Symbol synchronization and sampling frequency synchronization techniques in real-time DDO-OFDM systems

Analog-to-digital and digital-to-analog interfaces (ADIs and DAIs) constitute the essential link between the analog physical world and digital signal processing systems. As modern communication systems demand higher bandwidths,improved linearity, and increased energy efficiency, imperfections such as linear and nonlinear distortion and sampling errors increasingly limit achievable performance. Such imperfections require compensation techniques that are both effective and computationally efficient for high-speed, high-resolution implementations. This thesis contributes low-complexity solutions for linearization,equalization, and sampling-frequency synchronization, enabling efficient signal processing in high-speed data-conversion systems. Firstly, the design of low-complexity digital linearizers for ADIs is addressed. Several novel linearizers are introduced that are inspired by neuralnetwork architectures, but avoid the high training complexity associated with neural-network-based approaches. These linearizers can outperform classical linearizers, such as Wiener and Hammerstein, while requiring lower implementation complexity. The proposed designs cover both memoryless and memory (frequency-dependent) linearizers and are applicable to nonlinear distortion occurring either before or after sampling. All designs enable closed-form parameter estimation via matrix inversion, thereby eliminating the need for unpredictable iterative nonconvex optimization. In addition,an efficient memoryless linearizer based on 1-bit quantization is introduced,enabling lookup-table-based implementations with only one multiplication per corrected sample. Secondly, equalization of digital-to-analog converters (DACs) frequency response using linear-phase finite impulse response (FIR) filters is considered. For several DAC pulse shapes operating across multiple Nyquist bands,minimax-optimal equalizers are designed, and their properties are analyzed. Based on these designs, expressions for the required filter order are derived as explicit functions of bandwidth and target equalization accuracy, using symbolic regression followed by further refinement. The resulting expressions provide accurate order estimates across different pulse shapes and operating conditions. Thirdly, a low-complexity time-domain sampling frequency offset (SFO)estimation and compensation framework based on the Farrow structure for interpolation is presented. By reusing the Farrow structure already employed for SFO compensation, the proposed approach enables a unified estimation and compensation architecture with significantly reduced overall implementation complexity. The method operates on arbitrary bandlimited signals, supports joint estimation of SFO and sampling time offset, and allows estimation using only a single component (real or imaginary) of a complex signal. A Newton-based estimator exploiting the structure of the problem is developed to reduce computational complexity, while an alternative iterative least-squares-based design provides an even lower-complexity solution. The resulting estimators are robust to other synchronization errors and are well suited for practical receiver implementations. In addition, motivated by the appearance of low-order time-index-powered sums in the Farrow-based formulation, a general cascaded-accumulator framework is developed as a supplementary contribution, enabling efficient causal computation of time-index-powered weighted sums of arbitrary order without data buffering and reducing the multiplicative complexity from order K N to only K+1 constant multiplications (where N is the number of terms and K is the power in the sum), which is applicable both to SFO estimators and to other signal processing applications beyond the SFO problem.

A data clipping and normalization technique is employed to improve the performance of the overall direct detection optical orthogonal frequency division multiplexing (DCO-OFDM) system. A detailed analysis of clipping distortion introduced by digital clipping and normalization is provided. The normalization operation amplifies the clipped data signal to the maximum input amplitude of a digital-to-analog converter (DAC). Based on the analysis, a BER formula of the proposed scheme is derived over the AWGN channel and single fiber channel. Performance of an optical clipped OFDM with normalization is assessed through numerical simulations and Monte Claro simulation over the AWGN channel. Theoretical analysis and simulation results both show that the clipping and normalization scheme can greatly improve the BER of an optical OFDM. In particular, BER performance of the proposed transmission scheme was measured in a practical OFDM transmission platform. The measured experimental results show that the clipped and amplified OFDM signal exhibits superior performance in comparison with the conventional OFDM signal. The received sensitivity at a BER of 10−3 for a 4 Gsamples/s (2.6667 Gbits/s) clipped and normalized OFDM signal with clipping ratio of 4 after 100 km standard single-mode fiber (SMF) transmission was improved by 4.3 dB when compared with the conventional OFDM system. The measured results also showed that the clipped OFDM signal exhibits superior performance in comparison with the conventional OFDM signal. Therefore, a clipping and normalization at the transmitter is most effective, and a substantial performance improvement can be obtained by a simple normalization after clipping.

