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In this paper, a second-order bang–bang digital phase-locked loop (BBPLL) with dominant random walk phase noise and transport delay is analyzed using Fokker–Plank equations. Explicit closed-form expressions are derived for the timing error probability distribution function, jitter variance, and power spectral density (psd). For the type-II BBPLL considered in this paper, the timing error distribution is shown to be Laplacian and not Gaussian distributed as previously assumed, while the derived psd is Lorentzian, which is consistent with earlier works. The analytical solutions are valid as long as the continuous-time approximation of the BBPLL dynamics is accurate as is the case for typical operating loop bandwidths. The accuracy of the derived expressions is validated via simulation.

With increased levels of integration in modern system-on-chips, the coupling of supply noise in a phase-locked loop (PLL) has become the dominant source of performance degradation in many systems. In this paper, an all-digital approach to canceling the effects of supply noise is presented. By sensing the supply noise using an analog-to-digital converter (ADC), an observer–controller loop filter jointly processes the ADC and phase detector outputs to determine the oscillator control signals that minimize the output jitter. The proposed digital PLL is shown to be significantly more robust to supply noise compared with a conventional PLL.

When analyzing a bang-bang phase locked loop (BBPLL), the hard nonlinearity is often linearized for analysis purposes with limited accuracy. This paper presents an accurate mathematical model of a BBPLL based on Markov Chains that is valid for all operating conditions. The proposed methodology is used to compute the BBPLL output steady-state jitter probability density function (PDF). Based on the analytical model, the loop filter gain is also optimized to minimize the output jitter. The analytical results show close agreement with simulation.

A practical approach for detecting packet-based orthogonal-frequency-division multiplexing (OFDM) signals in the presence of phase noise is presented. An OFDM packet consists of several OFDM symbols with full-pilot symbols at the beginning followed by consecutive data symbols. Based on the full-pilot OFDM symbol, a frequency-domain joint phase noise and channel vector estimator is first derived. It is shown that the phase noise vector can be estimated by maximizing a constrained quadratic form without requiring knowledge of the channel vector. This estimated phase noise vector is then used to compute the least squares channel estimator. Assuming that the channel is constant during each packet, the estimated channel is used in subsequent data OFDM symbols for equalization and data detection. Since phase noise changes from one OFDM symbol to the next, the scattered pilots in each data OFDM symbol are used to non-iteratively estimate and mitigate the phase noise induced interference. A significant improvement in the signal-to-interference-plus-noise ratio is achieved using the proposed algorithm.

The maximum likelihood estimate of the impulse response of a frequency-selective channel in the presence of phase noise and I/Q imbalance is derived. The complexity of the joint estimator is reduced using approximate cost functions for both phase noise and I/Q imbalance. The proposed estimator is first applied to OFDM transmission in a single-input single-output system and then generalized to multi-input multi-output OFDM systems. The bit error rate performance of popular space-time codes for two and four transmit antennas is evaluated under zero-forcing, minimum mean squared error and maximum likelihood detection rules. An expression for the residual inter-carrier interference variance after phase noise and I/Q imbalance compensation is derived and compared to the uncompensated case. Significant improvement in signal-to-interference-noise is obtained with the proposed algorithm.

The observer-controller loop filter proposed in the author's prior work is extended to include the effect of flicker noise in the digital-controlled oscillator (DCO). We show that the same implementation structure, as in the author's prior work but with modified gain values to account for the effect of flicker noise, can be used to achieve near-ideal jitter performance. A frequency domain analysis of the observer-controller loop filter is presented to provide a more intuitive understanding of the loop filter operation. The analysis shows that a system zero is introduced at dc to filter out the flicker noise and that the observer-controller based digital phase-locked loop (DPLL) remains effectively a second-order system regardless of the transport delay in the digital feedback loop. A comparison with conventional DPLL loop filter is also provided, which shows that in the presence of flicker noise, the jitter performance is even further improved than in the author's prior work.

A digital phase-locked loop (DPLL) has been recently developed to exploit the increasing transistor speed of modern process technology. By employing a digitally controlled oscillator (DCO) and a time-to-digital converter (TDC), the loop filter of a DPLL becomes all-digital. Instead of designing the loop filter by digitizing a continuous-time loop response as has been commonly done, more sophisticated control schemes can be employed. In this paper, we propose to design the feedback loop in the time-domain by first modeling the DCO and TDC as a noisy ?plant? in state-space form. Based on a Kalman observer of the ?plant,? the proposed approach then generates optimal control signals that accurately account for the additive noise as well as the transport delay in the digital feedback system. The proposed observer-controller loop filter achieves rapid transient response time and significantly reduces the steady-state phase noise jitter compared to the conventional DPLL. Furthermore, the proposed approach enables modeling of other noise sources such as due to oscillator pulling, which is a common problem in many modern transceivers. By employing the observer-controller loop filter, the effect of oscillator pulling can be effectively removed without degrading the overall phase noise performance.

A novel phase-noise (PHN) compensation method is proposed in this paper. The proposed approach uses the information provided by an additional signal path that is added with modest hardware overhead to better estimate the PHN. In this signal path, the oscillator output is self-downconverted to the baseband by mixing itself with a delayed and conjugated replica, so as to provide PHN information that is free from data modulation. A joint prediction and smoothing Wiener filter can then be employed to obtain the minimum mean-squared error estimate of the PHN. There are generally two types of PHN models commonly used in the literature: stationary PHN and Wiener PHN. Both types of PHN are considered in this paper. Adaptive schemes are also presented using the least-mean square algorithm and recursive least-square algorithm. Simulations of a 64-quadrature amplitude modulation receiver confirm the analysis results of the PHN estimation performance, and show that the proposed method can improve the receiver performance significantly over the conventional schemes.

