Fast resynchronization system for high-speed data transmission

Abstract: A system for resynchronizing the timing and carrier phases of a modem receiver signal to enable the receiver to quickly reacquire the timing phase and the carrier phase, and thereby restart the demodulation process. The system provides accurate estimates of the timing and carrier phases, as well as a gain correction factor to provide for proper alignment for decoding. The discrete Fourier transform of the received signal is multiplied by the complex conjugate of the discrete Fourier transform of the transmitted signal to produce estimates of the desired phases. Gain control and carrier phase control are performed to determine corresponding error signals to adapt the resultant estimated timing and carrier phases, and gain correction.

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to improving receiver resynchronization in half-duplex or polled modem systems and, more particularly, to a procedure for estimating carrier and timing phases of a signal transmitted by a remote modem to allow immediate continuation of data reception. 2. Description of Related Art High-speed data transmission has become an accepted and expected feature of newer and more complex modems. Generally, transmission occurs as full-duplex (FDX) or half-duplex (HDX). In HDX transmission, information may travel from one end to the other, e.g., from a local modem to a remote, at any given time, thus causing a need to regularly change the direction of transmission. For example, in facsimile transmission, after a "page" is transmitted from one side to the other, the receiving end must indicate whether the page was received without error, or whether a retransmission is needed. This causes an interruption in transmission, and when the next page is to be transmitted, it is important to quickly resume transmission at a high speed. Similarly, FDX transmission generally begins in HDX mode, where training procedures will require a similar "turning around" of the direction of transmission. Generally, modem transmission begins with a training phase when a receiver configures itself to best receive a modem signal over the channel. This training involves correcting for the level attenuation of the channel (gain control), training up an equalizer which is a filter resembling the inverse of the channel, synchronizing the receiver to the phase and frequency offset of the signal carrier induced by the channel, as well as synchronizing to the symbol timing phase and clock offset between the two modems. Once the receiver has adapted to the remote signal and the channel's effect on it, data transmission can proceed at a high data rate. However, if an interruption occurs, perhaps due to channel "turn-around" mentioned above, this synchronization will be lost. When transmission resumes, it will be necessary to reacquire the symbol timing and carrier phase to continue high-speed reception of data. The equalizer, however, can generally be stored during the interruption, and the carrier frequency offset and symbol timing clock offset generally do not change. Channel attenuation generally does not change either, and can either be stored or re-estimated. More particularly, during the initial training sequence which is relatively long, when the timing and carrier recovery loops as well as the equalizer are trained up, the frequency offsets of the timing and carrier loops are determined via the modem controller. Normally, this is a four-point or sixteen-point uncoded signal constellation, generated from a pseudorandom bit generator. For resynchronization, the timing recovery requires that the "center" of the symbol be determined, while the carrier recovery finds the "reference" phase of the carrier. For example, if the transmitter carrier is cos (ωt+a), the receiver demodulates using cos (µt + b). The carrier recovery adapts µ toward ω and b toward a, such that µ and b begin at 0 or some other predetermined value, and are then corrected such that they gradually approach their targets. That is, µ approaches ω, and b approaches a. In general, the most crucial parameter to reacquire is the timing, or sampling, phase. The timing phase is the symbol reference. The timing recovery is performed by calculating a timing error signal that gives an indication of the error of the symbol phase estimate. For example, its sign may be positive if the timing of the symbol phase is too early and negative if it is too late. The magnitude of the error signal will generally reflect how far off the timing is from the correct symbol phase estimate. This error signal is then passed through a low-pass filter and used to shift the timing phase, either by varying a sampling clock or by controlling an interpolator. Since, by