A time domain carrier frequency offset estimation method for OFDM systems

The estimation of carrier frequency offset (CFO) is an important issue in the study of the orthogonal frequency division multiplexing (OFDM) systems. In the past, many CFO estimation methods have been proposed. In this paper, we propose a new blind CFO estimation for OFDM systems based on the so-called remodulated received vectors [8]. The CFO estimate is given by a closed form formula. The proposed method has very low complexity and its performance is robust to different modulation symbols and the presence of virtual carriers.

Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems; however, none of the existing methods takes into account the effect of synchronization errors such as carrier frequency offset (CFO). In general, CFO can significantly degrade the channel estimation performance of orthogonal frequency division multiplexing (OFDM) systems. Motivated by this, we investigate the effect of CFO on channel estimation for RIS-aided OFDM systems. Furthermore, we propose a joint CFO and channel impulse response (CIR) estimation method for these systems. Simulation results demonstrate the effectiveness of our proposed method, and also demonstrate that the use of time-domain rather than frequency-domain estimation in this context results in an improvement in the mean-squared error (MSE) performance of channel estimation as well as in a significantly lower overall computational complexity.

Hardware impairments effects on Massive MIMO system's capacity were investigated and seem to vanish asymptotically at the base station when equipped with a larger array. Surprisingly, the effect of the local oscillator (LO) phase noise does not strictly obey the same law as the additive noise when a common LO is utilized. Having a close look at large array base station utilizing OFDM signaling, one would expect that the sampling rate and carrier frequency offsets (SRO and CFO) to introduce similar effects as the phase noise due to the time (subcarriers and OFDM symbols indices) dependence of the channel vector's phase terms. For practical reasons, we use simulation to investigate the effect of such offsets on massive MIMO utilizing low computational complexity precoding techniques such as conjugate beamforming (CBF) and zero forcing beamforming (ZFBF). A reduced computational complexity ZFBF utilizing polynomial expansion technique is considered to assess sensitivity to such offsets. The simulation results show that without accurate compensation or calibration methods, the effect of sampling rate and carrier frequency offsets is very dramatic on massive MIMO performance. Increasing the array size does not provide an economically viable solution to alleviate the negative effects of such offsets.

The greatest threat to the OFDM system is the loss of orthogonality between subcarriers due to the carrier frequency offset (CFO) which results in significant performance degradation. In addition to this last problem was the effect of propagation over multipath fading channel. Hence, both the channel and the CFO need to be estimated and corrected at the receiver for subsequent symbol detection. A new joint semi-blind CFO and channel estimation methods for OFDM systems based on maximum-likelihood (ML) is investigated in this paper. The proposed algorithm is based on virtual subcarriers (VSCs) and on a new design of pilot patterns in OFDM blocks. The simulation results are given to verify the validity of the proposed methods.

In this paper, a blind carrier frequency offset (CFO) estimation method for multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is proposed. The proposed method is based on minimizing the power difference between all subcarriers in two consecutive space-time coding (STC) blocks. The cost function has a simple closed-form expression and the CFO can be estimated accurately using only three trial values. The performance of the proposed estimator is assessed via Monte Carlo simulation. Simulation results illustrate the superior performance of the proposed scheme for MIMO-OFDM systems when compared with other blind techniques.

In uplink orthogonal frequency division multiple access (OFDMA), carrier frequency offsets (CFO) and/or timing offsets (TO) of other users with respect to a desired user can cause significant multiuser interference (MUI). In this paper, we derive analytical bit error rate (BER) expressions that quantify the degradation of BER due to the combined effect of both CFOs as well as TOs; such an analytical BER derivation has not been reported so far for uplink OFDMA in the presence of CFOs and TOs. For the case when the desired user is perfectly frequency/time aligned (and other users have non-zero CFOs/TOs), we obtain an exact closed-form expression for the BER. For the case when the desired user also has non-zero CFO/TO, we obtain an approximate BER expression involving a single integral. Analytical and simulation results are shown to match quite well.

In the cooperative relay system, different frames from different relays are not aligned in the time domain, and have different carrier frequency offsets (CFOs). Estimation of these timing offsets and CFOs is a crucial and challenging task. In this study, a new training structure is proposed, and a novel time and frequency synchronisation scheme is presented for orthogonal frequency division multiplexing-based (OFDM-based) cooperative systems. The coarse time synchronisation is accomplished by using the symmetric conjugate of the training symbol and the fine time synchronisation is accomplished by segment-moving correlation. The fractional frequency offset is estimated by using the phase difference of the received signal and the integral frequency offset is estimated by utilising the good autocorrelation of the training symbol in frequency domain. The analysis and the simulation results show that, compared with the traditional scheme, the proposed scheme has better timing and frequency offset estimation performance and lower complexity for OFDM-based cooperative systems.

Aimed at addressing the problem of carrier synchronization for satellite-based Automatic Identification System (AIS) signals, a novel data-aided carrier frequency offset estimation method in the intermediate frequency is proposed in this paper. AIS signals use Gaussian Minimum Shift Keying (GMSK) for transmission, and a nonlinearity of the GMSK signal is shown to be a sine wave with frequency related to the carrier frequency offset. Based on that, this method constructs an auxiliary function with the available symbols to avoid the influence of the modulated phase information, and it estimates the frequency offset due to Doppler shift with a new interpolated FFT method. Moreover, this method performs better when the signals are filtered by band pass filter even through the bandwidth is as low as the 1/3 nominal bandwidth. Computer simulations are used to assess the synchronizer performance on AWGN channels.

