# Toneless Carrier Recovery

Original Publication Date: 1974-Oct-01

Included in the Prior Art Database: 2005-Feb-28

## Publishing Venue

IBM

## Related People

## Abstract

The described device allows the recovery of the demodulating carrier directly from the received data without using side tones, when the transmission mode is the modulation by signal elements (also called ECHO MODULATION) giving two orthogonal channels also delayed with respect to each other by Tc/4 (Fc = 1/Tc = carrier frequency).

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__Page 1 of 4__**Toneless Carrier Recovery **

The described device allows the recovery of the demodulating carrier directly from the received data without using side tones, when the transmission mode is the modulation by signal elements (also called ECHO MODULATION) giving two orthogonal channels also delayed with respect to each other by Tc/4 (Fc = 1/Tc = carrier frequency).

Before describing the device, some theoretical points relating to the used signals will be discussed.

The above-cited definitions of the transmission mode result in having the received signal represented by formula 1 (see the figure). In the formula Epsilon represents the frequency shift, and Ai, Bi are equal to + 1 when the transmitted information elements are binary.

In practice, the received signal must be demodulated by a carrier signal cos 2 Pi (2Fc + Epsilon)t to reconstitute the transmitted signal; the information is then recovered by double sampling at instants 0, T, 2T, ... and -Tc/4, T - Tc/4, 2T - Tc/4, ... (T is the information element period on each channel).

The above-cited demodulating signal can be generated in the receiver; but then it may have a phase difference with respect to its theoretical timing and it may also present instantaneous frequency differences (equivalent to instantaneous phase differences). Such signal is represented by formula 2: cos [2 Pi (2Fc + Epsilon)t + Alpha] (2).

If the received signal is demodulated by the signal of formula 2 and by the orthogonal signal of formula 3 sin [2 Pi (2Fc + Epsilon)t + Alpha] (3). the respective signals y(t) and y(t) are obtained. If T and Tc are linked by relation T = Lambda Tc/2 (Lambda = integer), formula 4 y(kT) cos Alpha(1k) + y(kT) sin Alpha(1k) = (Ak Pi /T) cos k Lambda Pi (4). gives the relation between y(t) and y(t) at instants t = kT (k = 0, 1, ...); Alpha(1k) is the value of Alpha at instant kT.

Similarly, the relation given by formula 5 y(kT - Tc/4) cos Alpha (2k) + y(kT - Tc/4) sin Alpha (2k) = (Bk Pi /T) cos k Lambda Pi (5) exists between signals y(t) and y(t) at instants t = kT - Tc/4 = kT - T/2 Lambda ; Alpha is the value of Alpha at instant kT - Tc/4. Formulae 4 and 5 allows computation of Alpha which is, in turn, used to force Alpha to zero by acting on the generator delivering demodulating signals of formulae 2 and 3; in practice, in normal running, Alpha is always small and, for example, formula 4 can be written as in formula 6: y(kT) . Alpha (1k) = (Ak Pi /T) . cos k Lambda Pi - y(kT) (6). A formula 6' (not written) very similar to formula 6 is obtained from formula 5. In formulae 4, 5, 6, 6', the term in cos k Lambda Pi is equal to 1 for any k if Lambda is even, or for k even if Lambda is odd (Lambda and k are integers); then (Ak Pi /T - y(kT) = Delta [y(kT)] which is the deviation of the received signal from its ideal value.

In practice, binary phase corrections are introduced in the phase-locked oscillator of the demodulating signal generator; accordingly, formula 6 can be used in the...