Joint Estimation of Carrier Frequency and Phase Offset Based on Pilot Symbols in Quasi-Constant Envelope OFDM Satellite Systems

Spectral efficiency and energy efficiency are two important performance indicators of satellite systems. The Quasi-Constant Envelope Orthogonal Frequency Division Multiplexing(QCE-OFDM) technique can achieve both high spectral efficiency and low peak-to-average power ratio(PAPR). Therefore, the QCE-OFDM technique is considered as a promising candidate multi-carrier technique for satellite systems. However, the Doppler effect will cause the carrier frequency offset(CFO), and the non-ideal oscillator will cause the carrier phase offset(CPO) in satellite systems. The CFO and CPO will further result in the bit-error-rate(BER) performance degradation. Hence, it is important to estimate and compensate the CFO and CPO. This paper analyzes the effects of both CFO and CPO in QCE-OFDM satellite systems. Furthermore, we propose a joint CFO and CPO estimation method based on the pilot symbols in the frequency domain. In addition, the optimal pilot symbol structure with different pilot overheads is designed according to the minimum Cramer-Rao bound(CRB) criterion. Simulation results show that the estimation accuracy of the proposed method is close to the CRB.

Polynomial rooting based frequency offset estimation for MIMO OFDM systems

Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） systems is extensively investigated. By designing the training sequences to meet certain conditions and exploiting the Hermitian and real symmetric properties of the corresponding matrices, it is found that the roots of the polynomials corresponding to the cost functions are pairwise and that both meger CFO and fractional CFO can be estimated by the direct polynomial rooting approach. By analyzing the polynomials corresponding to the cost functions and their derivatives, it is shown that they have a common polynomial factor and the former can be expressed in a quadratic form of the common polynomial factor. Analytical results further reveal that the derivative polynomial rooting approach is equivalent to the direct one in estimation at the same signal-to-noise ratio（SNR） value and that the latter is superior to the former in complexity. Simulation results agree well with analytical results.

Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

Efficient integer frequency offset estimation for OFDM systems

An efficient scheme of integer frequency offset estimate for orthogonal frequency division multiplexing （OFDM） systems is proposed based on a training symbol with several identicalparts. In this scheme, the received training symbol is first reshaped into several sub-symbols.It shows that the reshaping process in-troduees time diversity multiplexing.After a special fast Fourier transform （FFT） algorithm is applied to the sub-symbol,the integer frequency is estimated by finding the maximum magnitude of the resulting fre-quency domain signal.To improve the estimate performance,diversity combining methods are presented to makefull use of the multiple frequency domain sub-symbols.Compared to the traditional scheme, theproposed one has an improved estimate performance demonstrated by the computation simulation, while maintaining a very low complexity.

ESTIMATION OF CARRIER FREQUENCY OFFSETS FOR MIMO SYSTEMS WITH DISTRIBUTED TRANSMIT ANTENNAS

The problem of estimating the carrier frequency offsets in Multiple-Input Multiple-Output (MIMO) systems with distributed transmit antennas is addressed. It is supposed that the transmit antennas are distributed while the receive antennas are still centralized, and the general case where both the time delays and the frequency offsets are possibly different for each transmit antenna is considered. The channel is supposed to be frequency flat, and the macroscopic fading is also taken into consideration. A carrier frequency offset estimator based on Maximum Likelihood (ML) is proposed, which can separately estimate the frequency offset for each transmit antenna and exploit the spatial diversity. The Cramer-Rao Bound (CRB) for synchronous MIMO (i.e., the time delays for each transmit antenna are all equal) is also derived. Simulation results are given to illustrate the per- formance of the estimator and compare it with the CRB. It is shown that the estimator can provide satisfactory frequency offset estimates and its performance is close to the CRB for the Signal-to-Noise Ratio (SNR) below 20dB.

