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.

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.

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.

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.

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.

Frequency offset estimation based on peak power ratio in LTE system

Orthogonal frequency division multiplexing （OFDM） is one of the key techniques for long term evolution （LTE） system. Frequency offset estimation of OFDM is an essential issue. Especially in the high-speed environment, the frequency offset will become large. Based on the features of LTE uplink physical random access channel （PRACH）, this paper proposes a new frequency offset algorithm by using peak power ratio to enlarge the range of frequency offset estimation. According to the relation between frequency offset and the power delay profile （PDP）, the ratio of the peak power of the PDP at the main window to that at the negative window or positive window is utilized to estimate frequency offset. Simulation results show that the new proposed algorithm extends the estimation range of frequency offset from 1 000 Hz to 1 250 Hz. Meanwhile the accuracy of frequency offset estimation is almost not lost. Particularly in low signal noise ratio （SNR）, the new algorithm has lower mean square error （MSE） compared with traditional phase differential algorithm.

Joint channel and carrier frequency offset estimation for multi-user MIMO-OFDM uplink transmissions

This article proposes a new algorithm of joint channel and carrier frequency-offset OCCFO） estimation for multi-user multi-input and multi-output orthogonal frequency division multiplexing （MIMO-OFDM） systems. A least square （LS） channel estimation and a carrier frequency offset （CFO） correlation estimation are combined in this contribution. CFOs are generally estimated using training sequences in a special synchronization timeslot. In this contribution, CFO estimation is further improved by taking advantages of channel estimation based on pilot symbols in traffic timeslots. The CFOs can be first obtained from the primary channel estimation. And then, with the knowledge of the CFOs estimated, channel estimation can be enhanced greatly. Computer simulation results indicate that the proposed JCCFO scheme is of good performance. Besides, the computational complexity is low.

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.

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.

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.

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.

Pseudo-noise preamble based joint frame and frequency synchronization algorithm in OFDM communication systems

Frame and frequency synchronization are essential for orthogonal frequency division multiplexing （OFDM） systems. The frame offset owing to incorrect start point position of the fast Fourier transform （FFT） window, and the carrier frequency offset （CFO） due to Doppler frequency shift or the frequency mismatch between the transmitter and receiver oscil ators, can bring severe inter-symbol interference （ISI） and inter-carrier interference （ICI） for the OFDM system. Relying on the relatively good correlation charac-teristic of the pseudo-noise （PN） sequence, a joint frame offset and normalized CFO estimation algorithm based on PN preamble in time domain is developed to realize the frame and frequency synchronization in the OFDM system. By comparison, the perfor-mances of the traditional algorithm and the improved algorithm are simulated under different conditions. The results indicate that the PN preamble based algorithm both in frame offset estimation and CFO estimation is more accurate, resource-saving and robust even under poor channel condition, such as low signal-to-noise ratio （SNR） and large normalized CFO.

Carrier frequency offset and impulse noise estimation for underwater acoustic orthogonal frequency division multiplexing

The carrier frequency offset（CFO）and impulse noise always affect the performance of underwater acoustic communication_systems.The CFO and impulse noise could be estimated by using the null subcarriers to cancel the effects of the two types of interference.The null subcarriers estimation methods include optimal separate estimation and joint estimation.The separate estimation firstly estimates the CFO value and then estimates the impulse noise value.However,the CFO and impulse noise always affect each other when either of them is estimated separately.The performance could be improved by using the joint estimation.The results of simulations and experiments have showed that these two optimization methods have good performance and the joint estimation has better performance than the separate estimation method.There is 3 dB performance gain at the BER value of 10^（-2）when using the joint estimation method.Thus these methods could improve the system robustness by using the CFO compensation and impulse noise suppression.

Fast Frequency Offset Acquisition and Accurate Tracking in OFDM Systems

A new carrier frequency offset estimation scheme for Orthogonal Frequency-Division Multiplexing (OFDM) systems is proposed. The carrier frequency offset estimation includes acquisition and tracking. The acquisition range of the proposed algorithm is as large as one half of the overall signal bandwidth. Comparison of the proposed scheme with Schmidl's algorithm by computer simulation illustrates the superior performance of the proposed scheme with regard to estimation accuracy in both AWGN channel and multipath channels.

Accurate and Simple Time Synchronization and Frequency Offset Correction in OFDM System

We present a new synchronization scheme for Orthogonal Frequency-Division Multiplexing (OFDM) systems. In this scheme, time synchronization and carrier frequency offset correction can be performed in one identical training symbol. Time synchronization algorithm is robust and simple operated, and its performance is independent of the carrier frequency offset. We derive the theoretical variance error for our time synchronization algorithm in AWGN channel. We also derive the performance lower bound of our frequency offset correction algorithm. The frequency offset correction algorithm is high accuracy and its performance will degrade very little under multipath fading environment.

Research and simulation on synchronization algorithm of PSS in a 5G system based on block cross-correlation

In response to the downlink synchronization requirements of the user equipment(UE)or third-party radio equipment in fifth-generation(5G)mobile communication systems,a synchronization algorithm of primary synchroni-zation signal(PSS)was designed and developed in the 5G system based on block cross-correlation.According to the new characteristics of the 5G synchronization channel and broadcast channel,starting from the traditional downlink synchronization algorithm of long-term evolution(LTE),the detection performance of the algorithm under a low signal-to-noise ratio(SNR)is improved by introducing an incoherent accumulation,and the new scheme of joint coarse frequency offset estimation is used to improve the frequency offset estimation performance.Finally,the performance of the proposed synchronization algorithm is verified by conducting a simulation on a 5G downlink simulation platform based on MATLAB software.Simulation results show that the improved downlink synchronization algorithm has stable performance in the tapped delay line-C(TDL-C)and additive white Gaussian noise(AWGN)channels with large frequency deviation and low SNR.

Synchronization for the Environment of OFDM Cooperative Communications Based on Preamble Design and Phase Rotation

Timing and carrier frequency offset estimation are critical issue for OFDM cooperative communications. In view of the complexity and high accuracy requirement, 1/2 and 1/4 pilot symbol cycle CAZAC sequence structures are defined as the pilot frequency sequence. Estimation within one symbol cycle is carried out through averaging samples of two neighboring symbol cycles, after which the operation is expanded to all the symbol cycles in one band group. Taking multipath effect into account, the concept of phase rotation is proposed for a further step. Adjust the phase difference of estimated symbols by phase rotation, and cross estimation could be done. Meanwhile, timing scheme works within one cycle training sequence. Theoretical and simulation analysis indicate that CRLB does not only relate to estimation symbol length, but also be influenced by phase difference of estimation symbols seriously. In the condition that the length of estimation is fixed, the bigger the phase rotation angle is, the smaller the CRLB is. The complexity of proposed algorithm is less than full cycle average estimation method for almost 50%. Meanwhile, the estimation accuracy is approximate with the full cycle average estimation method as well. Timing scheme with the defined preamble structure is also proposed. Simulation proves its efficiency.