Frequency synchronizer

A frequency synchronizer system is based on the maximum likelihood criterion from estimation theory and that can achieve both frequency acquisition and frequency tracking without requiring knowledge at the receiver of the carrier's phase angle, baud timing, or a preamble consisting of known signal symbols. The synchronizer includes a processor for executing the following sequence of operations: a) initializing an estimated frequency correction factor; b) determining a corrected frequency offset value from a first product of a sample signal and the estimated frequency correction factor; c) filtering a first sample of the corrected frequency offset value to obtain a filtered corrected frequency offset value; d) imparting a delay to a second sample of the corrected frequency offset value to obtain a delayed corrected frequency offset value; e) determining a conjugate product value from a second product of the filtered corrected frequency offset value and a conjugate of the filtered corrected frequency offset value; f) determining a delay conjugate value from a third product of the delayed corrected frequency offset value and the conjugate product value; g) determining an error signal from the delay conjugate value; h) determining a frequency offset value from the error signal; and i) determining an updated value of the estimated frequency correction factor from the frequency offset value.

BACKGROUND OF THE INVENTION

The present invention generally relates to frequency synchronizers for digital communications systems, and more particularly, to frequency synchronizers that are based on the maximum likelihood criterion from estimation theory and that can achieve both frequency acquisition and frequency tracking without requiring knowledge at the receiver of the carrier's phase angle, baud timing, or a preamble consisting of known signal symbols.

All digital communications systems operate on the basis of a finite number of possible waveforms available for transmission during any particular signaling interval. The digital receivers must process versions of these transmitted waveforms which are corrupted by noise, channel fading, multipath, distortion, unintentional interference, and jamming, for example. The receiver's task is to determine which was the transmitted waveform for a particular signaling interval. Acceptable performance requires that this determination be achieved with high probability of correctness.

The degree of success potentially achievable by a digital communications system depends on the accuracy of reference signals at the receiver in their representation of the possible transmitted waveforms, as they would appear at the receiver, including the effects of noise, etc. To a large degree, achieving good reference signals is synonymous with having the receiver be synchronized with the transmitted waveforms arriving over a transmission channel.

Synchronization in a particular case may involve several parameters. For example, the receiver's reference signals should be based on the correct carrier frequency, which may be unknown due to oscillator drifts or doppler shifts. For best performance, the receiver should have a timing reference to know the beginning of each signaling waveform. For Time-Division-Multiplex (TDM) and/or Time-Division-Multiple Access (TDMA) systems, the level of timing information must be extended to knowing the beginning of groups of time slots (frame synchronization). In order to have the performance improvement potentially available from coherent detection; the receiver requires accurate knowledge of the carrier's phase angle (phase synchronization). For spread-spectrum systems, synchronization to a hopping-frequency pattern and/or a spread-spectrum code sequence is required. For all levels of synchronization, typically the receiver's synchronizers are required to provide good estimates of the unknowns (frequency, phase, timing, etc.) during an initial start-up period (so-called “acquisition”) and to continue to provide good estimates as the system proceeds to operate (so-called “tracking”).

Two general approaches have been useful for designing synchronizers for digital receivers. Many existing synchronizers are based on good engineering reasoning as to what can work (so-called “ad hoc” procedures), as opposed to being mathematically derived based on various math models and theoretical reasoning. Synchronizers of the latter type typically are derived, and implemented, by using the tools of Estimation Theory based upon the Maximum-Likelihood criterion of goodness (maximization of appropriate conditional probability density functions).

The choice and/or design of synchronizers for a particular system greatly depends on the digital modulation technique to be employed and the channel over which the communication is to take place. Practical solutions have long existed for conventional digital modulation techniques such as Phase Shift Key (PSK), Frequency Shift Key (FSK), Amplitude Shift Key (ASK), and Quadrature Amplitude Modulation (QAM), particularly for the case of a Gaussian noise channel. To meet requirements of transmitting data at high rates, with high accuracy, and with minimal bandwidth usage, newer digital signaling techniques have been found. These include Trellis-Coded Modulation (TCM) and Continuous-Phase Modulation (CPM). Generally, the synchronizers for the older, conventional digital receivers are inadequate for the newer techniques. In fact, there are many theoretical versions (special cases) of the energy-efficient and bandwidth-efficient CPM which would be preferred choices for applications but for the lack of good, achievable synchronizers. Since general solutions are unknown, each category of CPM requires finding specialized solutions for the synchronizer designs required for system operation.

