MIMO time-varying channel tracking using annealed particle filtering

ABSTRACTWhile inter-symbol interference is not of concern, inter-carrier interference that is caused by carrier frequency offset (CFO) is more concerned in orthogonal frequency division multiplexing (OFDM) systems. The estimation of channel impulse response (CIR) is another important parameter of interest in the system. Recently, a number of approaches for the joint estimation of CFO and CIR in OFDM systems have been proposed in the literature, and most of them are traditional maximum-likelihood-based approaches. In this paper, we propose a number of mixture cost-reference particle filtering (CRPF) approaches for joint estimation of CIR and CFO, and a couple of them can be applied without the knowledge of both state and measurement noise statistics. Conventional least mean squares algorithm or recursive least squares algorithm is jointly employed with recently developed CRPF for nonlinear and multiple parameters estimation in OFDM systems. The computer simulation results show that mixture CRPFs are more robust against particle impoverishment (PI) problem than standard mixture particle filtering (PF) and mixture regularized PF (RPF) approaches although RPF was particularly developed to tackle the PI problem. In this paper, we investigate a number of mixture PF approaches including ones that do not need the information of noise statistics for the joint estimation of CFO and channel in OFDM systems.

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.

Particle filter with ant colony optimization for frequency offset estimation in OFDM systems with unknown noise distribution

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.

For the uplink interleaved single carrier frequency division multiple access (SC-FDMA) system, one of the main problems is that the multiple carrier frequency offsets (CFO), caused by Doppler shift in high-speed wireless communications, will cause severe inter-subcarrier interference (ICI), so as to influence the system performance. In this paper, we propose an effective multiple CFO compensation scheme, for reducing the ICI influence in the uplink interleaved SC-FDMA. On the one hand, the optimal CFO compensation value, which maximizes the signal-to-interference ratio (SIR), is achieved to compensate the CFO for each user at the receiver. On the other hand, the residual ICI is analyzed and an improved minimum mean square error (MMSE) frequency domain equalizer (FDE) receiver is developed which suppresses both ICI and noise. Theoretical analysis and simulation results show that the proposed CFO compensation scheme can effectively reduce the influence of ICI and im-prove the system performance.

Multiple Input Multiple Output (MIMO) system with orthogonal frequency division multiplexing (OFDM) is a promising physical layer candidate for the current and future wireless standards. MIMO increases system throughput while OFDM maximizes spectrum efficiency. To reduce the impacts of frequency selective fading and increase the capacity, MIMO requires precise channel state information (CSI). The presence of carrier frequency offset (CFO) introduces intercarrier interference (ICI) among the subcarriers which degrades the system performance. MIMO channel estimation is done under the assumption of perfect frequency synchronisation between the transmitter and receiver, or zero CFO. However, such an assumption is incorrect for time-varying and frequency-selective wireless channels, and the presence of CFO has an impact on channel estimation accuracy. In the existing methods, CFO and channel estimations are carried out independently using separate training sequences which reduces the spectral efficiency. As a result, the pilot aided interpolation approach is proposed in this paper for the joint estimate and compensation of CFO and channel effects using the same set of pilot tones. Theresults show that the proposed method offers precise CFO and channel estimation which improves the bit error rate performance and carrier to interference power ratio (CIR) of MIMO-OFDM system.

In the uplink system, different carrier frequency offsets (CFO) of different users at the receiver resulting multiuser interference (MUI) and thus degrade the performance of Multicarrier Code Division Multiple Access (MC-CDMA) system. In the previous study, Modified Minimum Mean Square Error Frequency Domain Equalization (Modified MMSE-FDE) has been proposed by Agnihotri which results in a better performance than the conventional MMSE. However, the achieved Bit Error Rate (BER) is not smaller than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for Signal to Noise Ratio (SNR) below 20. This paper proposed a new algorithm to improve Modified MMSE-FDE performance in mitigating multiuser interference (MUI) in single cell MC-CDMA system, that is called as Carrier Frequency Offset Estimation-Minimum Mean Square Error Frequency Domain Equalization (CFO Estimation-MMSE FEQ). CFO Estimation-MMSE FEQ takes into account the rest of MUI as well as Modified MMSE-FDE to design equalization coefficient, but CFO Estimation-MMSE FEQ uses CFO estimation that is not on Modified MMSE-FDE. The value of CFO is estimated and regenerated in the receiver and then used to estimate MUI. In order to get signal processing more efficient, CFO Estimation-MMSE FEQ only takes the real trace of equalization coefficient matrix. MC-CDMA with CFO Estimation-MMSE FEQ has better performance than MC-CDMA with Modified MMSE-FDE. However, the complexity of CFO Estimation-MMSE FEQ is higher than Modified MMSE-FDE. By taking only the real trace of equalization coefficient matrix, the complexity of CFO Estimation-MMSE FEQ is getting simpler than taking the whole of equalization coefficient matrix. Furthermore, CFO Estimation-MMSE FEQ that takes only the real trace of equalization coefficient matrix is 2.9 % more efficient than CFO Estimation-MMSE FEQ that takes the whole of equalization coefficient matrix.

