Time and Frequency Synchronisation in 4G OFDM Systems

We consider joint estimation of carrier frequency offset and channel impulse response (CIR) for orthogonal frequency division multiplexing (OFDM) systems with pilot symbols and virtual subcarriers (VCs). We derive the receive-signal correlation structure due to the pilots and VCs, give the evidence of joint multivariate Gaussian distribution of the received samples, and derive an approximate maximum likelihood (ML) frequency offset estimator. We also derive the asymptotic mean-square error (MSE) and an approximate Cramer-Rao bound (CRB) and establish the asymptotic unbiasedness. Without pilots, in high signal-to-noise ratio, our estimator is equivalent to Liu and Tureli's estimator with Nv virtual carriers. When the pilot number (Np) is greater than the channel length L, our estimator acts as a subspace-based estimator with Nv + Np - L virtual carriers. A decision-directed joint ML estimator is derived to iteratively update the estimates of frequency offset, data symbols and CIR. The optimal pilot and virtual carrier placement strategies are also discussed. The resulting decision-directed joint estimator performs within 0.8 dB of the ideal case even when the frequency offset is as large as 20%

Enabling bistatic radar sensing within the context of integrated sensing and communication (ISAC) for future sixth-generation (6G) mobile networks demands strict synchronization accuracy, which is particularly challenging to be achieved with over-the-air (OTA) synchronization. Existing algorithms handle time and frequency offsets adequately but provide insufficiently accurate sampling frequency offset (SFO) estimates that result in the degradation of obtained radar images in the form of signal-to-noise ratio loss and migration of range and Doppler shift. This article introduces an SFO estimation algorithm named tilt inference of time offset (TITO) for orthogonal frequency-division multiplexing (OFDM)-based ISAC. Using available pilot subcarriers, TITO obtains channel impulse response (CIR) estimates and extracts information on the SFO-induced delay migration to a dominant reference path with constant range, Doppler shift, and angle between transmit and receive ISAC nodes. TITO then adaptively selects the delay estimates that are only negligibly impaired by SFO-induced intersymbol interference (ISI), ultimately employing them to estimate the SFO. Assuming a scenario without a direct line of sight (LoS) between the aforementioned transmitting and receiving ISAC nodes, a system concept with a relay reflective intelligent surface (RIS) that is used to create the aforementioned reference path is proposed. Besides a mathematical derivation of accuracy bounds, simulation and measurements at 26.2 GHz are presented to demonstrate TITO’s superiority over existing methods in terms of SFO estimation accuracy and robustness.

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.

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).

A successive interference cancellation (SIC)-based weighted least-squares (WLS) estimation for the carrier frequency offset (CFO) and the sampling frequency offset (SFO) is presented for wireless local area networks (WLANs) based on orthogonal frequency division multiplexing (OFDM). The proposed SIC-based WLS performs the estimation by exploiting the phase rotation in the frequency domain caused by the CFO and the SFO. SIC-based WLS estimates the CFO and the SFO successively instead of by traditional simultaneous estimation. The estimation of CFO based on the Taylor series is performed first, and then the WLS estimation of SFO based on successive cancellation of the CFO is carried out. The simulation results show that the SIC-based WLS can estimate the CFO and the SFO effectively. Compared to the WLS scheme, a performance improvement of more than 0.6 dB is achieved by SIC-based WLS, and nearly 10 percent of the complexity is reduced.

We study impacts of frequency and time offsets on cooperative multi-user MIMO-OFDM systems. In such systems, frequency offsets cause multi-user interference in addition to the inter-carrier interference effects typically seen in traditional MIMO-OFDM systems. Also, the impact of time offsets is more severe since the time offsets are larger due to transmitter synchronization imperfections and different propagation delays from the transmitters to the receivers. We derive an expression for the SINR seen at the receiver, showing especially how frequency offsets rotate the equivalent channel, thereby causing precoding imperfections. We simulate the interference impacts in the context of LTE-Advanced with realistic assumptions. Simulation results clearly show that the impacts of time and frequency offsets are more severe in cooperative MIMO-OFDM systems than in traditional MIMO-OFDM systems.

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.

