# Tracking Carrier Phase Intercept, Frequency Shift and Phase Jitter in Synchronous Data Transmission Systems

Original Publication Date: 1976-Sep-01

Included in the Prior Art Database: 2005-Mar-03

## Publishing Venue

IBM

## Related People

## Abstract

Carrier phase intercept, frequency shift and phase jitter are obstacles to high-speed data transmission over telephone lines. Discussed below is the application of the Viterbi algorithm for minimization of the effects of these obstacles in the receiver of a synchronous data transmission system employing general combined amplitude and phase modulation. The algorithm is described in the case of a recursive search over eight signalling periods (M = 8), and the six paths explored (P = 6). Let Phi(n)(k) with k = 0,1, ...5 be the k/th/ largest estimate of the carrier phase jitter at the n/th/ signalling time. Phi(n)(5) < Phi(n)(4) < Phi(n)(3) < Phi(n)(2) < Phi(n)(1) < Phi(n)(0), V n (1).

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__Page 1 of 4__**Tracking Carrier Phase Intercept, Frequency Shift and Phase Jitter in
Synchronous Data Transmission Systems **

Carrier phase intercept, frequency shift and phase jitter are obstacles to high-speed data transmission over telephone lines. Discussed below is the application of the Viterbi algorithm for minimization of the effects of these obstacles in the receiver of a synchronous data transmission system employing general combined amplitude and phase modulation. The algorithm is described in the case of a recursive search over eight signalling periods (M = 8), and the six paths explored (P = 6). Let Phi(n)(k) with k = 0,1, ...5 be the k/th/ largest estimate of the carrier phase jitter at the n/th/ signalling time. Phi(n)(5) < Phi(n)(4) < Phi(n)(3) < Phi(n)(2) < Phi(n)(1) < Phi(n)(0), V n (1).

Assuming phase jitter behaves as a Wiener process with discrete binary increments + or - Sigma. Phi(n)(k) - Phi(n)(k+1) = 2 Sigma ; k = 0,1, ... 4 (2) where sigma is a step size, whose value is for instance: sigma = 2 pi /256.

Assuming a phase jitter sample phi(n)(k) at time n, data detection takes place by finding which among the constellation states if the closest of the received complex sample z(n) after a rotation of -phi(n)(k). Let a(n) (k) be this state, i.e., the state which minimizes the distance square:

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This operation is carried out once a baud for each of the value of the parameter k. In other words, six detections and six rotations per baud, instead of a single one, are completed.

Since phi(n)(k) differs from Phi(n)(k+1) by a few degrees, a(n)(k+1) is equal either to a(n)(k) or to a state adjacent to this one.

Distance squares D(n)(k) are accumulated together from one baud to the next one in order to get an unlikelihood measure:

J(n)(Phi(n)(k) for the path ending at Phi(n)(k). The process described here is a Minimum Unlikelihood Sequence Estimation (MUSE) rather than a Maximum Likelihood Sequence Estimation (MLSE).

The smallest metrix J(n)(Phi(n)(k)) is subtracted from the whole set of metrics (k=o,1, ... 5) in order to prevent those from reaching excessive values.

The paths are built as follows. At time n-1, six phase estimates Phi(n-1)(0), Phi(n-1)(1), ...Phi(n-1)(5) and a state variable F(n-1) are available, F(n-1) = 0 or 1 indicating-whether phase estimates have propensity for decreasing or increasing versus time. This variable is used to build six new phase estimates at time n.

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Starting at time n-1 and ending at time n, there is only one path leading to phi(n)(5) and two paths leading to Phi(n)(k), with k=0,l, ... 4. phi(n)(k) = phi(n- 1)(k)-sigma = phi(n-1)(k+1) + sigma (5) k = 0,1,...4.

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__Page 2 of 4__Therfore, each of these new phases corresponds to two metrics: J/*/(n)(phi(n)(k)) is associated with the path passing through phi(n-1)(k) and phi(n)(k).

Jn(Phi(n)(k)) is associated with the path passing thru phi(n-1)(k+1) and phi(n)(k).

(Image Omitted)

A comparison is made between J(n-1)(phi(n-1)(k)) a...