Normalized Doppler Frequency Research Articles

Wrap-Around Based Frequency-Varying Viterbi Detection for Windowed OFDM Systems in Doubly Selective Fading Channels

In doubly selective fading channels, the conventional orthogonal frequency division multiplexing (OFDM) system suffers high inter-carrier interferences (ICIs). To deal with the ICIs, combining the time-domain windowing and Viterbi detection, we propose a wrap-around based frequency-varying Viterbi detection scheme for windowed OFDM systems. In a doubly selective fading channel, we theoretically derive the input-output relationship of windowed OFDM systems. It is observed that by selecting a proper window function, the equivalent channel matrix is sparse. Therefore, the severe ICIs can be significantly mitigated by our proposed wrap-around based frequency-varying Viterbi detection scheme. It is shown by simulation results that our proposed scheme achieves the performance very close to that of the maximum likelihood detector, even when the normalized Doppler frequency is as high as 0.667. Furthermore, the computational complexity of our proposed detection method is linear to the number of subcarriers, given the maximum iteration times and the constraint length.

Estimation of Time-Varying Channels in Virtual Angular Domain for Massive MIMO Systems

This paper is concerned with the problem of channel estimation in virtual angular domain in massive MIMO orthogonal frequency division multiplexing (OFDM) systems, in the presence of time varying channels. The proposed channel estimator is based on dichotomous coordinate decent joint sparse recovery (DCD-JSR) algorithm, which was well suited for massive MIMO systems with channels static over several OFDM symbols, but it is not accurate for time-varying channels. The estimator proposed in this paper exploits the basis expansion model (BEM) for approximation of the time-variation of the channel and the sparsity of the channel in the virtual angular domain with a common support over OFDM subcarriers and OFDM symbols for joint estimation of the BEM expansion coefficients. It is shown that, when using the Legendre polynomials as the BEM and depending on the normalized Doppler frequency, only a small number of expansion coefficients is required to provide accurate channel estimation.

Learning based MIMO communications with imperfect channel state information for Internet of Things

Imperfect channel state information (CSI) may seriously worsen the system performance for classical MIMO communications. In order to overcome the impacts of imperfect CSI for Internet of things, we propose a deep convolutional neural network (DCNN) based MIMO detection algorithm, where the DCNN is trained offline and works online to refine the imperfect CSI and improve the bit error rate of the wireless systems. Two types of learning based detectors, i.e., with or without accurate CSI, are proposed in this paper to reduce the detrimental effects of imperfect CSI. The impacts of the important system parameters, such as normalized Doppler frequency and the correlation factor are evaluated in different setup scenarios. Simulation results suggest that, compared with the classical maximum likelihood detector, the proposed learning based detectors shows considerable gains.

Implementation of a Fast Link Rate Adaptation Algorithm for WLAN Systems

With a target to maximize the throughput, a fast link rate adaptation algorithm for IEEE 802.11a/b/g/n/ac is proposed, which is basically preamble based and can adaptively compensate for the discrepancy between transmitter and receiver radio frequency performances by exploiting the acknowledgment signal. The target system is a 1 × 1 wireless local area network chip with no null data packet or sounding. The algorithm can be supplemented by automatic rate fallback at the initial phase to further expedite rate adaptation. The target system receives wireless channel coefficients and previous packet information, translates them to amended signal-to-noise ratios, and then, via the mean mutual information, selects the modulation and coding scheme with the maximum throughput. Extensive simulation and wireless tests are carried out to demonstrate the validity of the proposed adaptive preamble-based link adaptation in comparison with both the popular automatic rate fallback and ideal link adaptation. The throughput gain of the proposed link adaptation over automatic rate fallback is demonstrated over various packet transmission intervals and Doppler frequencies. The throughput gain of the proposed algorithm over ARF is 46% (15%) for a 1-tap (3-tap) channel over 10 m–250 m (16 m–160 m) normalized Doppler frequencies. Assuming a 3-tap channel and 30 m–50 m normalized Doppler frequencies, the throughput of the proposed algorithm is about 31 Mbps, nearly the same as that of ideal link adaptation, whereas the throughput of ARF is about 24 Mbps, leading to a 30% throughput gain of the proposed algorithm over ARF. The firmware is implemented in C and on Xilinx Zynq 7020 (Xilinx, San Jose, CA, USA) for wireless tests.