An existing system for which better synchronizers are desirable is a special version of CPM known as dual-h, 4-ary, full-response. The meaning of these terms follows from the mathematical model of a signal having the specified CPM waveform, s(t), given below.s⁡(t)=2⁢EsT⁢ⅇjΨ⁡(t,α_)
with Esrepresenting the waveform's energy over its interval T, and Ψ(t,α) is the phase function. The function Ψ(t,α) depends on the data sequenceα=( - - - αi−1,αi,αi+1, - - - ) where each of the data symbols is randomly and independently selected from the four possibilities (±1, ±3), hence “4-ary.” Also, Ψ(t,α) depends on two constants h0and h1, called “modulation indexes,” and a function q(t), called the “phase response function,” as follows.Ψ⁡(t,α_)=2⁢π⁢⁢h0⁢∑i⁢⁢α2⁢i⁢q⁡(t-2⁢iT)+2⁢π⁢⁢h1⁢∑i⁢⁢α2⁢i+1⁢q⁡(t-2⁢i-T)
For “full response” CPM, the function q(t), is as shown inFIG. 1.

A method for synchronizing for the above CPM waveform case requires transmitting a preamble at the beginning of a message. The preamble is a sequence of non-data symbols, known to the receiver. This preamble sequence is transmitted by means of a modulation technique, less complex than the CPM used for data, called Minimum Shift Key (MSK). However, this method of synchronization has certain undesirable characteristics. For example, the requirement that a start-up interval be set aside for a known preamble means a reduction in information rate. A serious problem arises if the receiver is unable to detect the preamble, thus leading to the loss of the follow-on message. Another potential problem of great concern when operating in the presence of an adversary is that the use of a different modulation for a preamble from that for data offers the adversary significant information useful for a jamming attack.

Therefore, a need exists for synchronization processors/circuits that operate without a preamble and without changing modulation methods within a transmission.

SUMMARY OF THE INVENTION

The present invention provides a frequency synchronizer that does not require a transmitted known-sequence preamble prior to the transmission of information symbols as a message. Nor does the synchronizer require that the receiver be synchronized in time or carrier phase prior to its operation to obtain information allowing the receiver to become synchronized in frequency, so-called frequency acquisition. In addition to frequency acquisition, the frequency synchronizer provides the receiver with continual updates on reference-frequency changes during the time of message transmission, so-called frequency tracking.

The frequency synchronizer is based on the maximum likelihood criterion from estimation theory and that can achieve both frequency acquisition and frequency tracking without requiring knowledge at the receiver of the carrier's phase angle, baud timing, or a preamble consisting of known signal symbols. The synchronizer is part of a system that includes a processor for executing the following sequence of operations: a) initializing an estimated frequency correction factor, as for example, at zero; b) determining a corrected frequency offset value from a first product of a sample signal and the estimated frequency correction factor; c) filtering a first sample of the corrected frequency offset value to obtain a filtered corrected frequency offset value; d) imparting a delay to a second sample of the corrected frequency offset value to obtain a delayed corrected frequency offset value; e) determining a conjugate product value from a second product of the filtered corrected frequency offset value and a conjugate of the filtered corrected frequency offset value; f) determining a delay conjugate value from a third product of the delayed corrected frequency offset value and the conjugate product value; g) determining an error signal from the delay conjugate value; h) determining a frequency offset value from the error signal; and i) determining an updated value of the estimated frequency correction factor from the frequency offset value.

The frequency synchronizer is applicable for use in conjunction with receivers that detect communications signals that belong to a class of digital modulation waveforms known as dual-h, 4-ary, full-response, CPM.

