Timing recovery in binary electronics and communication systems with Nyquist shaped pulses can be accomplished using techniques such as the Gardner method. This method is limited since it is not very effective in higher order modulation schemes (e.g., QAM-16). In addition to requiring two samples per symbol, the Gardener method uses an algorithm that requires knowledge of the previous symbol's timing to estimate the timing error for the current symbol.
Electronics and communication systems with Nyquist shaped pulses using higher order modulation schemes often require pulse shaping, such as from a raised-cosine pulse shaping filter. In some cases, the pulse shaping can include a roll-off-factor (ROF) that is less than 0.1, which causes typical timing recovery systems and methods to be inadequate.
A timing recovery method that is independent of ROF has been described for electronics and communication systems with Nyquist shaped pulses that use higher order modulation schemes. That method includes extracting a clock tone from a signal, employing a phase-locked loop (PLL) to track the phase of the clock tone, and using a voltage controlled oscillator (VCO) to clock the system.
In some embodiments, a timing recovery method comprises a.) receiving a signal comprising Nyquist shaped pulses, b.) sampling the signal using an analog-to-digital converter (ADC) at a sampling rate, c.) generating a plurality of delayed sampled signals from the sampled signal, wherein each delayed sampled signal has a sampling rate and a different sampling delay, d.) resampling each delayed sampled signal to 1 sample per symbol, e.) taking the absolute value of each resampled signal, f.) raising the absolute value of each resampled signal to the fourth power, g.) taking the mean of the fourth power of the absolute value of each resampled signal, h.) feeding all of the mean values into a phase estimator, and i.) using an output from the phase estimator for timing correction.
In some embodiments, the timing recovery method described above further comprises feeding the output of the phase estimator back to the ADC for timing correction.
In other embodiments, the timing recovery method described above further comprises feeding the output of the phase estimator to an interpolating stage for timing correction, wherein the interpolating stage adjusts sampling instants of the sampled signals output from the analog-to-digital converter to have corrected timing.
In some embodiments, a timing recovery method comprises a.) receiving a signal comprising Nyquist shaped pulses, b.) sampling the signal using an ADC at a sampling rate to generate a sampled signal, c.) delaying the sampled signal using a sampling delay to generate a delayed sampled signal, d.) resampling each delayed sampled signal to 1 sample per symbol, e.) determining an absolute value of each resampled signal, f.) raising the absolute value of each resampled signal to the fourth power, g.) taking the mean of the fourth power of the absolute value of each resampled signal, h.) adjusting the sampling delay and repeating steps a.) through g.) with the adjusted sampling delay N times before proceeding to step i.) to generate N sampled signals with N delays, i.) feeding the N sampled signals with N delays into a phase estimator, and j.) using an output from the phase estimator for timing correction.
In some embodiments, the timing recovery method described above further comprises feeding the output of the phase estimator back to the ADC for timing correction.
In other embodiments, the timing recovery method described above further comprises feeding the output of the phase estimator to an interpolating stage for timing correction, wherein the interpolating stage adjusts sampling instants of the sampled signals output from the analog-to-digital converter to have corrected timing.
In some embodiments, a timing recovery method comprises a.) receiving a signal comprising Nyquist shaped pulses, b.) sampling the signal using an ADC at a sampling rate using a sampling offset to generate a sampled signal, c.) determining an absolute value of the sampled signal, d.) raising the absolute value of the sampled signal to the fourth power, e.) generating a spectral domain representation of the absolute value of the sampled signal, f.) determining a dominant signal energy peak in the spectral domain, and g.) maximizing the dominant signal energy peak amplitude in the spectral domain by adjusting the sampling offset.
In some embodiments of the timing recovery method described above, the adjusting the sampling offset to maximize the dominant signal energy peak amplitude in the spectral domain further comprises determining multiple signal energy values of the dominant signal energy peak in the spectral domain which correspond to multiple respective sampling offsets, fitting a sinusoidal function to the multiple signal energy values, and using the sinusoidal function to determine a sampling offset that maximizes the dominant peak signal energy amplitude in the spectral domain.
In some embodiments of the timing recovery method described above, the sampling offset that maximizes the dominant signal energy peak amplitude in the spectral domain is fed back to the ADC for timing correction.