In orthogonal frequency division multiplexing (OFDM) systems, most of the conventional sampling frequency offset (SFO) estimation methods work under the assumption of time-invariant or slow time-variant channels. In mobile environment, the time-variant channel significantly degrades the accuracy of SFO estimation. To solve the problem, we first analyze the properties of time-variant channels. If terminal moves within some tens of the wavelength of radio frequency (RF) signal, channel path delay almost remains unchanged. For most practical OFDM systems, our analysis indicates that channel path delay can be regarded as unchanged during the interval of some tens of OFDM symbols in time-variant channels. Based on the analysis, we propose a novel SFO estimation method for pilot-aided OFDM systems. Different from the conventional methods, the proposed method estimates SFO by detecting the variation of the symbol timing error caused by SFO. The detection is finished by implementing correlation between the channel impulse responses (CIRs) estimated by different OFDM symbols. Performance of the proposed method is simulated and compared with that of two conventional post-FFT methods. Numerical results show that, the proposed SFO estimation method performs better than the conventional methods not only in time-variant channels, but also at low SNRs and large residual carrier frequency offsets (CFOs).

We propose a scheme for a direct-detection optical orthogonal frequency-division multiplexing (OFDM) system based on blockwise signal-phase-switching (SPS). Experimental demonstration of 61 Gbits/s SPS direct-detection optical OFDM signal transmission over 80 km standard single-mode-fiber was successfully achieved with single polarization and a single photodetector.

It is well known that the cyclic property of transmitted signal can be used to achieve joint frame and carrier frequency synchronization, while the uncompensated sampling frequency offset (SFO) would still be a problem. Based on the observation that the impact of SFO on the received cyclic block and its replica is equivalent to a relative time shift, a joint synchronization scheme solely based on cyclic property is proposed to achieve frame, sampling frequency and carrier frequency synchronization simultaneously. A two-Dimensional Sliding-Window Auto-Correlator (2D-SWAC) is presented to implement the joint synchronization with low complexity. The proposed scheme is suitable for any transmission system with similar cyclic property. Meanwhile, it is robust to large sampling and carrier frequency offset and strong channel frequency selectivity, as demonstrated by the analysis and simulations.

A multiband orthogonal frequency-division multiplexing (MB-OFDM) system, which is one of the effective modulation techniques that have been adopted for high-speed ultrawideband (UWB) systems, is very sensitive to sampling frequency offset (SFO) due to the mismatch between local oscillators at the transmitter and the receiver. In this paper, we propose an iterative SFO estimation method for a high-data-rate MB-OFDM UWB system to improve its SFO estimation accuracy in the case of a long transmission packet. The proposed method is an iterative process of 2-D SFO estimation across pilot subcarriers and consecutive OFDM symbols, together with joint channel estimation. Furthermore, we derive the Cramer-Rao lower bound (CRLB) for the proposed SFO estimation method. This CRLB can be used as a guide for algorithm design and to explore the theoretical limit. Our performance analysis and simulation results show that the proposed iterative SFO estimation method is both practical and effective.

A precise estimation and compensation of SFO (Sampling Frequency Offset) is an important issue in OFDM (Orthogonal Frequency Division Multiplexing) system, because sampling frequency mismatch between the transmitter and the receiver dramatically degrades the system performance due to the loss of orthogonality between the subcarriers. However, the conventional method causes serious performance degradation of SFO estimation in low SNR (Signal to Noise Ratio) or large Doppler frequency environment. Therefore, in this paper, we propose two SFO estimation methods which can achieve stable operation in low SNR and large Doppler frequency environment. The proposals for SFO estimation / compensation are mainly specialized on DVB (Digital Video Broadcasting) system, and we verified that the proposed method has good performance and stable operation through extensive simulation.

In this paper we investigate the problem of timing synchronization for a linearly modulated burst transmission scheme. It has been assumed that there is a linear variation in symbols' timing offset, which is caused by sampling frequency offset. Moreover, passing through an Additive White Gaussian Noise (AWGN) channel, corrupts the received burst signal and exerts a fixed timing offset to the transmitted sequence. Unlike classical techniques that the timing offset is assumed to vary slowly with time and, therefore, it is considered as a constant parameter over the entire burst, the more challenging problem is addressed in this contribution where timing offset variation from symbol to symbol is not negligible. A unified gradient-based optimization algorithm to estimate both the sampling frequency and delay offset is presented that iteratively converge to the Maximum Likelihood (ML) estimation. Bit Error Rate (BER) Simulation results are derived and compared with perfect synchronization. The results confirm the system's efficiency.

High speed transmission systems (> 10 Gb/s) for cost-sensitive applications such as metropolitan network have attracted extensive interest due to the explosive data traffic growth in such applications. Optical orthogonal frequency division multiplexing (OFDM) based on direct modulation and direct detection for single-mode fiber (SMF) and multi-mode fiber (MMF) without optical amplification and chromatic dispersion (CD) compensation was proposed. Recent research has also shown that optical OFDM can be used with electronic dispersion compensation using direct detection in SMF. However, laser frequency chirp has been identified as a key limiting factor of capacity-versus-reach performance. In this paper, we present a novel concept of low cost optical OFDM with direct modulation of distributed feedback (DFB) lasers and coherent detection at 51.4 Gb/s and 64 QAM. A comprehensive theoretical model of the proposed system is developed. The proposed optical OFDM system concept and performance is based upon using electronic precompensation of laser frequency response, and electronic post compensation of DFB laser frequency chirp and CD. A numerical simulation of the transmission performance of the aforementioned system is conducted using different fiber lengths (40 km, 60 km, 120 km) and chirp parameters, which shows its attractiveness for access and metro applications.