Fractional Frequency Offset Estimation for OFDM Systems in Non-Cooperative Communication

The traditional fractional frequency offset(FFO) estimation schemes for orthogonal frequency division multiplexing(OFDM) in non-cooperative communication have the problems of susceptible performance with the frequency offset values and the number of OFDM symbols,a novel fractional frequency offset blind estimation scheme based on EKF for OFDM systems is conceived.The nonlinear function of the frequency offset is calculated by employing the correlation.And then the frequency offset is estimated by means of the iterative algorithm of EKF.The finally fractional frequency offset is estimated by adopting repeated the above process.Simulation results demonstrate that the proposed scheme is robust to the frequency offset values without any requirements of a prior knowledge.

Improved dichotomous search frequency offset estimator for burst-mode continuous phase modulation

A data-aided technique for cartier frequency offset estimation with continuous phase modulation （CPM） in burst- mode transmission is presented. The proposed technique first exploits a special pilot sequence, or training sequence, to form a sinusoidal waveform. Then, an improved dichotomous search frequency offset estimator is introduced to determine the frequency offset using the sinusoid. Theoretical analysis and simulation results indicate that our estimator is noteworthy in the following aspects. First, the estimator can operate independently of timing recovery. Second, it has relatively low outlier, i.e., the minimum signal-to-noise ratio （SNR） required to guarantee estimation accuracy. Finally, the most important property is that our estimator is complexity-reduced compared to the existing dichotomous search methods： it eliminates the need for fast Fourier transform （FFT） and modulation removal, and exhibits faster convergence rate without accuracy degradation.

Data-Aided Frequency Offset Estimation with Narrowband Interference

An algorithm for carrier frequency offset estimation with narrowband interference in burstmode transmissions is proposed.The algorithm is data-aided and has a feedforward structure that can be easily implemented digitally.The principle of the algorithm is based on a properly designed training sequence and an interpolation technique.Simulation results indicate that the estimation range is about ±20% of the symbol rate.The performance is satisfactory for a signal-to-noise ratio（SNR）as low as -13 dB and the mean square error（MSE）is approximately irrelevant to signal-to-interference ratio（SIR）values over -20 dB.

Particle filter for joint frequency offset and channel estimation in MIMO-OFDM systems

A particle filter is proposed to perform joint estimation of the carrier frequency offset （CFO） and the channel in multiple-input multiple-output orthogonal frequency division multiplexing （MIMO-OFDM） wireless communication systems. It marginalizes out the channel parameters from the sampling space in sequential importance sampling （SIS）, and propagates them with the Kalman filter. Then the importance weights of the CFO particles are evaluated according to the imaginary part of the error between measurement and estimation. The varieties of particles are maintained by sequential importance resampling （SIR）. Simulation results demonstrate this algorithm can estimate the CFO and the channel parameters with high accuracy. At the same time, some robustness is kept when the channel model has small variations.

An iterative interference cancellation based frequency offset estimation method for OFDMA uplink systems

In this paper, Moose scheme is used for frequency offset estimation in OFDMA uplink svstems due to that the signals from different users can be easily distinguished in frequency domain. However, differential multiple access interference （MAI） will deteriorate the frequency offset estimation performances, especially in interleaved OFDMA system. Analysis and simulation results manifest that frequency offset estimation by Moose scheme in block OFDMA system is more robust than that in interleaved OFDMA systern. And an iterative interference cancellation method has been proposed to suppress the differential MAI interference for interleaved OFDMA system, in which Moose scheme is the special case of the number of iteration is equal to one. Simulation results demonstrate that the proposed method can improve the performance with the increase of the number of iterations. In consideration of the performance and complexity, the proposed method with two iterations is selected. And the full comparison results of the proposed iterative method with two iterations and that with one iteration （conventional Moose scheme） are given in the paper, which sufficiently demonstrate that the performance gain can be obtained by the interference cancellation operation in interleaved OFDMA system.

