Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications, including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the $q$ -shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift $q$ , the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and $q$ -shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Cramer–Rao lower bound. Theoretical results are validated by extensive computer simulations.

Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients

The development of electronic equipment technology, followed by the advancement of electronic systems, has increased the sensitivity of signal identification. Control and monitoring is a matter that forces existing engineers to make decisions and protect systems. In this paper, the distributed least mean p-norm method (dLMP) has been evaluated and evaluated to estimate the distributed frequency of the signal in three incremental, consensus, and scattering strategies. In the proposed method, based on the definition of appropriate cost functions, a distributed method is used to estimate the frequency of common sinusoidal signals with a common frequency in a wireless sensor network. The results of simulation with MATLAB software showed that the proposed algorithm has better and more favorable performance compared to other methods such as single-sensor and distributed methods. In the proposed method simultaneously with the distributed frequency estimation, the domain and phase estimation with a suitable and fast convergence is possible locally. Due to this advantage compared to the distributed filter method, the proposed method is less complicated and the convergence rate is appropriate and better.

Frequency Estimation by the Method of Minimum Mean Squared Error and P-value Distributed in the Wireless Sensor Network

Although 4G (fourth generation) i.e. LTE (long term evolution) systems are now in use world-wide. But today’s 4G systems have some challenges left such as spectrum scarcity and energy efficiency. The prime objectives of near-by-future 5G (fifth generation) wireless communications are reliability, higher data rate, higher bandwidth, high spectrum efficiency, higher energy efficient and that too at lower latency. Channel coding tend to increase the reliability of the wireless communications system by adding extra bits in a controlled fashion and is considered to be most persuasive element of communication system. 4G LTE Turbo Codes have already been replaced by LDPC (low density parity check) Codes in many of the standards including mMTC (massive machine type communication), D2D (device to device communication) and URLLC (ultra-reliable low latency reliable communications). LDPC Codes and Polar Codes are securing much more observation because of their inherent advantages of excellent bit-error-rate performance, fast encoding and decoding procedures; which make them the strong contenders for 5G Channel Codes too. This paper provides the broad survey and comparison of the LDPC and Polar Codes along with their advantages and drawbacks which will aid in further improvement of the next generation wireless networks. In order to enlighten future research possibilities in this direction, issues addressed by distinct researchers have been explored too.

A survey on channel coding techniques for 5G wireless networks

Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of decoding algorithms with good error performance and efficient hardware implementation. One of the leading candidates in this regard is represented by successive-cancelation list (SCL) decoding. However, its hardware implementation requires a large amount of memory. Recently, a partitioned SCL (PSCL) decoder has been proposed to significantly reduce the memory consumption. In this paper, we consider the paradigm of PSCL decoding from a practical standpoint, and we provide several improvements. First, by changing the target signal-to-noise ratio and consequently modifying the construction of the code, we are able to improve the performance at no additional computational, latency, or memory cost. Second, we bridge the performance gap between SCL and PSCL decoding by introducing a generalized PSCL decoder and a layered PSCL decoder. In this way, we obtain almost the same performance of the SCL decoder with a significantly lower memory requirement, as testified by hardware implementation results. Third, we present an optimal scheme to allocate cyclic redundancy checks. Finally, we provide a lower bound on the list size that guarantees optimal maximum a posteriori performance for the binary erasure channel.

Decoder Partitioning: Towards Practical List Decoding of Polar Codes

The fifty-year progress of faster-than-Nyquist (FTN) signaling is surveyed. FTN signaling exploits non-orthogonal dense symbol packing in the time domain for the sake of increasing the data rate attained. After reviewing the system models of both the conventional Nyquist-based and FTN signaling transceivers, we survey the evolution of FTN techniques, including their low-complexity detection and channel estimation. Furthermore, in addition to the classic FTN signaling philosophy, we introduce the recent frequency-domain filtering and precoding aided schemes. When relying on precoding, the information rate of FTN signaling becomes related to the eigenvalues of an FTN-specific intersymbol interference matrix, which provides a unified framework for the associated information-theoretic analysis and simplifies the associated power allocation specifically designed for increasing the information rate attained. We show that the FTN signaling scheme combined with bespoke power allocation employing a realistic raised-cosine shaping filter achieves the Shannon capacity associated with ideal rectangular shaping filters.