definition, error correction reduces the error, the timing tends to converge toward the optimum phase. At high data rates, for example, where the number of bits per symbol can be as high as 10, the timing phase must be accurately estimated to within 1 to 2%. However, a regular phase-locked loop usually requires a significant amount of time to converge and settle to a good estimate of the symbol phase. The carrier phase is generally related to the timing phase. If, for example, the transmit clock is running faster than the receiver's clock, the carrier will have a higher frequency in the transmitter relative to the receiver. Further, the channel phase response will change the carrier phase, and may even change the frequency of the carrier (e.g., in Frequency Division Multiplex systems). The carrier recovery corrects for these effects. However, because of the relation to the symbol timing, it must do so either jointly with the symbol timing recovery or after it. A change or correction in symbol timing will produce a change in carrier phase, which may either be corrected via the knowledge of the timing correction, or simply by measuring the carrier phase error caused by the timing change and correcting for it. The current state of the art of the present invention is generally summarized by the following references: Uhl, C. et al., "A new Algorithm for a Frequency and Time Synchronization for Burst Mode Transmission, Proc. of the Mil. Comm. Conf. (MILCOM), San Diego Nov. 6-8 1995, vol. 1, 6 pages 788-792, U.S. Pat. No. 4,599,732 to Lefever, and US Pat. No. 4,320,517 to Godard et al. Uhl presents a synchronization algorithm for time and frequency in burst mode transmission. The method uses a preamble signal in the slot containing the demand assignment massage. The preamble signal contains a carrier whose frequency is varying in time as a double frequency slope and the method allows recovery of the Doppler frequency and the time delay. U.S. Pat. No. 4,599,732 to Lefever describes a signal processing scheme through which the receiver synchronizes or resynchronizes itself to the transmitted data signals. At the transmitter, bursts or sequences of known symbols are interleaved with unknown data. At the receiver incoming frames of signals (containing interleaved bursts of known data and unknown data) are processed in a manner similar to the processing of spread spectrum encoded data. A replica (or respective replicas) of the known signal burst(s) is (complex) correlated with the incoming signal to locate and lock onto a known (PN) reference symbol burst. Once a known symbol block has been located, a symbol rate clock (bit sync) is adjusted to track out any offset in the timing used for sampling the received data. This is followed by coarse and fine frequency offset adjustments to enable the local oscillator to lock onto the transmitted frequency. U.S. Pat. No. 4,320,517 to Godard et al. presents a system and method for effecting the initial adjustment of the clock during a turn-on period in the course of which the receiver is supplied with a known clock synchronization signal followed by a known equalizer training sequence. The incoming signal is sampled and the samples so obtained are stored in a storage means. The synchronization signal and the beginning of the training sequence are successively detected. When the beginning of the training sequence is detected, the storage locations for the samples of the received synchronization signal are known and a control signal controlling the initial adjustment of the clock is derived from these samples, which are stored in predetermined locations in the storage means. SUMMARY OF THE INVENTION It is an object of the present invention to provide a fast resynchronization procedure which enables high-speed data transmission to be quickly resumed in the event of interruptions. This and other objects and advantages are achieved in a resynchronization system which provides accurate estimates of timing phase and carrier phase, as well as a gain correction factor. Although the resynchronization procedure can be used with different types of data signals it is notably efficient if used with a repeated constant amplitude zero-auto correlation (CAZAC) sequence at the beginning of transmission. In the resynchronization system, one or more of the initial timing phase, carrier phase, or signal level are estimated by multiplying a discrete Fourier transform (DFT) of the received modem signal with the complex conjugate of the DFT of the transmitted signal. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a block diagram of a steady state modem receive in accordance with an embodiment of the present invention. Figure 2 is a block diagram of a fast resynchronization system in accordance with an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The following description is of the best presently contemplated mode of carrying out the invention. In the accompanying drawings, like numerals designate like parts in the several figures. This description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the accompanying claims. A modem receiver according to an embodiment of the present invention is shown generally in Figure 1. The received signal input y(n) is first scaled by a gain control signal 130, before being input into the timing phase interpolator/sampler 112. The gain control 130 can be performed using a variety of standard techniques. Essentially, the gain control incorporates an error signal which is generated by comparing the input signal level, after correction, to a reference value. The error signal is used to correct a gain estimate, which is generally logarithmic. The gain estimate is then used to produce a linear scale value to scale the input signal to give a constant input level. Preferably, embodiments of the present invention are implemented using a repeated CAZAC sequence at the beginning of transmission for fast estimation of the channel response. More particularly, a CAZAC sequence is desired because in the complex baseband, the signal points in the sequence have the same energy, such that correlation with its conjugate generally results in zero except when the two sequences are aligned. That is, if a repeated CAZAC sequence is sent over a channel, and the received signal y(n) is filtered with the CAZAC sequence, i.e., by using the complex conjugate of the CAZAC signal points as filter coefficients, the output will simply be the channel impulse response. In accordance with preferred embodiments of the present invention, the timing phase interpolator/sampler 112 provides a controlled signal timing phase, as part of the receiver's timing recovery. This can be done in several different ways. In one method, the time instant an analog signal is sampled by an A/D converter is controlled 132. A timing error controls a clock circuit to determine this sampling instant. Consequently, to shift the timing phase of the received signal, the sample time is then shifted to determine the controlled signal phase. When using newer sigma-delta A/D converters, interpolators are generally used to determine the signal timing phase. The interpolators typically comprise selectable filters which have the same frequency-amplitude response, and group-delay which is constant in frequency throughout the signal bandwidth. This constant delay, however, is different for each filter in the set. A timing error is used to update a timing phase estimate. Accordingly, to produce a given timing phase, the filter having delay characteristics closest to the desired delay is selected. As illustrated in the embodiment of Figure 2, the output of the timing phase interpolator/sampler 112 is input into demodulator 116, where the signal is translated in frequency by multiplying the signal with a complex exponential having a phase representing the inverse of the nominal carrier phase, followed by a low-pass filter. The output of the demodulator is then input into the equalizer 114, which is preferably an adaptive filter that is approximately the inverse of the channel. The output of the equalizer 114 is multiplied by a complex exponent with a phase that is the negative of the carrier phase estimate 128. That is, if  represents the phase estimate, the equalizer output 114 is multiplied by e -j- . In preferred embodiments, the carrier phase control 128, like the equalizer 114, is adaptive wherein it uses a carrier phase error signal to update its carrier phase estimate. The carrier phase estimate 128 is then applied to rotate the signal output from the equalizer 114 to remove the carrier phase offset. The gain control, timing recovery, equalizer and carrier recovery all operate on the general principle of applying a correction based on an estimate, measuring the resulting error, then using that error to improve the estimate. It will thus be recognized that, since these functions are linear, the operations of the gain control 130, interpolator/sampler 112, demodulator 116, equalizer 114, and carrier phase control 128 may be interchangeably performed and/or partially combined. If the reception is interrupted, however, the timing and carrier phase estimates will usually be incorrect. Using the steady state methods of adapting the estimates will at best require a significant amount of time before enabling high-speed data transmission. In many cases, the estimates may not converge at all since the error signals are only valid if the errors are small. Thus, embodiments of the present invention describe a method of obtaining initial estimates of the