In other embodiments of the timing recovery method described above, the sampling offset that maximizes dominant the signal energy peak amplitude in the spectral domain is fed to an interpolating stage for timing correction, wherein the interpolating stage adjusts sampling instants of the sampled signals output from the analog-to-digital converter to have corrected timing.
Electrical systems, radio-frequency (RF), and optoelectronic communication systems benefit from higher order modulation schemes and pulse shaping with tight spectral occupancy. In practice, this typically corresponds to systems employing small excess bandwidth (i.e., low roll-off-factor (ROF)) raised cosine (RC), or root-raised cosine (RRC) pulse shaped information-bearing waveforms. Timing recovery in systems employing such waveforms is challenging, and standard solutions such as those based on the Gardener method fail. Timing recovery systems using phase-locked loops (PLLs) and voltage controlled oscillators (VCOs) are complicated and difficult to implement in high speed commercial systems.
The timing recovery systems described herein can be applied to radio frequency (RF) and optoelectronic communication systems with higher order modulation schemes and pulse shaping for Nyquist pulses (i.e., pulses that satisfy the Nyquist ISI criterion) with low roll-off-factors (ROFs), and that do not require PLLs or VCOs. Some non-limiting examples of pulse shaping filters for Nyquist pulses in high-speed communication systems that can have low ROFs are raised-cosine filters, root-raised-cosine, Gaussian filters, and sinc filters. In some embodiments, the pulse shaping filters to generate Nyquist pulses, such as those listed above, can function as frequency-domain filters and/or temporal pulse shaping elements. Another benefit of the timing recovery systems and methods described herein is that oversampling beyond Nyquist frequency is not needed, even for signals with a small ROF (e.g., less than 0.1). There are several advantages of sampling at lower rates (e.g., less than 2 samples per symbol (s.p.s.), or between 1+beta s.p.s. and 2 s.p.s., where beta is the ROF of the filters used to pulse shape the information-bearing waveforms) in communication systems, including a reduction in the power required by the system, and the ability to use less powerful system components, which can reduce the cost to implement and operate the system.
In some embodiments, the signal s(t) that is input into the timing recovery systems and methods described herein is a modulated signal with Nyquist pulses. In some embodiments, the modulated signal with Nyquist pulses is a pulse-amplitude modulated (PAM) signal, or a quadrature amplitude modulated (QAM) signal. In some embodiments, the signal is a quadrature phase shift keying (QPSK) signal, or an 8 QAM signal, or a higher order QAM signal (e.g., a 16 QAM signal, or a 32 QAM signal, or a 64 QAM signal, or a 128 QAM signal, or a 256 QAM signal).
In some embodiments, the signal s(t) that is input into the timing recovery systems and methods described herein is a digitally modulated signal with Nyquist pulses. In some embodiments, the signal contains pulses that are frequency filtered and/or temporally shaped using a raised-cosine filter, a root-raised-cosine pulse shape, a Gaussian filter, a super-Gaussian filter, or a sinc filter. In some embodiments, the signal s(t) is a digitally modulated signal with pulse shaping using a pulse shaping filter having a roll-off factor less than 0.5, or less than 0.2, or less than 0.1, or less than 0.01, or from 0.001 to 0.2. In some embodiments, the signal s(t) is a digitally modulated signal with pulse shaping using a raised-cosine filter having a roll-off factor less than 0.2, or less than 0.1, or less than 0.01, or from 0.001 to 0.2.
In general, timing recovery using the systems and methods described herein can be implemented using time domain operations, frequency domain operations, or a combination of both. In some embodiments of the time domain and frequency domain implementations, an oversampled input signal is sampled to create sampled signals with different sampling delays (i.e., different sampling offsets). Oversampling can be performed at a rate equal to the Nyquist frequency (i.e., at 1+beta samples per symbol (s.p.s.), where beta is the ROF of the filters used to pulse shape the information-bearing waveforms). For example, in the case where a system uses an RRC pulse shaping filter with an ROF equal to 0.1, then oversampling at 1.1 s.p.s. can be used. Oversampling can also be performed at a rate greater than the Nyquist frequency (e.g., at 2 s.p.s.), however, oversampling at a rate beyond the Nyquist frequency is not required. In some embodiments, each sampled signal is then decimated to 1 s.p.s., the absolute value is taken and raised to the fourth power, then the mean is taken, and then the collection of mean values are fed into a phase estimator with their corresponding delays to determine the optimal sample timing. In some embodiments of the time domain implementation of the timing recovery method, a series of points is generated by transforming the delayed sampled signals that are related to the symbol timing. The series of points is then used to optimize the sampling timing. In some embodiments of the frequency domain implementation of the timing recovery method, a peak in the transformed frequency spectrum of the sampled signal is used to optimize the sampling timing. The time domain and the frequency domain systems and methods are described more completely below.
