Multiplex communications – Communication techniques for information carried in plural... – Combining or distributing information via frequency channels
Reexamination Certificate
1998-03-10
2001-10-09
Jung, Min (Department: 2663)
Multiplex communications
Communication techniques for information carried in plural...
Combining or distributing information via frequency channels
C370S480000, C375S295000
Reexamination Certificate
active
06301268
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to data communication using frequency division multiplexing systems. More particularly, the invention relates to methods for encoding information for transmission by such systems.
BACKGROUND OF THE INVENTION
Frequency division multiplexing (FDM) is a multiplexing technique that has applications for both wireline and wireless applications. The former include, inter alia, applications to digital subscriber loop communications, and the latter include, inter alia, applications to WaveLan communications.
FDM in certain implementations is described in the discrete multitone (DMT) standard published by the International Telecommunications Union (ITU) under the publication number T1.413.
Very briefly, FDM operates by dividing a data stream into a temporal sequence of blocks. With reference to
FIG. 1
, the data in each block (the “information sequence”) are represented, in frequency space, by a sequence of tones
10
(also referred to as carriers). The number of tones used varies among the various implementations, but is typically in the range 32-512. Information is encoded by assigning to each tone a complex amplitude (that is, a positive magnitude and a phase). The complex amplitudes that can be assigned are not arbitrary, and they do not vary continuously. Instead, they are typically drawn from a discrete set, sometimes referred to as a constellation, of points in the complex plane. (An illustrative such constellation is shown in
FIG. 2.
) Although the number of points in such a constellation may vary, a typical number of points lies in the range 2-512. In the case, e.g., of 256 points, each complex amplitude represents log
2
256, or 8, bits of data. The sequence of amplitudes is referred to as the “signal sequence”, and each amplitude in this sequence is referred to as a “signal element”.
The transmitted signal (shown as element
20
in
FIG. 1
) is the Fourier transform of the sequence of tones. (Those skilled in the art will appreciate that what is precisely meant here is a real-valued reverse Fourier transform from the frequency domain to the time domain.) The receiver performs, in essence, another Fourier transform back into frequency space to recover the signal sequence. At the receiver, knowledge concerning the mapping between the information sequence and the signal sequence is used to recover the information sequence.
Those familiar with oscillatory phenomena will appreciate that when tones, with associated phase differences, are superimposed, constructive interference often leads to the emergence of peaks that extend to a significant height above the average amplitude of the combined waveform. When a transmitted signal exhibits this property, it is often useful to characterize the signal by its peak-to-average power ratio. It should be noted in this regard that the average transmitted power is directly related to the rate at which information can be communicated. That is, higher average power implies higher potential data-communication rate. The term “average” refers here to the statistical, or ensemble, average over all signals. The term “peak”, on the other hand, refers to a particular sequence.
For several reasons, it is desirable to limit the peak-to-average power ratio of a transmitted signal. In many instances, there are standards and regulations that impose a limit on this quantity. More fundamentally, the last amplification stage of the transmitter may be saturated by amplitude peaks in its input signal, resulting in clipping of the transmitted waveform and consequent errors in data transmission. In principle, an amplifier can be designed to handle essentially any given peak-to-average power ratio encountered in practice. However, the cost of the amplifier and also the power consumption of the amplifier increase as the maximum acceptable peak power increases. As a consequence, economic considerations militate for measures designed to minimize the probability that a peak will appear that cannot be transmitted without distortion. Although the greatest acceptable value for this probability depends on the specific application and on other factors, a typical value is 10
−5
.
One conventional approach to this problem is to limit the permitted signals to only those signals that have an acceptably low peak power. This approach is difficult to put into practice because it is difficult to identify a suitable set of signals in the frequency domain. Moreover, decreasing the population of available signals decreases the number of bits carried by each signal element. Because a substantial fraction of signals are typically eliminated by this approach, the transmitted data rate is significantly reduced.
SUMMARY OF THE INVENTION
We have discovered an improved method for decreasing the probability of an unacceptably high peak-to-average power ratio. In a broad aspect, our invention involves generating at least two distinct, alternative signal sequences, computing Fourier transforms of the respective alternative signal sequences, and selecting for transmission one of these sequences, based on the Fourier transform computations. More specifically, the selection of one sequence may be based, e.g., on the determination that the Fourier transform of that sequence has an acceptable peak power. Alternatively, a comparison may be made among the Fourier transforms of the respective signal sequences, and selection made of that sequence whose Fourier transform exhibits the lowest peak power. Those skilled in the art will understand that the term “Fourier transform” is used here to encompass any of several appropriate mathematical transforms, and that each can be implemented by any of several appropriate computational algorithms.
Desirably, the alternative sequences are generated in such a way that the joint probability that both will lead to unacceptable peak-to-average power ratios is significantly smaller than the individual probabilities that each alone will lead to such a ratio. This can be achieved by providing for near statistical independence between the respective alternative sequences. This independence may be achieved by operating upon the information sequence, or by operating upon the signal sequence, or in the coding procedure that maps between the information sequence and the signal sequence.
At the receiver, it should be possible to recover the same information sequence from either of the alternative signal sequences.
According to a currently preferred embodiment of the invention, the signal elements are generated by a differential encoding scheme, in which information is largely carried by the differences between pairs of signal elements. The signal elements are partitioned into two disjoint sets in such a way that each information-carrying pair belongs entirely to one or the other of the two sets. Given a signal sequence of signal elements, a further signal sequence is derived by applying a rotation in the complex plane to those signal elements that belong to one of the two disjoint sets. The rotation applied is a rotation under which the constellation of signal-element values is invariant.
According to an alternate embodiment of the invention, alternative information sequences are generated by forming at least one encrypted version of the original information sequence. Alternative signal sequences are generated simply by encoding respective alternative information sequences. Decryption information is available at the receiver so that the original information sequence can be recovered from either of the alternative signal sequences.
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Tan, B.T. et al., “Crest Factor Minimisation in
Laroia Rajiv
Richardson Thomas J.
Urbanke Rudiger L.
Finston Martin I.
Jung Min
Lucent Technologies - Inc.
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