We investigate the estimation error, convergence speed, and computational complexity of the three commonly used sampling frequency offset (SFO) estimation algorithms based on training sequence (TS), cyclic prefix (CP), and pilot under different signal-to-noise ratios (SNRs) and received optical powers (ROPs) by numerical simulation and offline experiment in a short-reach direct-detection optical OFDM transmission system. The results showed that the pilot-based algorithm’s estimation accuracy (< 14 ppm) is relatively low for the initial SFOs in the range of ±200 ppm, while the estimation error of both TS-based and CP-based algorithms is stable within 0.6 ppm. Moreover, pilot-based and TS-based algorithms exhibit a faster convergence speed than the CP-based one. And the computational complexity of the SFO estimation algorithms based on CP, TS, and pilot decreases sequentially.

A precise estimation of SFO (Sampling Frequency Offset) is an important issue in OFDM (Orthogonal Frequency Division Multiplexing) system. However, the conventional method causes serious performance degradation of SFO estimation in low SNR (Signal to Noise Ratio) or large Doppler frequency environment. Therefore, in this paper, we propose a SFO estimation method which can achieve stable operation in low SNR and large Doppler frequency environment. The proposals for SFO estimation /compensation are mainly based on DVB (Digital Video Broadcasting) system, and we verified that the proposed method has a good performance and stable operation through extensive simulation.

A pilot-aided scheme is proposed for the joint estimation and tracking of channel impulse response (CIR), carrier frequency offset (CFO) and sampling frequency offset (SFO) in burst mode, multiple-input-multiple-output (MIMO), and orthogonal frequency division multiplexing(OFDM) systems. First, a received signal model that takes into account nonlinear CFO/SFO effects is formulated. Then, based on the derived signal model and the received multicarrier signal samples containing the pilot tones in the frequency domain, an objective function that includes MIMO CIR, CFO, and SFO is introduced to develop a vector recursive-least-square (RLS)-based joint channel estimation and synchronization algorithm. The analysis and simulation results show that, over the large ranges of the CFO and SFO values, the proposed estimation and tracking scheme offers fast convergence, high stability, and a near-optimum receiver performance that is remarkably close to the ideal performance in the case of perfect channel estimation and synchronization over quasi-static Rayleigh multipath fading channels.

We report >100-Gb/s direct-detection (DD) transmission using an integrated silicon optical receiver, which comprised a fully-differential 28-nm complementary metal-oxide-semiconductor (CMOS) transimpedance amplifier (TIA) wire-bonded to a Silicon-Germanium (SiGe) balanced photodiode (PD). The fully-differential TIA architecture enabled significant bit-error-rate (BER) and signal-to-noise ratio improvements over a single-output TIA design when introducing it to the DD transmission. We experimentally validated its effectiveness in both back-to-back (B2B) and 2-km long standard single-mode fibre (SSMF) links using 50/100-Gb/s signals, including Nyquist on-off keying (OOK), Nyquist 4-ary pulse amplitude modulation (PAM4), uniformly-loaded DD optical orthogonal frequency division multiplexing (DDO-OFDM) and adaptively-loaded DDO-OFDM. Furthermore, we demonstrate that the integrated optical receiver was capable of balancing the trade-off between its electrical bandwidth and transimpedance gain by simply adjusting a voltage supply to the TIA. Without the need for optical amplification and while keeping the BERs below the 7% forward error correction limit, up to 173.22-Gb/s and 139.86-Gb/s adaptively-loaded DDO-OFDM transmission was achieved for B2B and 2-km transmission, respectively. The demonstrated results highlight the potential of the integrated silicon optical receiver, fabricated using the standard CMOS process for high-speed and short-reach optical interconnects.

We propose an optical signal-to-noise ratio (OSNR) estimation method for direct-detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems by calculating the electrical SNR of one pilot subcarrier based on correlation. Simulation and experiment are conducted to verify this OSNR estimation method in a 15-Gb/s DDO-OFDM system. The maximum OSNR estimation error is 0.8 dB within an OSNR range of 8-28 dB for 100- and 200-km transmission distances.

In this paper, a residual frequency offset (RFO) and sampling frequency offset (SFO) estimator is proposed for ultra- wideband multi-band orthogonal frequency division multiplexing (UWB MB-OFDM) systems. The proposed scheme uses a time-domain spreaded data samples which is provided in MB-OFDM system. To demonstrate the efficiency of the proposed RFO and SFO estimator, comparisons are made with other existing estimator.