The amplitude of the dominant peak at the center of the spectrum rises and falls over the time interval of one symbol period. The phase of the rising and falling of the amplitude of this peak corresponds to the phase of the symbol timing in the data pattern. In other words, the timing of the information stream can be reconstructed from the pulse itself. The timing recovery systems and methods described herein utilize this relationship to optimize the sample timing. On the other hand, a conventional timing recovery method for signals with higher order modulation schemes employing pulse shaping with low ROFs extracts the clock tone directly from the side band amplitude fluctuations (since the clock tone is in the side band and not in the center of the frequency spectrum). As can be seen in
Frequency recovery is equivalent to down converting the signal down to DC in the digital domain. If frequency recovery is performed in the system (e.g., as shown in processing block 220 in
In some embodiments, the timing recovery process is used to initialize the sample timing for the system. In some embodiments, the timing recovery process is performed periodically to correct the sample timing for the system. In some embodiments, the timing recovery process is performed continuously, continually, or at periodic intervals. In some embodiments, the timing recovery process includes operating on (e.g., taking the mean of) a group of 50 symbols, or 100 symbols, or 1000 symbols, or a group of any other appropriate number of symbols. In some embodiments, the timing recovery process described herein can be performed periodically, at a frequency of once for every 50 symbols, or 100 symbols, or 1000 symbols, or once per any other interval.
Continuing with
If frequency recovery is performed before timing recovery (e.g., if processing block 220 is used before processing block 230 as shown in
In some embodiments, a timing recovery method can be performed using the system described above. In some embodiments, the method includes receiving a signal with Nyquist pulses, generating a plurality of delayed sampled signals, decimating each sampled signal to 1 sample per symbol, taking the absolute value of each decimated signal, raising the absolute value of each decimated signal to the fourth power, taking the mean of the fourth power of the absolute value of each decimated signal, feeding all of the mean values into a phase estimator to determine the optimal sample timing of the system, and feeding the output from the phase estimator back to the ADC for timing correction (e.g., as feedback for the ADC 210 in
The transformed Nyquist pulse amplitudes with different sampling delays generated by the above method have the same phase as the symbol timing and therefore are used for timing recovery.
In some embodiments of the timing recovery systems and methods above, the signal is delayed (in some cases one of the delays includes no delay, as shown in the example in
In some embodiments, the signals input into the timing recovery systems and methods described herein are initially oversampled at a rate of 2 s.p.s. In some embodiments, the signals are oversampled from 1 to 2 times the Nyquist frequency (i.e., 1 to 2 times above twice the signal frequency), or greater than 1 times the Nyquist frequency, or greater than 1.2 times the Nyquist frequency, or greater than 1.1 times the Nyquist frequency, or greater than 1.01 times the Nyquist frequency.
In some embodiments of the timing recovery systems and methods above, after the signal s(t) is delayed by different amounts (e.g., in processing blocks 250), the delayed sampled signals are resampled to 1 s.p.s. Decimation, as described above, can be used when the signal is initially sampled at 2 s.p.s. and 1 s.p.s. is discarded. When the signal is sampled at less than 2 s.p.s., or at a value that is not 2 s.p.s., then other types of resampling can be used (e.g., at processing block 260 in
In some embodiments of the timing recovery systems and methods above, the phase estimation processing block 290 fits the sampled mean values of each of the delayed transformed signals to a sinusoidal function. In some embodiments, the phase estimator fits the sampled mean values to a different function, such as a saw-tooth function, or a continuous polynomial function, or a piece-wise continuous polynomial function. In some embodiments, the phase estimator fits the sampled mean values to a relationship contained in a look-up-table (LUT) that may or may not be described by a mathematical function. In some embodiments, the phase estimator uses a least mean square algorithm, or a root mean square algorithm, to fit the sampled mean values to a signal function.
