Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

In this article, we explore the use of neural networks (NNs) to enhance the performance evaluation of Universal Filtered Multi-Carrier (UFMC) systems, a key technology for modern communication networks such as 5G and beyond. Traditional methods of evaluating the Bit Error Rate (BER) and system efficiency in UFMC system can be computationally intensive and less accurate under dynamic conditions. To address these challenges, we propose a NN based approach that not only improves the accuracy of BER prediction but also significantly optimizes the system's overall efficiency. Channel state estimation (CSE) plays a major role for UFMC system to address the phenomenon of multipath channel fading. In order to achieve a high data rate using UFMC technology, it is necessary to have an effective CSE and very accurate signal detection. Recently, there has been significant interest in utilizing deep learning (DL) to enhance channel estimations. This article introduces a new method for channel estimation (CE) in UFMC system. The suggested approach utilizes DL models to improve the CE. For the UFMC system, we propose a detector based on bidirectional long short-term memory (Bi-LSTM). To identify the transmitted symbols, the suggested detector uses DL training data directly. Currently, a significant drawback of UFMC systems is the presence of a high peak-to-average power ratio (PAPR). The approach aims to reduce the BER and enhances the efficiency of the UFMC system. This is achieved by dynamically setting the constellation mapping and symbol damping on each subcarrier and sub-symbol. The results illustrate that the proposed model can accurately and efficiently recognize UFMC signals. The suggested model is being compared to Least Square (LS), LSTM, and Minimum Mean Square Error (MMSE) channel estimators. Through extensive simulations, our results demonstrate that the NN model reduces BER and enhances efficiency. The proposed model gives more effective performance in terms of enhanced efficiency and reduction of BER. The findings offer valuable insights for the design and optimization of next-generation communication systems, where accurate and efficient performance evaluation is critical.

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalisers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalisers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equaliser in a channel intersymbol interference (ISI) plus co-channel interference setting. A simulation study shows that the proposed algorithm has good convergence speed, and a small-size RBF equaliser trained by the LBER can closely approximate the performance of the optimal Bayesian equaliser. The results also demonstrate that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalisers because the minimum mean square error (MMSE) is clearly suboptimal in the equalisation setting.

In this paper, linear precoding (LP) algorithm has been studied to improve the bit error rate (BER) performance of large scale multiple input multiple output (MIMO) system. A new technique of enhancing the BER performance of linear precoding algorithm without complexity in hardware and mathematical calculations is proposed and it is used on a traditional LP algorithms like a Maximum Ratio Transmission (MRT), a Zero-Forcing (ZF), a Regularized Zero-Forcing (RZF), and a Minimum Mean Square Error (MMSE) for Millimeter wave MU-MIMO communication system. A new technique is also used to mitigate the BER gab problem between (ZF, MMSE) and (RZF, MMSE) linear precoding algorithms. The result shows that with using the new technique, the BER performance of modified LP significantly outperform their traditional LP by 10−5 when using 4 element of BS antenna, 10−6 when using 16 element of BS antenna and mitigate the BER gab problem at different signal to noise ratio (SNR).

In multiple-eigenvalue modulated nonlinear frequency division multiplexing (NFDM) systems, the noise degrades the accuracy of the nonlinear Fourier transform (NFT) algorithm, resulting in perturbations in the received eigenvalues and the corresponding discrete spectrum. Moreover, with the increase in the number of eigenvalues and the order of the modulation formats, the impact of noise on the performance of the system is even more. A noise equalization scheme based on complex-valued artificial neural network (c-ANN) for multiple-eigenvalue modulated NFDM systems is proposed. This sceheme inputs the eigenvalues perturbation and the impaired discrete spectrum corresponding to the eigenvalues into the c-ANN in complex form. The scheme constructs a complex-valued logic structure with both amplitude and phase information, overlapping reuse input features and, thereby, effectively reducing the effect of noise on the multiple-eigenvalue NFDM system. The effectiveness of the scheme is verified in long-haul seven-eigenvalue modulated single-polarization NFDM simulation systems with 1GBaud 16APSK/16QAM/64APSK/64QAM modulation formats, and the results show that the scheme outperforms the NFT receiving without equalization by 1 to 2 orders of magnitude in terms of bit error rate (BER). Among them, the transmission distance of the 64APSK signal after equalization exceeds 800km while the BER meets 7% forward error correction (FEC) threshold, which is 600km longer than that of the disequilibrium case, and the spectral efficiency (SE) can reach 1.85bit/s/Hz. Compared with other schemes, the proposed scheme has better equalization performance under the same complexity, and the complexity can be reduced by half or even under the same performance.