OFDM systems are sensitive to Carrier Frequency Offsets (CFO) that results in performance's degradation. Researchers have proposed various CFO compensation techniques. Some estimates the CFO's value then compensates for it using preamble methods. Others estimate the CFO value using the inherent construction of the time-domain OFDM symbol. Our proposed technique changes the conventional structure of the OFDM symbol to allow estimating the CFO values over a wide range. CFO estimation range, accuracy, transmitted data-rate, system complexity, and the compatibility of a specific estimator to be used in different applications are the most important parameters to be considered in researches. In this paper, a comparative analysis between preamble techniques (Moose, Training Symbol) and the OFDM internal construction-based estimators including blind and proposed schemes will be discussed. Simulations show the trade-offs between those techniques.

Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.

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.

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).

This paper evaluates the performance of a pilot-assisted fine carrier frequency offset (CFO) estimation scheme for orthogonal frequency division multiplexing (OFDM) in time-varying channels. An analytical closed-form expression of the mean square error (MSE), of the post-FFT based CFO synchronization scheme, is presented in terms of time-variant fading channels. To verify our analysis in this paper, simulations are carried out within the framework of mobile WiMAX systems.

The most widely used Wi-Fi wireless communication system, which is based on OFDM, is currently developing quickly. The receiver must, however, accurately estimate the carrier frequency offset between the transmitter and the receiver due to the characteristics of the OFDM system that make it sensitive to carrier frequency offset. The autocorrelation of training symbols is typically used by the conventional algorithm to estimate the carrier frequency offset. Although this method is simple to use and low in complexity, it has poor estimation performance at low signal-to-noise ratios, which has a significant negative impact on the performance of the wireless communication system. Meanwhile, the design of the communication physical layer using deep-learning-based (DL-based) methods is receiving more and more attention but is rarely used in carrier frequency offset estimation. In this paper, we propose a DL-based carrier frequency offset (CFO) model architecture for 802.11n standard OFDM systems. With regard to multipath channel models with varied degrees of multipath fadding, the estimation error of the proposed model is 70.54% lower on average than that of the conventional method under 802.11n standard channel models, and the DL-based method can outperform the estimation range of conventional methods. Besides, the model trained in one channel environment and tested in another was cross-evaluated to determine which models could be used for deployment in the real world. The cross-evaluation demonstrates that the DL-based model can perform well over a large class of channels without extra training when trained under the worst-case (most severe) multipath channel model.

In this paper, the non-recursive estimation algorithm using a batch filter based on particle filtering is developed and utilized for one-dimensional nonlinear example. For comparison study, algorithms of a batch filter based on unscented transformation and generic particle filtering are briefly reviewed and new algorithm of a batch filter based on particle filtering is presented. For verification of presented batch filter's performance, the numerical simulations and the accuracy assessment are achieved and results are compared with those of a batch filter based on unscented transformation for various nonlinear and non-Gaussian environments. The root mean square value of differences between observational values and computed values after convergence is used for precision check of filtering process, estimated initial state value and the difference between true initial state value and estimated initial state value are used for state accuracy check of nonlinear estimation. Large initial state and various type of measurement noise are used for nonlinear and non-Gaussian environments, respectively. Under large initial state error or large non-Gaussian measurement noise, the developed non-recursive estimation algorithm give more robust and accurate estimation results than those of a batch filter based on unscented transformation easily. Finally, the non-recursive batch filter based on particle filtering is effectively applicable for batch estimation problems under nonlinear and non-Gaussian environments.

Carrier frequency offset (CFO) of different users in the multicarrier DS-CDMA (MC-DS-CDMA) system may violate the orthogonality among subcarriers and induce inter-carrier interference (ICI) and inter-user interference (IUI). This paper develops a new algorithm based on pilot clusters for CFO estimation of the uplink of MC-DS-CDMA system. By exploiting the low-pass property of fast Fourier transform (FFT) vector of the complex exponential function as well as the non-coherent property of the pilot clusters among users, we can obtain a signal matrix in the frequency domain at the receiver and the CFO of all users can be estimated from its row vectors, which are made up of the complex exponential function sequences including CFO of different users. Under the case of CFO in the fine tracking phase and the slowly time-varying flat-fading channel, the simulation shows that the mean value of the CFO estimation error is close to 0.01% subcarrier spacing when the signal to noise ratio (SNR) is 10 dB.