Since the frequency synchronizer of the invention operates without a transmitted preamble, the energy efficiency and the bandwidth efficiency of the communications system are greater than for systems that require preambles. An important advantage of the invention is that it obviates the need for different modulation methods for signals that employ preambles.

Other advantages of the invention will become apparent upon review of the following specification, including the claims, and the accompanying figures.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed to a frequency synchronizer for synchronizing to a Continuous-Phase Modulation (CPM) signal that does not require phase or timing information from a detected signal prior to processing for frequency estimation. Nor does the invention require that there be a preamble of known symbols at the beginning of a transmitted sequence. Referring toFIG. 2, there is shown a block diagram of a method for implementing a frequency synthesizer10that embodies several features of the present invention. A received signal12consisting of a CPM signal s(t) of the dual-h, 4-ary, full-response type and an additive white Gaussian noise component w(t) may be represented as a function of time t by the equation r(t)=s(t)+w(t). Signal12is transformed by an anti-aliasing filter14into a time dependent signal16represented by x(t). The anti-aliasing filter14essentially removes from signal12those frequency components not essential for maintaining information contained in CPM signal, s(t), thereby reducing the inherent distortion produced by sampling time-limited analog waveforms. Signal16is sampled by sampler15at intervals spaced Tsseconds apart; i.e., at, a sampling rate of 1/Tssamples per second. The sample15is represented as a switch that opens and closes at a frequency 1/Ts. The signal18emitted by sampler15is a set of discrete time samples represented by x(kTs), where k is an integer index so that x(kTs) is the kthsample of the set x(kTs).

Signal22is a corrected frequency offset value that is represented by y(kTs), also a set of discrete time samples, produced by multiplying signal18[x(kTs)] by signal24at multiplication node20, where signal24represents an estimated frequency correction factor. At the initialization of the operation of frequency synchronizer10, signal24may be provided with an initial value of zero. Signal24is a discrete time sequence represented by e−j2πk{circumflex over (v)}Ts. The resultant product from node20is signal22, and represents a corrected version of signal18[x(kTs)], with the correction taking the form of subtracting from signal18an estimate {circumflex over (v)} produced by synchronizer10of the unknown frequency offset v from the actual carrier frequency of CPM signal s(t). Next, signal22, i.e., the sequence y(kTs), is filtered by a digital filter26having impulse response h(kTs). The impulse response h(kTs) is specified by the following equations:
h(kTs)=kF2(kTs), for −N≦k≦−1
=kF3(kTs), for 1≦k≦N
=0, forf=0 or |k|>N,
where N represents the number of samples for each information symbol interval, and where F2and F3are functions defined as follows:F2⁡(k1⁢Ts,k2⁢Ts)=⁢14⁡[1+(k2-k1)N][cos⁢⁢3⁢π⁢⁢h0⁡(k2-k1)N+⁢cos⁢⁢π⁢⁢h0⁢(k2-k1)N+cos⁢3⁢π⁢⁢h1⁡(k2-k1)N+⁢cos⁢π⁢⁢h1⁢(k2-k1)N]+14⁢⁢π⁢{[h13⁢(h02-h12)+⁢3⁢h1h02-9⁢h12]⁢sin⁢3⁢π⁢⁢h1⁡(k2-k1)N+⁢[h19⁢h02-h12+h1h02-h12]⁢sin⁢⁢π⁢⁢h1⁢(k2-k1)N+⁢[h09⁢h12-h02+h0h12-h02]⁢sin⁢⁢π⁢⁢h0⁢(k2-k1)N+⁢[h03⁢(h12-h02)+3⁢h0h12-9⁢h02]⁢sin⁢⁢3⁢⁢π⁢⁢h0⁡(k2-k1)N}=⁢F2⁡[(k2-k1)⁢Ts]
and where:F3⁡(k1⁢Ts,k2⁢Ts)=⁢14⁡[1-(k2-k1)N][cos⁢⁢3⁢π⁢⁢h0⁡(k2-k1)N+⁢cos⁢⁢π⁢⁢h0⁢(k2-k1)N+cos⁢3⁢π⁢⁢h1⁡(k2-k1)N+⁢cos⁢π⁢⁢h1⁢(k2-k1)N]+14⁢⁢π⁢{[h13⁢(h12-h02)+⁢3⁢h19⁢h12-h02]⁢sin⁢3⁢π⁢⁢h1⁡(k2-k1)N+⁢[h1h12-9⁢h02+h1h12-h02]⁢sin⁢⁢π⁢⁢h1⁢(k2-k1)N+⁢[h0h02-9⁢h12+h0h02-h12]⁢sin⁢⁢π⁢⁢h0⁢(k2-k1)N+⁢[h03⁢(h02-h12)+3⁢h09⁢h02-h12]⁢sin⁢⁢3⁢⁢π⁢⁢h0⁡(k2-k1)N}=⁢F3⁡[(k2-k1)⁢Ts]