Recently, multicarrier modulations is becoming the chosen modulation technique for wireless communications. The Wavelet Packet Modulation (WPM) is applied as a novel alternative to the Orthogonal Frequency Division Multiplexing (OFDM). In this paper, Wavelet Packet Transform based multicarrier modulation is presented and introduced using both Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) equalizers. They are proposed and compared for Wavelet based multicarrier modulation. First we have evaluated the performance of the classical OFDM and the WPT in term of Power Average Peak Ratio (PAPR). Second, the performances of proposed schemes are qualified for three types of wireless channels in the presence of Additive White Gaussian Noise (AWGN). Results of simulation illustrate a notable enhancement in Bit Error Rate (BER) for MMSE over ZFE equalization technique for different types of channel.

An asymptotically minimum bit error rate (BER) linear block precoder is determined for block-by-block communication systems employing linear minimum mean square error (MMSE) equalisation and disjoint detection. The problem is solved by a two-stage optimisation procedure in which a lower bound on the BER is first minimised, and then it is shown how this minimised lower bound can be achieved. Simulation results show that the BER performance of the proposed scheme is superior to the standard MMSE precoder and several other conventional systems such as orthogonal frequency division multiplexing. At reasonable BERs, the signal-to-noise ratio (SNR) gain can be of the order of several decibels.

OFDM(Orthogonal Frequency Division Multiplexing) 시스템에서 직교 불균형 문제는 송수신기의 front-end에서 발생하며, 성상도에 영향을 주게 되어 BER(Bit Error Rate)을 증가시킨다. 또한, 위상 잡음은 송수신시 국부 발진기에서 발생되는 잡음으로 각 부반송파의 직교성을 깨뜨림으로써 시스템 성능을 크게 저하시킨다. 기존 방식인 PNS(Phase Noise Suppression) 알고리즘은 이러한 위상 잡음을 효과적으로 제거하는 방법이지만 직교 불균형 이동시에 적용되면 오히려 성능이 감소된다. 본 논문에서는 OFDM 시스템의 수신기에서 하향 변환 시 발생하는 직교 불균형과 위상 잡음의 영향을 분석하고, 수신기 FFT(Fast Fourier Transform) 후단에서 파일럿 심볼을 사용하여 CPE를 먼저 제거하고 직교 불균형과 위상 잡음의 성분을 검출하여 등화기의 판정 기준으로 사용하여 보상하는 방법을 제시하였다. 또, 다른 기존 방식들은 FFT 후단에서 추정하고 피드백 시키거나 프리엠블과 같은 시퀀스를 사용하는 방식이지만, 본 논문에서는 FFT 후단에서 MMSE 등화기만을 사용하여 제거하므로 기존의 방법보다 복잡도가 줄어든다. 기존의 위상 잡음 제거 방식에 ICI(Inter Carrier Interference) 제거 기능을 추가하고 직교 불균형 성분을 추출하여 MMSE(Minimum Mean Square Error) 과정 중에 적응 forgetting factor를 적용하면 성능 개선과 직교 불균형 성분의 영향이 줄어들며 성능이 개선됨을 보인다. In the OFDM system, IQ imbalance problem happens at the RF front-end of transceiver, which degrades the BER(bit error rate) performance because it affects the constellation in the received signal. Also, phase noise is generated in the local oscillator of transceivers and it destroys the orthogonality between the subcarriers. Conventional PNS algorithm is effective for phase noise suppression, but it is not useful anymore when there are jointly IQ(In-phase and Quadrature) imbalance and phase noise. Therefore, in this paper, we analyze the effect of IQ imbalance and phase noise generated in the down-conversion of the receiver. Then, we estimate and compensate the IQ imbalance and phase noise at the same time. Compared with the conventional method that IQ imbalance after IFFT is estimated and compensated in front of FFT via the feedback, this proposed method extracts and compensates effect of IQ imbalance after FFT stage. In case IQ imbalance and phase noise exist at the same time, we can decrease complexity because it is needless to use elimination of IQ imbalance in time domain and training sequences and preambles. Also, this method shows that it reduces the ICI and CPE component using adaptive forgetting factor of MMSE after FFT.