Deep Learning-Based Secure MIMO Communications with Imperfect CSI for Heterogeneous Networks.

Perfect channel state information (CSI) is required in most of the classical physical-layer security techniques, while it is difficult to obtain the ideal CSI due to the time-varying wireless fading channel. Although imperfect CSI has a great impact on the security of MIMO communications, deep learning is becoming a promising solution to handle the negative effect of imperfect CSI. In this work, we propose two types of deep learning-based secure MIMO detectors for heterogeneous networks, where the macro base station (BS) chooses the null-space eigenvectors to prevent information leakage to the femto BS. Thus, the bit error rate of the associated user is adopted as the metric to evaluate the system performance. With the help of deep convolutional neural networks (CNNs), the macro BS obtains the refined version from the imperfect CSI. Simulation results are provided to validate the proposed algorithms. The impacts of system parameters, such as the correlation factor of imperfect CSI, the normalized doppler frequency, the number of antennas is investigated in different setup scenarios. The results show that considerable performance gains can be obtained from the deep learning-based detectors compared with the classical maximum likelihood algorithm.

Fast Telemetry and Communication Scheme Based on Doppler Diversity Reception under Large Dynamic Doppler for Hypersonic Vehicles

Large dynamic Doppler caused by high-speed flight of hypersonic vehicles brings a great challenge to acquisition, tracking and correct demodulation of telemetry and communication signals. Different from receiving schemes of existing telemetry and communications, a novel communication method based on Doppler diversity reception for hypersonic vehicles was proposed in this study. Firstly, the proposed method offers a coarse acquisition of Doppler frequency offset and its rate-of-change by fast-coarse acquisition method, and then decreases the large Doppler frequency offset into a certain range through compensation. Finally, signals with residual Doppler frequency offset are processed directly by Doppler diversity reception method without a complicated tracing method. Different from the traditional receiving scheme with acquisition and tracking module, the proposed scheme lowers requirements on acquisition accuracy and neglects the accurate tracking module, thus shortening telemetry and communication time significantly for hypersonic vehicles. Simulation results demonstrate that the proposed method can achieve satisfactory performance when the residual Doppler is no higher than 1 kHz with normalized Doppler frequency offset and when the normalized artificial frequency shift is 0.01 and 0.4 respectively.

Joint Carrier Synchronization Algorithm by Open-Loop Acquisition and Closed-Loop Tracking in High-Dynamic Environments

Considering the difficulty of carrier synchronization and the low tracking accuracy in high-dynamic environments, the joint open-loop acquisition and closed-loop tracking carrier synchronization algorithm is presented. Firstly, the algorithm derives the coarse estimation of Doppler frequency and Doppler rate via open-loop acquisition, then the residual Doppler frequency and Doppler rate are confined into a small range. Secondly, the residual Doppler rate is tracked by using a third-order phase-locked loop(PLL). The present algorithm has the advantages of fast acquisition and high tracking accuracy. Finally, the numerical simulation is conducted to verify the present synchronization algorithm. The simulation results indicate that at the signal to noise ratio(SNR) of and normalized Doppler frequency and Doppler rate ranging from to, the bit-error-rate(BER) performance degradation is as low as comparing with theoretical value.