Since filter26is non-casual, a time delay of D sampling intervals is incorporated into h(kTs) of filter26. By way of example, D may be set equal to 2N, but other choices are possible as might be suitable for particular applications. The filter26is thus shown as h[(k−D)Ts] so as to incorporate the necessary delay. The output of filter26is a signal28represented as a discrete time sequence w(kTs), which is transformed at step29into signal30, the conjugate sequence w*(kTs). Signal28represents a filtered corrected frequency offset value. Signal22[y(kTs)] is also delayed D sampling intervals by the delay32, which produces signal33, represented as y[(k−D)Ts] and described as a delayed corrected frequency offset value. The multiplier34forms a signal36which is a discrete time sequence and is the product of signals30and33, i.e., w*(kTs) y[(k−D)Ts]. Signal30is described as a conjugate produce value. Signal36, a delay conjugate value, is provided as an input to error generator38.

Error generator38transforms signal36into error signal40which is a discrete time sequence e(nT), with n being the positive integer index allowing for the generation of updated error signals at intervals of T seconds. T is the time for each separate CPM waveform and is NTs. The error signal40[e(nT)] for a particular value of n is calculated by error generator38from the summing of N real numbers comprising signal36, as follows:e⁡(nT)=∑k=n⁢⁢N(n+1)⁢N-1⁢⁢Im⁢{y⁡[(k-D)⁢Ts]⁢w*(kTs)}.

The error signal40is used by loop filter42to produce signal44, a frequency offset value, which is a sequence {circumflex over (v)}(nT) of estimates of the unknown frequency offset V. The sequence {circumflex over (v)}(nT) is produced iteratively by the discrete time loop filter42which is a first-order filter described by the difference equation
{circumflex over (v)}[(n+1)T]={circumflex over (v)}(nT)+γe(nT).
Thus, the next estimate {circumflex over (v)}[(n+1)T] of the unknown frequency offset is the present estimate of {circumflex over (v)}(nT) added to the error signal40[e(nT)] that is weighted by a step-size parameter constant γ selected from computer simulations for a particular application. The choice of γ is based upon a need to have the sequence {circumflex over (v)}(nT) converge toward v at a reasonable rate without having large overswings.

Signal44, represented as the sequence {circumflex over (v)}(nT), is converted by a discrete time voltage controlled oscillator (VCO)46into signal24, which was previously described above as the sequence e−j2πk{circumflex over (v)}Tsfor updating and correcting signal18[x(kTx)]. The frequency synchronizer10is, therefore, a discrete time closed-loop processor, suitable for both frequency acquisition and frequency tracking.

Referring toFIG. 3, frequency synchronizer10may be implemented as a sequence of executable operations in a discrete time digital data processor50which provides signal22(a corrected frequency offset) to a digital receiver52, which outputs a signal54. Signal54is a data sequence that represents an improved estimate of the data encoded in signal12, or s(t). The operation of frequency synchronizer10may be repeated any integral number of times to provide increasingly refined values for the corrected frequency offset value as represented by signal22.