A FREQUENCY OFFSET ESTIMATION ALGORITHM FOR OFDM SYSTEMS

A new fine carrier frequency offset estimation algorithm in Orthogonal Frequency Division Multiplexing (OFDM) system is proposed. The correlation item is the training sequence instead of the received signal in the new algorithm. Simulation results show that the performance of the new algo- rithm is 4dB-9dB better than that of Schmidl's algorithm. Coarse frequency offset estimation is also discussed in this paper, which is the improvement of Zhang's method. The estimation range using the improvement method is twice as that using the Zhang's method. Based on the hardware of the receiver and the improved algorithm, a method using Fast Fourier Transform (FFT) is proposed to implement the coarse frequency estimation. The chip area of OFDM system can be reduced by using the proposed method.

JOINT ESTIMATION OF CARRIER FREQUENCY OFFSET AND POWER DELAY PROFILE FOR MIMO-OFDM SYSTEMS

This paper develops a Cyclic Prefix(CP)based joint Maximum-Likelihood(ML)estima-tion algorithm of Carrier Frequency Offset(CFO)and Power Delay Profile(PDP)for Multi-InputMulti-Output Orthogonal Frequency Division Multiplexing(MIMO-OFDM)systems.However,theexact solution of the joint ML estimation is very complex since it needs a search over amulti-dimensional domain.Thus a simplified method is proposed to estimate the CFO and the PDPiteratively via the alternating-projection method which could induce the multidimensional searchproblem to a sequence of simple one-dimensional searches.Simulations show that the proposed algo-rithm is more accurate and robust than the existing algorithms.

Deep learning based Doppler frequency offset estimation for 5G-NR downlink in HSR scenario

In the fifth-generation new radio(5G-NR) high-speed railway(HSR) downlink,a deep learning(DL) based Doppler frequency offset(DFO) estimation scheme is proposed by using the back propagation neural network(BPNN).The proposed method mainly includes pre-training,training,and estimation phases,where the pre-training and training belong to the off-line stage,and the estimation is the online stage.To reduce the performance loss caused by the random initialization,the pre-training method is employed to acquire a desirable initialization,which is used as the initial parameters of the training phase.Moreover,the initial DFO estimation is used as input along with the received pilots to further improve the estimation accuracy.Different from the training phase,the initial DFO estimation in pre-training phase is obtained by the data and pilot symbols.Simulation results show that the mean squared error(MSE) performance of the proposed method is better than those of the available algorithms,and it has acceptable computational complexity.

A high performance frequency offset estimator for OFDM

This paper proposes a simple method to enlarge the estimation range of conventional carrier frequency offset (CFO) estimation methods based on correlations among the identical parts of the preamble. A novel preamble is designed, which is composed of one regular OFDM training block with even numbers of identical parts and one irregular OFDM training block with odd numbers of identical parts. The initial estimates obtained over the two training blocks are next exploited to jointly estimate the CFO. By elaborately selecting the numbers of identical parts for the two training blocks, the proposed CFO estimator can estimate frequency offset over tens of the subcarrier spacing. Simulation results showed that the proposed CFO estimator satisfies the estimate range requirement for the practical OFDM systems, while achieving a very good estimate performance.

Modulation Recognition with Frequency Offset and Phase Offset over Multipath Channels

Modulation recognition becomes unreliable at low signal-to-noise ratio(SNR)over fading channel.A novel method is proposed to recognize the digital modulated signals with frequency and phase offsets over multi-path fading channels in this paper.This method can overcome the effects of phase offset,Gaussian noise and multi-path fading.To achieve this,firstly,the characteristic parameters search is constructed based on the cyclostationarity of received signals,to overcome the phase offset,Gaussian white noise,and influence caused by multi-path fading.Then,the carrier frequency of the received signal is estimated,and the maximum characteristic parameter is searched around the integer multiple carriers and their vicinities.Finally,the modulation types of the received signal with frequency and phase offsets are classified using decision thresholds.Simulation results demonstrate that the performance of the proposed method is better than the traditional methods when SNR is over 5dB,and that the proposed method is robust to frequency and phase offsets over multipath channels.