Improved distance metric technique for deriving soft reliability information over Rayleigh Fading Channel

This paper presents an improved Distance Metric (DM) technique for deriving soft reliability information over Rayleigh fading channel. We compared this proposed DM technique with the conventionally used DM technique in the literature. The conventional DM method derives the soft reliability information from the output received symbols while the proposed DM method derives the soft reliability information from the Channel State Information (CSI) which result due to variations in the channel gain. Performance analysis of these DM methods are verified over flat Rayleigh fading channels, and on time-varying frequency-selective Rayleigh fading channels using rectangular M-QAM and OFDM systems respectively. Also, two channel estimation techniques are used to derived the CSI assuming different normalized Doppler frequency and frame length size. The performance of the conventional and proposed soft reliability derivation methods are documented through computer simulations assuming Koetter and Vardy, Reed-Solomon (KV-RS) soft decision decoding algorithm as the Forward Error Correction (FEC) scheme. From the computer simulation results, the proposed DM method offers significant improvement in Codeword Error Rate (CER) performance in comparison with the conventional DM method with no significant increase in computational delay and time complexity. Keywords: CSI, cubic estimators, DM, fading channels, KV-RS decoder, LMMSE, OFDM, R-matrix, 16QAM

A Semidefinite Relaxation Approach to OFDM-IM Detection in Rapidly Time-Varying Channels

In this paper, the signal detection of orthogonal frequency division multiplexing with index modulation (OFDM-IM) in the rapidly time-varying channel is studied. Due to the inter-carrier interference, the conventional block detectors based on the successive interference cancellation (SIC) strategy, e.g., the signal power (SP) detector, suffer from severe error propagation especially in the case with large normalized Doppler frequency. To address this problem, a semidefinite relaxation (SDR) approach is first proposed. In the proposed SDR detector, the signal feature of OFDM-IM is presented properly as the convex constraints in the SDR programming problem and utilized in the randomization procedure. The SDR detector can avoid the error propagation effectively with a cost of higher polynomial complexity. To reduce the complexity, the group-based SIC-SDR detector is then proposed, where the subcarriers in one OFDM symbol is partitioned into multiple groups, and the SDR detection is performed over each group successively in conjunction with the ordered SIC strategy. However, similar with the SP detector, the SIC-SDR detector also suffers from the error propagation. To boost the performance, we propose to take the solution of the SIC-SDR detector as the initial estimation of a further local search algorithm (LSA). Concretely, after a proper definition of the nearest neighbors of an OFDM-IM signal vector, the proposed combined detector employing the likelihood ascent-search as the LSA is presented. Finally, the validity of the proposed detectors is justified by simulation results, and the combined detector achieves an excellent performance-complexity trade off.

Multi-segmental OFDM signals equalization with piecewise linear channel model over rapidly time-varying channels

For rapidly time-varying channels, the performance of (orthogonal frequency division multiplexing) OFDM systems with the conventional one tap equalizer will be significantly degraded. Because the orthogonality between subcarriers is destroyed, the conventional way to combat the inter-carrier interference (ICI) is employing the banded minimum mean square error (MMSE) equalizer, which can save computational efforts introduced by a large number of subcarriers. However, the width of the banded channel matrix is mainly determined by the normalized Doppler frequency in the sense that with the high Doppler frequency the complexity of equalization for one OFDM block will significantly increase with the band width D. In order to reduce the equalization complexity, the authors proposed multi-segmental OFDM signal equalization method with piecewise linear model (PLM) to approximate the time variations and mitigate the corresponding ICI. Its complexity is significantly reduced with the small segments. Furthermore, an alternative MMSE method with the iterative rank-1 matrix updates is proposed to further reduce the complexity. We also derive the theoretical pre-equalized and equalized signal to interference ratio (SIR) for different normalized Doppler frequencies and segment numbers, which implies that the larger segment number can achieve the better performance. Simulation results demonstrate that the proposed method outperforms the conventional banded MMSE equalizer and the partial fast Fourier transform (FFT) method in terms of bit error rate (BER) with almost the same complexity.