Additionally, a timing recovery process in the time domain can be accomplished using a set of looped operations, rather than a parallel pipeline set of operations as described above. Many of the unit operations in the process using looped operations are the same as those in the process using parallel operations, however, the phase estimation procedure can be somewhat different. The system for the timing recovery using looped operations is also somewhat different than the system in
In some embodiments, a timing recovery method includes down converting a set of transformed signals down to DC (e.g., as is accomplished using frequency recovery processing block 220 in
In some embodiments of the timing recovery method above, adjusting the sampling offset such that the fitted sinusoidal function has a desired phase includes: a.) determining four or more multiple transformed signal values at DC (e.g., 4, or 6, or 8, or 10, or from 4 to 10) that correspond to multiple respective sampling delays, b.) fitting a sinusoidal function to the multiple delayed and transformed signal values and determining a calculated phase of the sinusoidal function, c.) using the calculated phase of the fitted sinusoidal function to determine a sampling offset that corresponds to the difference between the calculated phase of the fitted sinusoidal function and the desired phase of the fitted sinusoidal function, and d.) correcting the sampling timing using the determined sampling offset. In some embodiments, the sinusoidal function is cosine-like and the desired phase of the sinusoidal function is the phase where an extrema (i.e., a minimum or a maximum of the function) is located at the exact center of the symbol period (i.e., as shown in
In some embodiments, a timing recovery method includes frequency domain operations. In some embodiments, a timing recovery method includes receiving a signal, sampling the signal using an ADC using an initial sampling offset, determining an absolute value of the sampled signal, raising the absolute value of the signal to the fourth power, generating a spectral domain representation of the absolute value of the sampled signal, determining a dominant signal energy peak in the spectral domain, and adjusting the sampling offset to maximize the dominant signal energy peak in the spectral domain. In some embodiments, the absolute value of the signal can be raised to a power higher or lower than the fourth power (e.g., 2nd power, 8th power, or 12th power) before generating the spectral domain representation. An example of the signal in the spectral domain after the fourth power of the absolute value is taken is shown in
In some embodiments of the timing recovery method above, adjusting the sampling offset to maximize the dominant signal energy peak in the spectral domain includes: a.) determining four or more multiple signal energy values of the dominant peak in the spectral domain which correspond to multiple respective sampling offsets (e.g., 4, or 6, or 8, or 10, or from 4 to 10), b.) fitting a sinusoidal function to the multiple signal energy values, and c.) using the sinusoidal function to determine a sampling offset that maximizes the dominant signal energy peak amplitude in the spectral domain. In some embodiments, the fitting can be done using a different function, such as a saw-tooth function, or a continuous polynomial function, or a piece-wise continuous polynomial function. In some embodiments, the fitting can be done using a relationship contained in a look-up-table (LUT) that may or may not be described by a mathematical function.
The timing recovery methods with frequency domain operations described above work well for Nyquist pulses with ROF less than 0.1, or less than 0.01, or from 0.001 to 0.1. For this method, a lower ROF is advantageous, because as ROF gets larger (e.g., 0.1, or 0.2, or greater), the dominant peak at the center of the spectrum carries less power, and responds with a smaller variation when the delays are applied, which makes the sinusoidal fit more difficult.
Similar to the timing recovery performed in the time domain, the sampling offset that maximizes the dominant signal energy peak amplitude in the spectral domain (i.e., the phase shift needed for timing recovery) can be fed back to the ADC for timing correction of future sampled signals, or to an interpolation stage to correct the timing of previously sampled signals.
Reference has been made in detail to embodiments of the disclosed invention, one or more examples of which have been illustrated in the accompanying figures. Each example has been provided by way of explanation of the present technology, not as a limitation of the present technology. In fact, while the specification has been described in detail with respect to specific embodiments of the invention, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily conceive of alterations to, variations of, and equivalents to these embodiments. For instance, features illustrated or described as part of one embodiment may be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present subject matter covers all such modifications and variations within the scope of the appended claims and their equivalents. These and other modifications and variations to the present invention may be practiced by those of ordinary skill in the art, without departing from the scope of the present invention, which is more particularly set forth in the appended claims. Furthermore, those of ordinary skill in the art will appreciate that the foregoing description is by way of example only, and is not intended to limit the invention.
The application claims the benefit of U.S. Provisional Patent Application No. 62/538,151 filed on Jul. 28, 2017 and entitled “TIMING RECOVERY FOR NYQUIST-LIKE SHAPED PULSES;” which is hereby incorporated in its entirety by reference for all purposes.
Number | Date | Country | |
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62538151 | Jul 2017 | US |