Decoupled estimation of frequency-dependent IQI and channel for OFDM systems with direct-conversion transceivers

The in-phase and quadrature-phase imbalance (IQI) is one of the major radio frequency impairments existing in orthogonal frequency division multiplexing (OFDM) systems with direct-conversion transceivers. During the transmission of the communication signal, the impact of IQI is coupled with channel impulse responses (CIR), which makes the traditional channel estimation schemes ineffective. A decoupled estimation scheme is proposed to separately estimate the frequency-dependent IQI and wireless channel. Firstly, the generalized channel model is built to separate the parameters of IQI and wireless channel. Then an iterative estimation scheme of frequency-dependent IQI is designed at the initial stage of communication. Finally, based on the estimation result of IQI, the least square algorithm is utilized to estimate the channel-related parameters at each time of channel variation. Compared with the joint estimation schemes of IQI and channel, the proposed decoupled estimation scheme requires much lower training overhead at each time of channel variation. Simulation results demonstrate the good estimation performance of the proposed scheme.

Blind estimation of phase offset in OFDM subcarrier for coherent demodulation

An adaptive algorithm named low complexity phase off- set estimation （LC-POE） is proposed for orthogonal frequency division multiplexing （OFDM） signals. Depending on the requirement, the estimation procedure is divided into several scales to accelerate the adaptive convergence speed and ensure the estimation accuracy. The true phase offset is estimated through shrinking the detection range and raising the resolution scale step by step. Both the convergence performance and complexity are discussed in the paper. Simulation results show the effectiveness of the proposed algorithm. The LC-POE algorithm is promising in the application of OFDM systems.

Bayesian integer frequency offset estimator for MIMO-OFDM systems

Carrier frequency offset （CFO） in MIMO-OFDM systems can be decoupled into two parts： fraction frequency offset （FFO） and integer frequency offset （IFO）. The problem of IFO estimation is addressed and a new IFO estimator based on the Bayesian philosophy is proposed. Also, it is shown that the Bayesian IFO estimator is optimal among all the IFO estimators. Furthermore, the Bayesian estimator can take advantage of oversampling so that better performance can be obtained. Finally, numerical results show the optimality of the Bayesian estimator and validate the theoretical analysis.

A Novel Two-step Frequency Offset Estimator for OFDM

Based on an orthogonal frequency division multiplexing(OFDM) training symbol with L identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems. The CFO is estimated in two steps, fine estimate and coarse estimate. In the first step, the fine estimation is performed based on the principle of minimum variance. However, the fine estimation has ambiguity since its estimate range is limited. In the second step, the coarse estimation is obtained, which results in a larger estimate range but less precision. Using the coarse estimation, the ambiguity of fine estimation is resolved. To fully use the correlation among L identical parts, the fine estimation resolved the ambiguity and the coarse estimation are optimally combined to obtain the final estimation. Furthermore, the estimation variance of the proposed method is derived. Simulation results demonstrate that the novel two-step estimator outperforms the conventional two-step estimator in terms of estimate performance and computational complexity.

A NOVEL INTEGER FREQUENCY OFFSET ESTIMATOR FOR OFDM

One of the principal disadvantages of Orthogonal Frequency Division Multiplexing (OFDM) is very sensitive to carrier frequency offset. The integer frequency offset has no effect on the orthogonality among the subcarriers, but it causes a circular shift and phase rotation of the received data symbols sequence, resulting in a Bit Error Rate(BER) of 0.5. In this paper,a novel integer frequency offset estimator for OFDM is derived based on maximum likelihood estimation technique and exploration of the differential relation between two consecutive OFDM data symbol sequences in frequency domain. Its performance is compared with the conventional method by computer simulations for the additive white Gaussian noise channel and a multipath fading channel. Simulation results show that the performance of the proposed estimator is better than the conventional estimator.