaussian noise channel with SNR essentially equal to the geometric mean of the subchannel SNRs. [6] This geometric SNR can be compared against the unbiased SNR of equalized passband and baseband systems' SNR directly. This SNR can be improved considerably when the available energy is distributed nonuniformly over all or a subset of the parallel channels, allowing a higher performance in multichannel systems. [7] The process of optimizing the bit and energy distribution over a set of parallel channels is known as loading and is studied in the next subsection.
2.5.3 Loading AlgorithmsThe process of assigning information and energy to each of the subchannels is called loading in multichannel transmission. Reference [1] studies early loading algorithms in detail, and Chapter 3 introduces several improved methods for ADSL. 2.5.4 Channel PartitioningChannel partitioning is the means of dividing the transmission channels into a set of parallel independent ISI-free subchannels. General channel partitioning is of strong interest, but as yet only DMT finds wide use. A general discussion of how to partition channels is found in Chapters 4 and 5 of [2]. 2.5.5 Discrete Multitone Transmission (DMT)In DMT, a packet of channel output samples, y, can be related to a packet of input samples, x, by y = Hx + n. n is a packet of noise samples, and H is a channel matrix. A guard period between blocks of N samples called DMT symbols contains a cyclic prefix. The samples in the prefix must repeat those at the end of the symbol, that is, x - i = x N - i i = 1, ..., n . When a cyclic prefix is used, the matrix H becomes what is called a square "circulant" matrix (the last n output samples of each transmitted packet are ideally ignored in DMT). Circulant matrices have the property they may be decomposed as where Q is a matrix corresponding to the discrete Fourier transform (DFT) and L is a diagonal matrix containing the N Fourier transform values for the sequence h k that characterizes the channel. The kl th element of Q starting from the bottom right at k = 0 , l = 0 and counting up is The DFT is a heavily used and well-understood operation in digital signal processing and a variety of structures exist for its very efficient implementation in N log 2 (N) operations rather than the usual N 2 for most matrix multiplication. Thus, DMT is a very efficient multichannel partitioning method. Even when H is real, the matrices in the DMT decomposition are complex. The input/output relation for the channel is Y = H x + n. The N x N circulant matrix H is written for DMT as: where the reader can verify implements circular convolution on the packet of inputs. The transmit symbol vectors are created by x = Q * X , where X is a frequency-domain vector of channel inputs. Each element of X is complex and can be thought of as a QAM signal. When the channel is real and thus the symbol x must also be real, the frequency-domain input must have conjugate symmetry, which means that meaning there are N /2 complex subchannels, not N . The energy of the cyclic prefix guard period is clearly wasted , thus effectively reducing the amount of power available for transmission by N/ ( N + again a set of parallel independent channels when the input noise is white. When the input noise is not white, the output noise vector tends to white as long as the block size is long enough, so noise prewhitening need not be used in reasonable DMT implementations . As block length goes to infinity, DMT becomes multitone and optimum. DMT for ADSL is described in more detail in Chapter 3. For more generally on the DMT system, see [1]. |
bits/dimension. The average number of bits is the sum of the numbers of bits carried on each channel divided by the number of dimensions (assumed here to be 
) on the average. This power penalty is in addition to an excess bandwidth penalty of the cyclic prefix, which is an additional factor of 
| Top |
EAN: 2147483647
Pages: 154