This correspondence is a response to Comments on the above article raised by Wen et al. (2023). The authors in Wen et al. (2023) insist that there might be some errors in the Kalman filter derivation procedure, mathematical expression, and computability of high-order error terms in Ko et al. (2022). However, the arguments are not always true. The authors in Wen et al. (2023) misunderstood the derivation of the Kalman filter by the assumption of an unbiased estimator. In addition, they also misunderstood the assumption of noise distribution for the Kalman filter design. In this correspondence, we analyze and refute the comments in a pointby-point fashion.

This work presents a design study of an antenna for future railway communications in the context of Internet of Things (IoT). 28-GHz resonance frequency has been considered for the 5G communication systems with end-fire radiations. The size of the proposed antenna array element is 100 mm$\times20$mm. The shark-fin cover is used to cover the antenna to protect it from the external environmental effects. The proposed antenna along with the 1.3-GHz bandwidth centered at 28 GHz results an expected end-fire radiation ($\theta =83^{\circ }$), with a gain of >10 dBi and its suitability to be installed on the roof of the train for communications to the front and back directions along with the track has been studied and discussed in detail.

Positioning is the most basic yet important process in a train control system. In practical train systems, the position of a train is determined with a track circuit, a radio frequency (RF) tag called a “balise”, or a tachometer. A train control center gives each train an automatic train protection (ATP) speed profile computed from the positioning information of both the train and the next train in front it. To successfully operate in a conventional train control system such as ATP/ATO, each train derives its own automatic train operation (ATO) speed profile from the ATP speed profile provided by the control center. However, existing train positioning schemes face many difficulties in terms of installation, maintenance, and repair. To address these difficulties, we consider using 5G NR (New Radio) signals which have a high probability for guaranteeing line-of-sight (LOS) as well as a high sampling rate because they do not require the additional installation of any infrastructure for positioning. In this paper, we propose two positioning schemes for high speed trains (HSTs) based on Kalman filters that make use of 5G NR signals. The first is an HST positioning scheme using a modified Kalman filter and the second is an HST positioning scheme using a deep Kalman filter. Simulation results show that the two proposed schemes achieve better performance in nonlinear non-Gaussian systems as well as in nonlinear Gaussian systems in terms of mean and worst 5% position errors when compared to the existing positioning scheme for HSTs that utilize 5G NR signals.

In conventional multi-user MIMO systems, Shannon capacity has been used mostly as the performance measure for user selection. In this paper, we propose two new MIMO scheduling techniques based on BER instead of capacity as the performance measure for rate maximization with target BER. One of the key contributions of this paper is to use BER instead of capacity as the user selection metric, and another is the novel power allocation techniques considering user scheduling for the rate maximization strategy. Simulation results show that the proposed BER based algorithms produce higher rate compared to the conventional capacity based user selection algorithm with much lower computational complexity as well as the schemes meet target BER.

It has been well known that channel aware systems (closed-loop) have better performance than channel unknown systems (open-loop). In order to know channel in the transmitter, receivers should send own channel information the transmitter through reverse channel. However, the channel information should be fed back in Frequency Division Duplexing (FDD) additionally since forward link channel and reverse link channel are different each other. In FDD, the channel information is usually quantized as a codebook and each receiver feedback the best codeword index within the codebook by any metric generally. The codebook has the characteristic that as codebook size is larger system performance increases but computational complexity to find the best codeword also increases exponentially in conventional codebook structure. In this paper, we propose some codebook design schemes which have hierarchical structure to overcome the complexity problem as well as achieves near-optimal performance.

The multiuser MIMO (MU-MIMO) systems tend to have inter-user interference in practical systems with limited feedback. Practical MU-MIMO systems with limited feedback can be divided into two classes in general. One is zero-forcing beamforming (ZFBF), and the other is per user unitary rate control (PU2RC) which is an extended version of random beamforming (RBF). To improve performance, ZFBF needs more feedback bits, and PU2RC needs a larger number of users. We propose a new hybrid MU-MISO system which has the advantages of the two MU-MIMO schemes simultaneously, and analyze the sum-rate performance and the quantization error of the hybrid scheme. The analysis shows how the number of feedback bits, the number of users, and the signal power affect the sum-rate. The throughput scaling laws are also derived in the high and the medium SNR regimes. Simulation results show that the proposed hybrid MU-MISO system performs better than either of the two MU-MIMO systems with the same number of feedback bits. Another advantage is that it has lower complexity for codeword search since it has a hierarchical codebook structure.