A Novel PRCC Scheme for OFDM Systems Over Frequency-Selective Fading Channels

Orthogonal frequency division multiplexing is a popular modulation technique for fourth-generation (4G) broadband multimedia wireless communication systems. However, for practical communications, the orthogonality between subcarriers may suffer from carrier frequency offset, resulting in intercarrier interference (ICI), which increases an irreducible error floor in proportion to the normalized Doppler frequency. The two-path transmission methods such as conjugate cancellation and phase rotated conjugate cancellation (PRCC) suppress ICI at the cost of reducing bandwidth efficiency. In this paper, a novel PRCC scheme with the method of separating the odd and even sequences of the transmission signals into two independent paths is studied and proposed to further mitigate the ICI over frequency-selective fading channels. Comparing with the conventional PRCC method, the proposed scheme can not only achieve higher data transmission efficiency, but also provide a better performance on bit error rate according to the final simulation results.

Performance analysis of polarization-space-time adaptive processing for airborne polarization array multiple-input multiple-output radar

In order to further improve the capabilities of clutter suppression and target detection in airborne multiple-input multiple-output (MIMO) radar space-time adaptive processing (STAP), the polarization-space-time adaptive processing (PSTAP) method based on polarization array MIMO radar is proposed. Firstly, by applying the novel polarization array to airborne MMO radar, the signal model of airborne polarization array MIMO radar PSTAP is established. Then based on the idea of resolution grid, the influence of clutter can be equivalent to the formation of independent point sources of clutter related to the clutter degree of freedom, and an equivalent expression for the covariance matrix in polarization array MIMO radar PSTAP is obtained. Next, combined with the equivalent covariance matrix, the signal-to-clutter-plus-noise ratio (SCNR) performance of the polarization array MIMO radar PSTAP is derived and analyzed. The effects of the polarization, spatial and temporal matching coefficients are discussed. When the target is located in the side-looking direction of the airborne radar, the normalized spatial frequency of the target is zero. Then the spatial transmit and spatial receive matching coefficients between the target and the clutter point source in the center of the space-time plane both approach to one. Meanwhile, the normalized Doppler frequency of the side-looking target is in direct proportion to the target speed. When the target speed decreases to zero, the temporal Doppler matching coefficient between the target and the central clutter source is near to one. Thus taking the spatial and temporal matching coefficients into consideration, the SCNR loss of the traditional MIMO-STAP is approximate to zero. It indicates that for traditional MIMO-STAP, its performance of detecting low-speed target is severely degraded by the clutter source, and target detection can hardly be realized just in space-time domains. However, through utilizing the additional polarization information to take advantage of the polarization matching coefficient, the polarization array MIMO radar PSTAP increases the SCNR loss and remarkably lessens the influence of the central clutter source. According to the above theoretical analysis, we can come to the conclusion that the polarization array MIMO radar PSTAP can effectively promote the capability of clutter suppression compared with the traditional MIMO-STAP, which is beneficial to the detection of the moving target with low-speed. Moreover, the improvement of output SCNR performance becomes more significant with increasing the differences between the polarization parameters of target and those of clutter. Therefore, the polarization array MIMO radar PSTAP has great application value for practical engineering. The simulation results verify the validity and superiority of the proposed polarization array MIMO radar PSTAP method.