A new approach to Semi–Blind Channel Estimation (SBCE) technique for Multiple Input Multiple Output (MIMO) wireless communication system is proposed in this paper. It combines the least squares (LS) and Minimum Mean Square Error (MMSE) Training–Based Channel Estimation (TBCE) scheme with whitening rotation–based SBCE scheme. In this approach, the singular value decomposition has to be applied only once, thereby reducing the computational complexity. The channel correlation matrix required by MMSE technique can be obtained based on latest channel conditions. The performance of this scheme is compared with whitening rotation–based SBCE under various parameters such as modulation schemes, Signal–to–Noise Ratio (SNR) and frame length. The performance of the new approach is found to be better in terms of Bit Error Rate (BER) for high SNR, higher modulation order and smaller frame lengths. With low SNR, lower modulation order and larger frame lengths, there is negligible reduction in performance.

This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and combine the received multipath components of the transmitted symbols in the delay-Doppler grid using linear diversity combining schemes like maximal ratio combining (MRC), equal gain combining and selection combining to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in the vector form by placing some null symbols in the delay-Doppler grid thereby exploiting the block circulant property of the channel matrix. Using the new input-output relation we propose a low complexity iterative detector based on the MRC scheme. The bit error rate (BER) performance of the proposed detector will be compared with the state of the art message passing detector and orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer. We also show that the frame error rate (FER) performance of the MRC detector can be improved by employing error correcting codes operating in the form of a turbo decision feedback equalizer (DFE).

This paper discusses a cyclic prefixed single carrier frequency-domain equalization (SC-FDE) scheme with two types of transmit diversity. Firstly, we propose a SC-FDE system with space-frequency block coding (SFBC). The transmit sequence of the proposed system is designed to have spatial and frequency diversities, which is equivalent to the SFBC. The corresponding combining receiver is derived under a minimum mean square error (MMSE) criterion. It is shown that the proposed system significantly outperforms the SC-FDE system with space-time block coding (STBC) over fast fading channels, while providing lower computational complexity than orthogonal frequency division multiplexing (OFDM) combined with SFBC. We verify the performance of two-branch transmit diversity systems including the proposed one through bit error rate (BER) analysis. Secondly, as a scheme that combines STBC and SFBC, a space-time-frequency block code (STFBC) SC-FDE system is presented. Computer simulation results show that the proposed STFBC SC-FDE system has better immunity to the distortion caused by both fast fading and severe frequency selective fading, compared to the SC-FDE system with the STBC or the SFBC scheme. Complexity analysis is also conducted to compare their computational loads of the transceiver. It is shown that the proposed STFBC SC-FDE system has lower computational complexity than the STFBC OFDM system.

This paper presents some experimental results on both the channel estimation based minimum mean square error Turbo equalizer (CE MMSE-TEQ) and the direct-adaptation turbo equalizer (DA-TEQ) in single-input single-output (SISO) underwater acoustic (UWA) channels. For CE MMSE-TEQ, we compare the soft-decision feedback Turbo equalizer (SDFE), the bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) and the classic linear Minimum Mean Square Error (MMSE) Turbo equalizer in terms of bit error rate (BER) performance. For DA-TEQ, the recently proposed soft-decision direct-adaptation TEQ (Soft DA-TEQ) is evaluated with the same set of experimental data. Both QPSK and multilevel modulations (8PSK and 16QAM) have been tested with the symbol rate of 9.77 ksymbols/s. Experimental results show that the CE-TEQs are more robust in SISO underwater acoustic transmission under harsh channel conditions. Especially, with low pilot overheads, the recently proposed Bi-SDFE achieved low BER performance in all cases.

To approach the potential MIMO capacity while optimizing the system bit error rate (BER) performance, the joint transmit and receive minimum mean squared error (MMSE) design has been proposed. It is the optimal linear scheme for spatial multiplexing MIMO systems, assuming a fixed number of spatial streams p as well as a fixed modulation and coding across these spatial streams. However, state-of-the-art designs arbitrarily choose and fix the value of the number of spatial streams p, which may lead to an inefficient power allocation strategy and a poor BER performance. We have previously proposed to relax the constraint of fixed number of streams p and to optimize this value under the constraints of fixed average total transmit power and fixed spectral efficiency, which we referred to as spatial-mode selection. Our previous selection criterion was the minimization of the system sum MMSE. In the present contribution, we introduce a new and better spatial-mode selection criterion that targets the minimization of the system BER. We also provide a detailed performance analysis, over flat-fading channels, that confirms that our proposed spatial-mode selection significantely outperforms state-of-the-art joint Tx/Rx MMSE designs for both uncoded and coded systems, thanks to its better exploitation of the MIMO spatial diversity and more efficient power allocation.