carrier and timing phases which ensures that the phase errors are small. Accordingly, high-speed transmission can resume quickly. More particularly, beginning with a transmit signal x(n), its DFT is represented as: Suppose the signal is time shifted relative to x , such that: x' ( n ) = x ( n -τ) then by rearranging the summation term of the DFT: x' ( n ) e - j 2π nk / N = x ( n -τ) e - j 2π nk / N = x ( n -τ) e - j 2π( n -τ) k / N e - j 2πτ k / N we find that: X '( k ) = e - j 2πτ k / N X ( k ). If the signal's carrier phase is also shifted, it becomes x ''( n ) = ε j  x '( n ). As a result, the DFT of the signal, after being time and phase shifted is X ''( k ) = e j (2πτ k / N ) X ( k ). Incorporating a scale factor thus provides a signal x'''(n): x''' ( n ) = α x'' ( n ). The DFT of a scaled, and time and phase shifted version of x(n) is then: X'''' ( k ) = α e j (-2πτ k / N ) X ( k ). Figure 2 shows a block diagram of a preferred embodiment of the present invention. The initially received signal, which is indicated to be y(n) in Figure 2 is first scaled 130 based on a previous gain estimate and its timing phase is shifted 112 by a previous estimate 132. At this time, the earlier estimate may be completely incorrect or inaccurate. The previously-determined estimates may also be values which have been initialized to zero. The signal is then passed through the equalizer 114 and its carrier phase is corrected 128 based on a previous estimate. This correction, like the timing phase correction estimate, may also be quite inaccurate at this point. Ultimately, the signal x''' ( n ) is determined, where the gain, timing phase and carrier phase offsets of the combined effect of the channel, the gain control 130, the timing phase interpolator/sampler 112 and the carrier phase control 128, respectively, are given by α, τ and . That is, x''' ( n ) = α e j  x ( n -τ). Thus, the DFT X''' ( k ) 120 of the received signal x''' ( n ) can be determined and multiplied by the complex conjugate 122 of the DFT X(k) of the transmitted signal to yield: X''' ( k )· X *( k ) = α e j (-2πτ k / N ) X ( k ) X * ( k ). And the scaling factor α can be estimated as: where D(k) = X'''(k) X*(k). Clearly, it may be advantageoius to design X(k) such that X ( k ) X * (k) = 1 at all k, in which case the scaling factor estimate becomes An estimate of the phase function can then be computed, where the phase function is given by: According to the resultant linear function, its value at k=0 represents the carrier phase shift, and the slope represents the timing phase shift. Utilizing the estimate of α, the values of ϕ(k) can be calculated by multiplying D(k) by 1/α 136, or by independently considering values of the imaginary part of D(k) divided by the real part; that is, Im[D(k)]/Re(D(k)]. Using the well-known minimum mean-square error (MMSE) solution for the parameters, given K samples ( x n ) and ( y e ) of a linear function y = ax + b , the MMSE estimates of a and b are given by: a = K ∑ x k y k - ∑ x k ∑ y k K ∑ x 2 k - ∑ x k 2 b = ∑ x 2 k Σ y k - ∑ x k ∑ x k y k K Σ x 2 k - ∑ x k 2 Thus, given samples of the phase function ϕ( k ), the values of τ and  can be estimated by the phase estimator 126. The above x k represent the sample frequencies, which are assumed to be evenly spaced at 2πτk/N. It will be recognized, however, that the characteristics of these frequencies can be easily generalized to where they are not uniformly spaced. After simplifying, τ and  are determined to be τ = - N 2π 2 K Σ k ϕ( k )-Σ k Σϕ( k ) K Σ k 2 - (Σ k ) 2 ϕ = ∑ k 2 ∑ϕ( k )-∑ k ∑ k ϕ( k ) K ∑ k 2 -(∑ k ) 2 Since many of the parameters can be precomputed, the following variables may be defined as: B = ∑ k C = ∑ k 2 D = ∑ϕ( k ) E = ∑ k ϕ( k ) and solution can be expressed more simply as: τ = - N 2π 2 A ( KE - BD )  = A ( CD - BE ) It can be seen that only D and E depend on the sample data, while A, B, and C can be precomputed. The values thus obtained are then added to the corresponding estimates in the timing phase control 132 and the carrier phase control 128. By accurately and quickly estimating the carrier phase offset  and the timing phase offset τ relative to the receiver, the timing and carrier phases can be quickly resynchronized, and thus aligned properly for decoding. It will be recognized that embodiments of the present invention may also be applied to phase jitter tracker resynchronization. Phase jitter tracker loops track periodic, typically sinusoidal, variations in the carrier phase. By applying the above-described scheme to consecutive blocks of received signals, and comparing the variation in carrier phase estimate from one block to another, an estimate of the phase jitter phase may be obtained if the phase jitter frequency has been determined previously.