Low Complexity ICI Mitigation for MIMO-OFDM in Time-Varying Channels

Time-varying channels destroy the orthogonality among subcarriers in orthogonal frequency division multiplexing (OFDM) systems, and introduce intercarrier interference (ICI). Lots of efforts have been devoted to mitigate ICI in OFDM systems, with different frame structures and channel models, but the computational complexity of the methods is usually very high. In multiple-input multiple-output (MIMO) systems, the complexity is even higher. In this paper, a low-complexity ICI mitigation method is proposed for MIMO-OFDM systems under the assumption of linear time-varying channels. It reduces the complexity of ICI compensation from $ {O(K^{3}(N^{3}+MN^{2}+MN)+NK\log (K))}$ to $ {O(K(N^{3}+2MN^{2}+2MN+2M^{2}+N\log (K)))}$ , where ${K}$ is the number of subcarriers, ${M}$ the number of transmitters, and ${N}$ the number of receivers. It requires channel estimation based on the linear time-varying channel model, and no transmission overhead is needed. The proposed algorithm applies to all OFDM systems as long as linear time-varying channel estimation is applicable. Time-domain synchronous-OFDM naturally suits for the proposed ICI mitigation algorithm because its receiver is able to easily estimate linear time-varying channels. Simulation with QPSK and 16QAM modulation demonstrates the performance of the proposed method, in comparison with no ICI mitigation case. It shows that 2 dB signal to noise gain is achieved when the uncoded bit error rate is $ {10^{-3}}$ and the normalized Doppler frequency is 0.1.

A Channel Estimation Method for OFDM Based Wireless Communication System in High Speed Environment

This paper investigates the channel estimation in an Orthogonal Frequency Division Multiplexing system under a fast-varying channel, by exploiting a frequency shifted complex exponential basis expansion models (CE-BEM). The conventional CE-BEM model suffers from power leakage and consequential modelling error floor, especially at the channel boundaries. The proposed BEM model reduces the leakage power efficiently by exploiting a fractional frequency on the coefficients of CE-BEM matrix. Numerical results show that the performance of the proposed channel modeling and coefficients estimation method are robust against various normalized Doppler frequency. The modeling error at the channel boundaries can be reduced substantially.

Optimization of Pilot Overhead in Communications With ARQ-Feedback

In this letter, we optimize the pilot overhead in communication with retransmission and investigate the dependence of this overhead on various system parameters, e.g., fading rate, target rate, and signal-to-noise ratio. We formalize the optimization and frame it in terms of throughput maximization; this leads to an accurate optimal pilot overhead closed-form expression. Results show that the optimal overhead expressions are roots of quartic polynomials. At a high-power regime, they decrease with the target rate and increase with the normalized Doppler frequency, and at low-power regime, they are only function of the target rate.

Proposal of channel estimation method for wireless two-way relay system of using SFBC MIMO-OFDM technique

In a two-way relay communication system, two user terminals (UTs) can communicate and exchange their information data through a relay station by using two timeslots. To realize the two-way relay communication system, each UT is required to estimate channel frequency responses (CFRs) both for up and down links in two timeslots efficiently which be employed in the demodulation of the other user's information data with frequency domain equalization. To satisfy this requirement, this paper proposes a novel CFR estimation method for the wireless two-way relay communication system of using SFBC MIMO-OFDM technique. The salient feature of proposed CFR estimation method is to employ the maximum likelihood estimation method for the proposed scattered pilot subcarriers assignment which can achieve higher CFR estimation accuracy even in higher time-varying fading channel and when the transmission OFDM signal is sampled by the non-Nyquist rate. In the proposed system, the SFBC technique is also employed for the data subcarriers both for the pilot symbols including data subcarriers and data symbols consisting of all data subcarriers in the frequency axis to improve the bit error rate (BER) performance in the two-way relay system. From the computer simulation results, this paper demonstrates the effectiveness of proposed two-way relay communication system of using SFBC MIMO-OFDM technique. To demonstrate the effectiveness of proposed two-way relay communication system of using SFBC MIMO-OFDM technique, this paper conducts various computer simulations as comparing with the conventional methods in higher time-varying fading channel. From the computer simulation results, this paper confirms that the proposed method even at the non-Nyquist rate can achieve higher channel estimation accuracy evaluated by the normalized mean square error (NMSE) and better BER performances by 5 and 22 times, respectively as comparing with the conventional methods when the normalized Doppler frequency ($$f_dT_S$$fdTS) is $$10^{-2}$$10-2 and the carrier to noise power ratio (C/N) is 25 dB.