We address the impact, estimation and compensation of time and frequency offsets in LTE CoMP. In LTE CoMP, transmissions may come from a different transmission point in every subframe of one millisecond. Due to propagation delay differences and time-frequency synchronization imperfections between the transmission points, the user equipment (UE) receiver is thus exposed to different time- frequency offsets in every subframe. In this paper we illustrate both analytically and numerically the impact of these time and frequency offsets on channel estimation performance and finally on LTE CoMP link-level demodulation performance. Furthermore, we study the applicability of existing LTE reference signals to the time-frequency offset estimation problem. In particular we compare two approaches in which the UE is either aware or unaware of the exact transmission point. Finally, we show with LTE link-level simulations that using the proposed approaches the impacts of time-frequency offsets can be almost perfectly compensated.

The estimation of carrier and sampling frequency offsets is considered, for IEEE 802.11a-based OFDM wireless LAN (WLAN) systems, based on the guard interval and two long symbols (GI2L) in the preamble of an OFDM WLAN packet. The model of the measurement of the GI2L is developed, in the presence of both carrier and sampling frequency offsets. Based on this model, a method is proposed, based on the GI2L. Improved performance, measured by estimation error and bit error rate, is achieved by the proposed method, as compared with some relevant existing methods.

This work explores amplify-and-forward (AF) two-way relay networks (TWRNs) working under flat-fading non-reciprocal channels conditions in the presence of both timing and frequency offsets. We showcase a novel pilot-based maximum likelihood estimator for the joint channel and carrier frequency offsets (CFOs), assuming the timing offsets are known. The proposed estimator has reasonable complexity, and we show that it meets the Cramer-Rao bound (CRB) for our model.

In this letter, we propose and experimentally investigate a training-aided iterative frequency offset estimation (IFOE) method, which can track dynamic frequency offset (FO) drift in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. In contrast to existing FO estimation algorithms that compute specific FO values, in IFOE, only the sign value of FO is judged and recorded without any phase calculation. The estimated FO is updated once for every data block based on FO signs obtained from multiple previous blocks, which helps combat noise and allows the shortening of the employed training symbol. We experimentally investigate the performance of IFOE in a 160-km CO-OFDM system. The results show that IFOE achieves superior bit error rate performance to a one-time FO estimator (without FO tracking) and approaches the performance of multiple separate FO estimators that use longer training symbols.

We evaluate the performance improvement in orthogonal frequency-division multiplex access (OFDMA) achievable with cooperative relaying in the presence of frequency offsets. The relays can operate in either the amplify-and-forward (AF) or decode-and-forward (DF) mode. In each transmission, node S has M relays when transmitting its own signal, and it also helps the other M relays transmit their signals. The total power used to transmit each symbol, including the power consumed in S and the relays, is kept constant. The outage information rates of the proposed cooperative transmission scheme are first derived. The performance improvement in the frequency offset estimation by using cooperative relay is then analyzed. Channel estimation in a cooperative OFDMA network in the presence of frequency offsets is also evaluated, and the pairwise error probability (PEP) of orthogonal space-time coding in cooperative OFDMA due to both the frequency offset and channel estimation errors is derived. Numerical results illustrate the superior performance of the proposed scheme over the conventional transmission with regard to outage information rate, frequency offset estimation error and the PEP.

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.

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.

We design a new kind of fractional Fourier transform superimposed training sequence (TS) to simultaneously estimate linear distortions including chromatic dispersion (CD), timing offset (TO), and frequency offset (FO), etc. Without sacrificing additional spectrum efficiency, the scheme can reduce the computational complexity sharply compared to a regular estimation method. The feasibility of the proposed scheme is verified by simulations of 28 GBaud dual polarization quadrature phase-shift keying (DP-QSPK) and 16-ary quadrature amplitude modulation (DP-16 QAM) system. Simulation results show that the superimposed TS has negligible negative effects on the transmission performance considering 7% forward error correction while the TO, FO, and rough CD estimation perform well after a long distance transmission. The max TO estimation (TOE) errors are, respectively, eight samples and 12 samples for QPSK and 16 QAM, and the max FO estimation errors are, respectively, 5.7 and 3.6 MHz for QPSK and 16 QAM. The rough CD estimation (CDE) error is below 946 ps/nm. The TOE and rough CDE separately decrease the complexity of frame synchronization and CDE. In total, the computation complexity of the estimations decreases by 91.8% compared to a regular blind estimation method.