Claims: A system for resynchronizing timing and carrier phase by estimating a timing phase offset and a carrier phase offset of a received signal y(n) corresponding to a known transmitted signal x(n) for resuming high-speed data reception of a transmitted signal, the system comprising: means for modifying the received signal y(n) to produce a modified signal x"' (n) using a scaling means (130), a time phase shifting means (132), or a carrier phase shifting means (128) ; means (120) for determining a discrete Fourier transform (DFT) X''' (k) of the modified signal x'''(n) at more than one value of k, the DFT having plural input samples; means for determining a DFT X(k) of the known transmitted signal at more than one value of k; means (122) for determining a complex conjugate X* (k) of the DFT of the known transmitted signal; a multiplier for multiplying X'''(k) by X*(k); a phase estimator (126) for obtaining an estimate of a phase function:  (k) =  - 2πτk/N the phase function being a linear function of k with a value at k = 0 representing carrier phase offset  and a slope 2πτ/N representing timing phase offset; and means for estimating (112) the timing phase offset τ and the carrier phase offset  according to the phase function. The system of claim 1, further comprising a gain estimator (124) for providing a scale factor α which is proportional to the product of X'''(k) and X*(k). The system of claim 2, wherein the scale factor α is determined according to: where D(k) = X''' ( k ) X *( k ). The system of claim 2, wherein the scale factor α is determined according to: where D(k) = X'''(k)X * (k) , and X ( k ) X *(k) = 1 at all k. The system of claim 2, wherein the phase function is determined according to: where X''' ( k )· X * ( k ) = α e j (-2πτ k / N ) X ( k ) X *( k ) The system of claim 5, wherein the time phase offset τ and carrier phase offset  are estimated according to the equations: τ = - N 2π 2 K Σ k ϕ( k )-Σ k Σϕ( k ) K Σ k 2 - (Σ k ) 2  = Σ k 2 Σϕ( k )-Σ k Σ k ϕ( k ) K Σ k 2 - (Σ k ) 2 The system of claim 1, wherein the input received signal y(n) is periodic. The system of claim 1, wherein the input received signal y (n) is a constant amplitude zero-autocorrelation (CAZAC) sequence. The system of claim 8, wherein the CAZAC sequence is periodic. The system of claim 1, further comprising a gain controller (130) for determining an error signal and adjusting a gain estimate based on the error signal, wherein the gain controller provides a scale factor to be multiplied by the received signal y (n) . The system of claim 10, further comprising a timing phase interpolator/sampler(112) for processing the received signal y (n) multiplied by the gain controller scale factor to determine a controlled signal phase. The system of claim 11, further comprising a demodulator (116) coupled to the timing phase interpolator/sampler (112) for translating the received signal y(n) in frequency. The system of claim 11, further comprising: an equalizer (114) for receiving the controlled signal phase of the timing phase interpolator/sampler (112) ; and a carrier phase controller (128) for adapting the estimated carrier phase according to an error signal, wherein the output of the carrier phase controller (128) is applied to the output of the equalizer (114) to update the estimated carrier phase. The system of claim 13, wherein the equalizer (114) comprises an adaptive filter. The system of claim 11, wherein the timing phase interpolator (112) comprises a selectable filter having predetermined phase characteristics. A method for resynchronizing timing and carrier phases by estimating by a timing phase offset and a carrier phase offset of a received signal y(n) corresponding to a known transmitted signal x(n) for resuming high-speed data reception of a transmitted signal, the method comprising: modifying the received signal y(n) to produce a modified signal x''' (n) using a scaling means (130) , a time phase shifting means (132) , or a carrier phase shifting means (128) ; determining (120) a discrete Fourier transform (DFT) X '''( k ) of the modified signal x '''(n) at more than one value of k, the DFT having plural input samples; determining a DFT X(k) of the known transmitted signal; calculating (122) a complex conjugate X*(k) of the DFT of the known transmitted signal; multiplying X''' (k) by X*(k) ; obtaining an estimate of a phase function: (k) =  - 2πτk/N the phase function being a linear function of k with a value at k = 0 representing carrier phase offset  and a slope 2πτ/N representing timing phase offset; and estimating (112) the timing phase offset τ and the carrier phase offset  according to the phase function. The method of claim 16, further comprising the step of calculating a scale factor α which is proportional to the product of X'''(k) and X*(k) The method of claim 17, further comprising the step of determining the phase function according to: where X''' ( k )· X *( k ) = α e j (-2πτ k / N ) X ( k ) X *( k ). The method of claim 18, wherein the time phase offset τ and carrier phase offset  are estimated according to the equations: τ = - N 2π 2 K Σ k ϕ( k )-Σ k Σϕ( k ) K Σ k 2 - (Σ k ) 2  = Σ k 2 Σϕ( k )-Σ k Σ k ϕ( k ) K Σ k 2 - (Σ k ) 2 The method of claim 16, wherein the input received signal y(n) is a constant amplitude zero-autocorrelation (CAZAC) sequence.

Inventors: OLAFSSON SVERRIR, OLAFSSON, SVERRIR
Applicants: ROCKWELL INTERNATIONAL CORP, ROCKWELL INTERNATIONAL CORPORATION
Application year: 1997
Main classification: H04L7
IPC codes: H04L27, H04L7