Doppler Mitigation in OFDM-Based Aeronautical Communications

Doppler spectrum in an aeronautical channel is modeled with dual-Doppler shift instead of classical Jakes model. Orthogonal frequency division multiplexing (OFDM)-based systems are sensitive to Doppler shifts/spread, since the time variation of the channel causes inter-carrier interference (ICI). ICI analysis is provided here for OFDM-based systems in the aeronautical channel. The effect of ICI on the received signal is presented and its power is derived. As compared with terrestrial channels, where ICI is generally overcome by increasing the subcarrier spacing and bounding the normalized Doppler frequency (NDF), we propose to mitigate the effect of Doppler shifts in aeronautical channels, as follows. First, we use parametric spectrum estimation methods to extract the Doppler shifts by exploiting the predictable number of paths. Then, a beamforming-based method is introduced to resolve the incoming rays by separating them individually. Finally, paths are Doppler-compensated and combined using diversity combining techniques. Computer simulations are performed to provide numerical results. It is shown that a mean square error (MSE) performance ofis achieved with the parametric estimation methods, and bit error rate (BER) performance approaching the no-Doppler scenario is obtained with the beamforming-based mitigation method.

Signal detection through circular convolution reconstruction for OFDM system in fast varying channel

A signal detection algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) system in the presence of fast time-varying channel. The channel is represented by a piece-wise linear variant model with normalized Doppler frequency of less than 0.2. The channel parameters are extracted through ISI/ICI (inter-symbol interference/inter-carrier interference) cancellation and circular convolution reconstruction. Meanwhile, an improved OFDM symbol detection algorithm is also proposed based on circular convolution reconstruction. The channel state information in the OFDM symbol duration can be obtained accurately from the adjacent two block pilots in a linear model. The simulation results show that the proposed method can not only track the channel variation, but also promise better performance gain in the OFDM symbol detection. Furthermore, the bit error ratio (BER) is close to the performance with the perfect channel state information.

Nondata-Aided Joint Channel Estimation and Equalization for OFDM Systems in Very Rapidly Varying Mobile Channels

This paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization—maximum a posteriori probability (SAGE-MAP) technique which is particularly well suited to multicarrier signal formats. The algorithm is implemented in the time-domain which enables one to use the Gaussian approximation of the transmitted OFDM samples. Consequently, the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate (SER) performance. Based on this Gaussian approximation the exact Bayesian Cramér Rao lower bound (CRLB) as well as the convergence rate of the algorithm are derived analytically. To reduce the computational complexity of the algorithm, discrete Legendre orthogonal basis functions are employed to represent the rapidly time-varying fading channel. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal. The computational complexity of the algorithm is shown to be <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim}O(NL)$</tex></formula> per detected data symbol and per SAGE-MAP algorithm cycle where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$N$</tex></formula> is the number of OFDM subcarriers and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L$</tex></formula> is the number of multipath components.

Low-Complexity Channel Estimation for Wireless Block Transmission Systems in Time-and Frequency-Selective Rayleigh Fading Channels

Mobility-induced Doppler spread and multipath propagation introduce the time- and frequency-selectivity (doubly selectivity) in fading channels. Based on the complex exponential basis expansion model (BEM) to approximate the doubly selective channel (DSC), a low-complexity channel estimation scheme for block transmission systems over DSC are developed in this paper. Using the developed scheme, the long data block is divided into a few short data subblocks in terms of the maximum normalized Doppler frequency and block length, and each subblock is performed to respective channel estimation. Thus the total calculation complexity is effectively decreased because the number of the BEM channel coefficients to estimate is greatly reduced for each sub-block. Moreover, by utilizing these channel estimation values to refit the true channel, we can obtain better channel estimation. Besides, the normalized mean square error (NMSE) expressions for the developed scheme and the existing scheme are derived in detail, respectively. Compared to the existing scheme, the proposed scheme has lower calculation complexity and superior performance. The simulation results verify the effectiveness of the developed scheme, and the theory values of the derived NMSE accord with corresponding simulation values.