A novel blind carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM) systems using constant modulus constellations is proposed in this study. CFO is estimated by minimizing a hybrid cost function which is formulated using properties of the covariance matrix and the magnitude of two nearby OFDM symbols. The performance of the proposed method is compared with that of the conventional estimation techniques under noisy time varying multipath channels. The performance comparison for different Doppler frequencies is also investigated. The superiority in performance of the proposed method over conventional methods is illustrated based on Monte Carlo simulations.

A self-cancellation scheme is proposed to cope with the sample frequency offset (SFO) problem in OFDM systems in the presence of a carrier frequency offset (CFO). Making use of the symmetry between the phase shifts caused by SFO and the subcarrier index, we put the same constellation symbol on symmetrical subcarriers, and combine the pairs at the receiver coherently. In this way, the SFO effects are approximately cancelled with the price of cutting down the bandwidth efficiency by half. However some array gain and diversity gain are obtained from the symmetrical combining. Our scheme can work well together with the phase tracking for residual CFO, so that both SFO and residual CFO can be removed with low complexity. Simulations show that, our scheme effectively removes the effect of SFO; the proposed system outperforms the ideal normal OFDM systems (with no SFO) under the same energy efficiency at high SNR, so the proposed system will also outperform the normal system that using the same overhead for SFO estimation. Finally, a mixed system is proposed to mitigate the drawbacks of our design and the normal OFDM systems for the SFO compensation. Our scheme may be helpful for the synchronization of multiple SFOs in the cooperative transmission.

In this paper, we propose a novel pilot-aided joint carrier frequency offset (CFO) and channel estimation method for orthogonal frequency division multiple access (OFDMA) uplink systems operating in doubly-selective fading environments. The method makes use of Bernstein basis polynomials (BBP) for capturing the time variations of the channel. By representing the channel in terms of basis functions, we need to track only the slowly varying basis expansion coefficients instead of the actual channel impulse response. The exact solution to this problem requires a multidimensional search which is highly computationally complex. Our proposed method makes use of space alternating generalized expectation maximization (SAGE) algorithm which replaces the multidimensional search with many one dimensional searches. Hence it is suitable practical implementation like mobile wireless communication. Simulation studies demonstrate that the proposed method gives excellent performance even at high mobile velocities.

In this study, a blind carrier frequency offset (CFO) estimation method is proposed using the time-frequency symmetry of the transmitted signals of a weighted Fourier transform (WFrFT) communication system. Blind CFO estimation is achieved by focusing on the property that results in matching the signal waveforms before and after the Fourier transform when the WFrFT parameter is set to a certain value. Numerical simulations confirm that the proposed method is more resistant to Rayleigh fading than the conventional estimation methods.

In this paper, we study the joint estimation of inphase and quadrature-phase (I/Q) imbalance, carrier frequency offset (CFO), and channel response for multiple-input multipleoutput (MIMO) orthogonal frequency division multiplexing (OFDM) systems using training sequences. A new concept called channel residual energy (CRE) is introduced. We show that by minimizing the CRE, we can jointly estimate the I/Q imbalance and CFO without knowing the channel response. The proposed method needs only one OFDM block for training and the training symbols can be arbitrary. Moreover when the training block consists of two repeated sequences, a low complexity two-step approach is proposed to solve the joint estimation problem. Simulation results show that the mean-squared error (MSE) of the proposed method is close to the Cramer-Rao bound (CRB).

In this paper, we study carrier frequency offset (CFO) and symbol timing offset (STO) estimation in the uplink of multiuser offset QAM filter bank multicarrier (FBMC) communication systems. A low-complexity frequency-domain CFO estimator using periodical training sequence is proposed. Also a good estimate of STO is obtained by maximizing the energy of subcarriers subject to training sequence at the output of analysis filter bank. Furthermore we derive the theoretical MSE for the proposed CFO estimator. Computer simulations show that the derived MSE matches the simulated MSE closely. Compared with state-of-the-art time domain estimator, the proposed estimator achieves better performance with a lower computational complexity.

As a critical technology of 5G air interface waveform, filtered orthogonal frequency division multiplexing (F-OFDM) not only inherits the technical advantages of OFDM, but also has outstanding advantages in system flexibility and spectrum efficiency. However, as a multi-carrier technology, it is still extremely sensitive to sample timing offset (STO) and carrier frequency offset (CFO). In this letter, an improved Park frequency domain training sequence (FS-Park) is proposed to complete STO and CFO estimation of F-OFDM system. Firstly, a real-value pseudorandom number (PN) sequence is sent to each subcarrier as training sequence in frequency domain, the corresponding time domain training symbol has a conjugate symmetry structure. Secondly, the training symbol is utilized for timing synchronization, then the fractional frequency offset is estimated based on the cyclic prefix in time domain. Finally, the integer frequency offset is estimated in frequency domain based on the auto-correlation of PN sequence. The simulation results illustrate that the FS-Park algorithm not only has a single pulse timing metric curve and great STO estimation accuracy, but also has better performance of CFO estimation than classical Park algorithm and Liang Xiao’s method.