Specification of downlink-fixed reference channel DL-FRC for 5G new radio technology

<p>The next generation for mobile communication is new radio (NR) that supporting air interface which referred to the fifth generation or 5G. Long term evolution (LTE), universal mobile telecommunications system (UMTS), and global system for mobile communication (GSM) are 5G NR predecessors, also referred to as fourth generation (4G), third generation (3G) and second generation (2G) technologies. Pseudo-noise (PN) code length and modulation technique used in the 5G technology affect the output spectrum and the payload of DL-FRC specification, in this paper quadrature phase shift keying (QPSK), 16 QAM modulation approaches tested under additive white Gaussian noise (AWGN) in term of bit error rate (BER) which used with 5G technology system implemented with MATLAB-Simulink and programing and, resulting of 1672, 12296 bit/slot payload at frequency range FR1 from 450 MHz-6 GHz and 4424, 20496 bit/slot payload at frequency range FR2 from 24.25 GHz-52.6 GHz, also determining subcarrier spacing, allocated source block, duplex mode, payload bit/slot, RBW (KHz), sampling rate (MHz), the gain and the bandwidth of main, side loop where illustrated.</p>

L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

Data-Driven and Model-Driven Joint Detection Algorithm for Faster-Than-Nyquist Signaling in Multipath Channels

In recent years, Faster-than-Nyquist (FTN) transmission has been regarded as one of the key technologies for future 6G due to its advantages in high spectrum efficiency. However, as a price to improve the spectrum efficiency, the FTN system introduces inter-symbol interference (ISI) at the transmitting end, whicheads to a serious deterioration in the performance of traditional receiving algorithms under high compression rates and harsh channel environments. The data-driven detection algorithm has performance advantages for the detection of high compression rate FTN signaling, but the current related work is mainly focused on the application in the Additive White Gaussian Noise (AWGN) channel. In this article, for FTN signaling in multipath channels, a data and model-driven joint detection algorithm, i.e., DMD-JD algorithm is proposed. This algorithm first uses the traditional MMSE or ZFinear equalizer to complete the channel equalization, and then processes the serious ISI introduced by FTN through the deepearning network based on CNN or LSTM, thereby effectively avoiding the problem of insufficient generalization of the deepearning algorithm in different channel scenarios. The simulation results show that in multipath channels, the performance of the proposed DMD-JD algorithm is better than that of purely model-based or data-driven algorithms; in addition, the deepearning network trained based on a single channel model can be well adapted to FTN signal detection under other channel models, thereby improving the engineering practicability of the FTN signal detection algorithm based on deepearning.

Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small remainder” property

The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

Generalized Receiver with Parallel Interference Cancellation for Multiuser Detection

Parallel interference cancellation is considered as a simple yet effective multiuser detector for direct -sequence code-division multiple-access (DS-CDMA) systems. However, system performance be deteriorated due to unreliable interference cancellation in the early stages. Thus, a detector with the partial parallel interfere-nce cancellation in which the partial cancellation factors are introduced to control the interference cancellation level has been developed as a remedy. Although the partial cancellation factors are crucial, complete solutions for their optimal values are not available. In this paper, we consider a two-stage decoupled generalized receiver with the partial parallel interference cancellation. Using the minimum bit error rate (BER) criterion, we derive a complete set of optimal partial cancellation factors. This includes the optimal partial cancellation factors for pe-riodic and aperiodic spreading codes in channels with the additive white Gaussian noise and multipath chann-els. Simulation results demonstrate that the considered theoretical optimal partial cancellation factors agree clo-sely with empirical ones. The proposed two-stage generalized receiver with the partial parallel interference can-cellation using the derived optimal partial cancellation factors outperforms not only a two-stage, but also a three-stage conventional generalized receiver with the full parallel interference cancellation.

Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small remainder” property

The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small division” property

The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).