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.

Multi-antenna downlink system with limited feedback can provide enormous capacity gains. In practical, two systems can be considered. One is zero-forcing beamforming (ZFBF), and the other is per user unitary rate control (PU2RC) which has been proposed for emerging cellular standards. In order to have good performance, ZFBF requires many feedback bits, and PU2RC requires many users. Recently, the authors proposed a hybrid multi-user MISO system which has merits of those two schemes simultaneously. In this paper, we analyze the sum-rate performance and quantization error of the hybrid scheme. The throughput scaling laws are also derived in high and medium SNR regimes.

In a multiuser MIMO cellular system where there are many candidate users, it is critical to select a user group which maximizes the overall throughput of the system. However, the optimal scheduling strategy is computationally prohibitive when the total number of users is large. In this paper, we propose a determinant based user selection algorithm which reduces the search complexity without much performance degradation. In order to reduce pilot overhead by precoding matrix for multiuser MIMO, we also propose a new pilot scheme with only one set of pilot, and the new pilot scheme is combined with the proposed scheduling algorithm. Simulation results show that the proposed scheduling algorithm with a new pilot scheme reduces computational complexity and pilot overhead with negligible performance degradation compared to the exhaustive scheduling with a conventional pilot scheme which uses two sets of pilots.

In this paper, we analyze channel quality indicator (CQI) mismatch probabilities of multiuser orthogonal random beamforming (ORBF) systems. First, we derive the CQI mismatch probability of the ORBF system with M transmit antennas and K users equipped with one receive antenna. Using that result, we also derive the upper and lower bounds of the per user unitary and rate control (PU2RC) system with 2 transmit antennas and K users equipped with one receive antenna, which is being adopted in the IEEE 802.16m standard. Finally, we compare theoretical results with numerical results from simulation.

This paper presents closed-form expressions of the distribution of signal-to-interference-plus-noise ratios (SINRs) and the average bit error rate (BER) for an orthogonal random beamforming system in multiple-antenna Gaussian broadcast channels. First, we derive the statistical distribution of the SINR of the scheduled transmit signals and confirm that the approximate form of the cumulative distribution function (cdf) of the SINR is equivalent to the formula in \cite{sharif} and \cite{letaief}. We then obtain a closed-form expression for the total average BER of the system by using the approximate cdf. Our theoretical results are compared to the Monte Carlo simulation results.

It has been shown that multiuser MIMO systems have better capacity performance than single-user MIMO systems. For a large number of users, the transmitter selects a subset of users with good channels to maximize the system performance. Shannon capacity has been used most of the time as the performance measure for multiuser MIMO systems. In this paper, we consider BER as an alternative performance metric, and propose two new user selection algorithms with block diagonalization (BD), which eliminates inter-user interference in a multiuser MIMO system. The first approach is BER minimization with fixed rate, and the second approach is rate maximization with fixed target BER. Simulation results show that the proposed algorithms produce lower BER and/or higher rate when they are compared to the conventional capacity based multiuser MIMO user selection algorithm with comparable computational complexity.

Multiuser MIMO (MU-MIMO) system with limited feedback can be divided into two classes generally. One is zero-forcing beamforming (ZFBF), and the other is per user unitary rate control (PU2RC) which is an extended technique of random beamforming (RBF). However, in order to perform well, ZFBF requires many feedback bits, and PU2RC requires many users. These drawbacks of the existing MU-MIMO systems limit system performance in real environment. In this paper, we propose a new MU-MISO system which has merits of two MU-MIMO schemes simultaneously. Simulation results show the new MU-MISO system has good performance with simple feedback and low complexity user selection.