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Phase Jitter Attenuation Using a Kalman Predictor

IP.com Disclosure Number: IPCOM000084839D
Original Publication Date: 1976-Jan-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 4 page(s) / 113K

Publishing Venue

IBM

Related People

Desblache, A: AUTHOR [+2]

Abstract

An approach is made to minimize the phase jitter effects at the receiver in phase modulated data transmission systems. In these systems, the phase Theta(k) of the received signal at the kth sampling instant can be expressed in the form: Theta(k) = Phi(k) + Phi(o) + Phi(s)(k) + phi(j)(k) + Delta Phi(k). where; phi(k) is the information bearing component; phi(o) is the phase intercept; phi(s)(k) is the phase shift due to frequency shift; Phi(j)(k) is the kth phase jitter sample; and DeltaPhi(k) is a white noise due to additive channel noise and residual intersymbol interference.

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Phase Jitter Attenuation Using a Kalman Predictor

An approach is made to minimize the phase jitter effects at the receiver in phase modulated data transmission systems. In these systems, the phase Theta(k) of the received signal at the kth sampling instant can be expressed in the form: Theta(k) = Phi(k) + Phi(o) + Phi(s)(k) + phi(j)(k) + Delta Phi(k). where; phi(k) is the information bearing component; phi(o) is the phase intercept; phi(s)(k) is the phase shift due to frequency shift; Phi(j)(k) is the kth phase jitter sample; and DeltaPhi(k) is a white noise due to additive channel noise and residual intersymbol interference.

The proposed scheme for recovering phi(k) is shown in Fig. 2. Phase intercept Phi(o) and phase shift Phi(s)(k) are first cancelled by filtering means. Then, an estimate phij (k, k-1), computed at the (k-1) th sampling instant Kappa Kappa by a Kalman predictor is substracted from the received phase signal. A decision logic provides the detected phi(k). Estimate phij (k, k-1) is provided by a Kalman predictor under the assumption the phase jitter is a sinusoidal signal with unknown phase and frequency.

The Kalman filter method is described, for example, in the first sections of "Application of the Kalman filter Algorithm to Automatic Adjustment of Transversal Equalizers for Data Transmission Channels" by D. Godard, IBM Journal of Research and Development, May 1974. Only the method of deriving the state equations of the mathematical model will be summarized below.

The analog signal phi(j)(t) is the solution of the second-order differential equation: d2 over dt2 phij (t) + omega/2/(j) phij (t) = 0, (1) where: omega(j) = 2 pi f(j)

Equation (1) can be expressed in the form of a system of two first-order differential equations: d over dt phi/1/j (t) = omega(j) phi/2/j (t) (2) d over dt phi/2/j
(t) = -omega(j) phi/1/j (t) where phi/1/j (t) and phi/2/j(t) are the quadrature and in- phase components of phi j (t), respectively.

The difference equations corresponding to (2) can be expressed in the matrix form:

(Image Omitted)

where T is the sampling period.

Assuming r (k) is a sinusoidal reference signal, whose frequency fo is very close to f(j), and in proper phase with phij (k), and denoting r/1/ (k) and r/2/(k) the sampled values of its quadrature and in-phase components, respectively, then:

(Image Omitted)

The x (k) vector, from (6), satisfies the linear difference equation: x (k) = Psi
(k) x (k - 1) + F (k) (10)

1

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This equation being linear, the state variables x (k) can be estimated by a Kalman filter. Such a Kalman filter provides an estimate of the difference between phi j (k) and the ref...