/pdf/the-evolution-of-faster-than-nyquist-signaling-1kqh14j094.pdf

The Evolution of Faster-Than-Nyquist Signaling

Cyclic redundancy check (CRC) assisted list successive cancellation decoding (SCLD) makes polar codes competitive with the state-of-art codes. In this letter, we try to find the optimal CRC for polar codes to further improve its performance. We first analyze the undetected error probability of CRC-aided SCLD as well as the characteristics of Hamming weight distribution of polar codes. Based on these characteristics, a multilevel SCLD-based searching strategy with moderate list size is proposed to compute the minimum Hamming weight distribution (MHWD) of different CRC-concatenated polar codes. Using the searched MHWD, the optimal CRC for polar codes are presented in this letter. Simulation results show that the performance of optimal CRC-aided SCLD significantly outperforms the standard one, especially at high code rate.

CRC Code Design for List Decoding of Polar Codes

Frequency estimation of a single complex exponential waveform is an important problem in many fields. In this letter, a new frequency estimator for a complex exponential sine waveform observed under the additive white Gaussian noise (AWGN) is proposed. The proposed estimator is obtained by solving the nonlinear functions. The new estimator has an analytical expression based on interpolation method with three DFT samples. Numerical results demonstrate that the performance of the proposed estimator has lower SNR threshold to closely reach the Cramer-Rao bound (CRB) in the low SNR region and its performance also outperforms previous estimators in the high SNR region.

A New and Accurate Estimator With Analytical Expression for Frequency Estimation

Faster-than-Nyquist (FTN) signaling is regarded as a potential modulation format of 5G communication system for its high spectral efficiency. To further improve the spectral efficiency, researchers have extended the FTN signaling to the frequency dimension. However, the two-dimensional FTN signaling called multicarrier FTN (MFTN) signaling induces intersymbol interference and intercarrier interference (ICI), which challenges the receiver. Even the subcarriers are orthogonal, the MFTN signaling still induces the ICI. In this paper, we propose a new MFTN signaling transceiver with an FTN mapper and a linear minimum mean square error (LMMSE) equalizer. The FTN mapper is deployed on every subcarriers independently, which means that the MFTN is ICI-free. The proposed transceiver is compatible with the existing orthogonal frequency division multiplexing (OFDM) system and can detect the MFTN signal efficiently. The numerical results show that the bit error rate performance of the transceiver is close to the convolution code line. At the same time, the MFTN system with high-order modulation has power gains than the traditional OFDM system.

A Faster-Than-Nyquist (FTN)-Based Multicarrier System

In this paper, a parallel concatenated structure is proposed to improve the performance of polar codes in finite length in which multiblocks systematic polar codes (SPC) and recursive systematic convolutional codes (RSC) are combined. We first design a weighted iterative decoding algorithm for the proposed structure such that better bit error rate performance can be obtained. Then, a deliberated interleaver is optimized for the new scheme. Thereafter, we introduce a strategy to estimate the minimum distance of the concatenation codeword, where an asymptotic performance and convergence behavior analysis are elaborated. Finally, the error performance of the proposed scheme is evaluated via simulations. The results show that our scheme almost outperforms all the existed concatenation ones using polar codes, making the codes more practical.

Practical Design and Decoding of Parallel Concatenated Structure for Systematic Polar Codes

A parallel concatenated coding structure, which can improve the performance of polar codes in finite-length regime, is proposed. In the proposed structure, the encoder is built using two systematic polar codes (SPCs), and the decoder adopts iterative belief propagation decoding algorithm. Numerical results in the binary-input additive white Gaussian noise channel indicate that the proposed coding scheme can improve BER performance of polar codes significantly. Specially, BER of the proposed coding scheme with length 192 is almost equal to that of original SPCs with length 256, when the code rate is 1/3.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/el.2015.2592

Qingshuang Zhang

Papers

CRC Code Design for List Decoding of Polar Codes

A New and Accurate Estimator With Analytical Expression for Frequency Estimation

A Faster-Than-Nyquist (FTN)-Based Multicarrier System

Practical Design and Decoding of Parallel Concatenated Structure for Systematic Polar Codes

Parallel concatenated systematic polar codes