Phase-to-digital converter (PDC) is a critical building block in digital phase-locked loops (DPLL). To improve its phase noise performance, an integer-N DPLL that employs an analog-to-digital converter (ADC) to digitize the phase error is presented. Compared to the conventional time-to-digital converter (TDC), the proposed ADC-based PDC with the same number of bits can be shown to reduce the quantization noise contribution to the DPLL output jitter variance by more than an order of magnitude. Design examples are presented to verify the functionality and performance of the proposed approach.

The bit error rate performance of orthogonal frequency division multiplexing (OFDM) systems is severely degraded in the presence of phase noise. The effect of phase noise on an OFDM signal has been studied in the literature. The OFDM signal sub-carriers are distorted due to phase noise in two ways. First is the constant phase shift of all the sub-carriers, and second is the inter-carrier interference. A pilot structure is proposed to estimate the phase noise spectral components in every data OFDM symbol. The pilot design parameters are specifically optimized for an OFDM system in the presence of phase noise.

In this paper, the bit error rate performances of multi-input multi-output orthogonal frequency division multiplexing transmission schemes for two and four transmit antennas are studied and compared in the presence of phase noise, I/Q imbalance and channel estimation errors. It is shown that for matched rates and same decoding complexity, maximum diversity schemes such as the Alamouti code, perform better than the maximum capacity schemes such as spatial multiplexing. The simulation environment comply with IEEE 802.11n standard.

In this paper, we propose a robust non-iterative pilot-aided channel estimator for multi-input multi-output orthogonal frequency division multiplexing systems in the presence I/Q imbalance and phase noise. We show that by exploiting the phase noise and I/Q imbalance properties, the joint cost function for estimating them reduces to separate cost functions, each of which can be readily solved. Mean-squared-error performance of the proposed estimator is evaluated for IEEE 802.11n wireless local area network applications.

In this paper, we derive the maximum likelihood (ML) channel estimate in the presence of phase noise (PHN) and I/Q imbalance for OFDM systems. Since it is estimated jointly with I/Q and PHN, the channel estimate is more robust to these RF impairments compared to the conventional schemes. The complexity of the joint estimator is reduced using an approximate cost functions for both PHN and I/Q imbalance. The performance of the proposed estimator in terms of both channel mean squared error (MSE) and bit error rate (BER) is also presented and compared to the case of perfect channel knowledge.

A new method for detecting packet-based OFDM signals in the presence of phase noise is presented. The scattered pilots in each data OFDM symbol are used to noniteratively estimate and mitigate the phase noise induced inter-carrier interference (ICI). A significant improvement in the bit error rate (BER) is achieved using this technique, especially for systems suffering from high phase noise.

A frequency domain channel estimator for OFDM is derived in the presence of phase noise. In an OFDM frame transmission (e.g., WLAN), channel estimation is performed based on the full-block pilot symbol at the preamble. The estimate is then used to decode subsequent OFDM data symbols in the same frame. Channel estimation, however, can be severely degraded in the presence of phase noise. The proposed approach removes the effect of phase noise when estimating the channel response. When this improved channel estimate is used to detect OFDM data symbols, large improvement in bit error rate is observed.

A simple linear periodic time-varying circuit model is proposed to rigorously analyzed the noise behavior in active mixers. Explicit formulas for thermal noise folding factor and flicker noise leakage are derived. Based upon our analysis, mixers operating at the off overlap mode are shown to provide better noise performance. The analysis is validated against simulations and measurements

A novel phase noise (PHN) compensation scheme for communication transmitters is proposed. The proposed scheme downconverts the transmitted passband signal and oscillator output to the baseband by multiplying themselves with delayed and conjugated replicas. The baseband information provided by the additional signal paths helps to estimate the oscillator PHN. In the literature, there are two commonly used PHN models: Wiener PHN and stationary PHN. The proposed scheme compensates both types of PHN effectively. Simulation results show that the proposed scheme can significantly reduce the PHN.

The phase noise (PHN) of the local oscillator affects the overall receiver performance, especially when a noisier oscillator is chosen to lower the receiver cost. A novel PHN compensation method is proposed. It uses the information provided by an additional signal path that is added with small hardware overhead to estimate the PHN better. A Wiener smoothing filter can then be employed to obtain the minimum mean-squared error (MMSE) estimate of the PHN. Adaptive schemes are also presented using the least-mean-square (LMS) algorithm and recursive-least-square (RLS) algorithm. Simulations of a 64-QAM receiver show that the proposed method can improve the receiver performance significantly.

A fully integrated frequency synthesizer that generates multiple frequencies for use in frequency channelized receivers is designed in 0.25 /spl mu/m CMOS technology. Many of the unique features of this receiver have been exploited to design a highly integrated and power efficient multi-output frequency synthesizer, including poly-phase filters. The synthesizer generates 4, 5, 6, and 7 GHz signals while dissipating 120 mW.

This paper analyzes the performance of a direct-conversion receiver (DCR) with ac coupling in the presence of dc-offset and 1/f noise. The performance metric employed is the SNR after the digital signal processing, as it is ultimately the most relevant measure of performance. The ac coupling, which is employed to overcome the dc-offset noise, introduces intersymbol interference (ISI), whose effects can be effectively mitigated using an equalizer. Similarly, the equalizer can also be used to mitigate the 1/f noise, which is equivalent in its effect to ISI. Our analysis shows that the performance of the ac-coupled DCR is much more sensitive to the 1/f noise compared to the ac-coupling corner frequency. This suggests that minimizing the 1/f rolloff frequency is essential for achieving high performance direct-conversion reception.