Large Number Of Antennas Research Articles

Planning of Optical Connections in 5G Packet-Optical xHaul Access Network

One of the main challenges in dense 5G radio access networks (RANs) is provisioning of low-cost connectivity between a large number of antennas, located at remote sites, and a central site (hub) in which baseband processing functions are performed. Packet-switched Ethernet and wavelength division multiplexing (WDM) are two principal transport network technologies enabling the reduction of the demand for direct optical fiber connections between the antennas and the hub. Whereas Ethernet allows for statistical multiplexing of multiple xHaul (fronthaul/midhaul/backhaul) flows and their aggregation in a high-capacity transmission link, WDM makes it possible to establish a number of such links (using different wavelengths) in a single optical fiber. Additional savings in the amount of fibers required can be achieved by means of optical add-drop multiplexers (OADMs) that allow for obtaining access to unused wavelengths by intermediate remote nodes, whenever the capacity on the WDM system is not fully utilized by the end remote node. In this work, we focus on the problem of planning optimal fiber connections, including the placement of OADMs for a set of wavelength demands at remote sites, with the aim of minimizing the amount of fibers used in a packet-optical xHaul access network carrying 5G traffic. We consider a passive WDM system in which the maximum transmission distance, estimated using an optical power-budget model, depends on the number of OADMs that are present on the transmission path. To formulate and solve the optimization problem, we make use of integer linear programming (ILP). We apply the ILP model in network analysis. In particular, by means of numerical experiments performed for two different network topologies, we study the impact of traffic load (in terms of the number of requested wavelengths) and optical multiplexer loss on the number of transmission paths that have to be established in the network. Obtained results show that the savings in fiber connections of up to 65% can be achieved in a packet-optical xHaul network if OADMs are used when compared to the scenario without OADMs.

Deep learning for fast channel estimation in millimeter-wave MIMO systems

Channel estimation has been considered as a key issue in the millimeter-wave (mmWave) massive multi-input multioutput (MIMO) communication systems, which becomes more challenging with a large number of antennas. In this paper, we propose a deep learning (DL)-based fast channel estimation method for mmWave massive MIMO systems. The proposed method can directly and effectively estimate channel state information (CSI) from received data without performing pilot signals estimate in advance, which simplifies the estimation process. Specifically, we develop a convolutional neural network (CNN)-based channel estimation network for the case of dimensional mismatch of input and output data, subsequently denoted as channel (H) neural network (HNN). It can quickly estimate the channel information by learning the inherent characteristics of the received data and the relationship between the received data and the channel, while the dimension of the received data is much smaller than the channel matrix. Simulation results show that the proposed HNN can gain better channel estimation accuracy compared with existing schemes.

A Sparse Optimization Approach for Beyond 5G mmWave Massive MIMO Networks

Millimeter-Wave (mmWave) Massive MIMO is one of the most effective technology for the fifth-generation (5G) wireless networks. It improves both the spectral and energy efficiency by utilizing the 30–300 GHz millimeter-wave bandwidth and a large number of antennas at the base station. However, increasing the number of antennas requires a large number of radio frequency (RF) chains which results in high power consumption. In order to reduce the RF chain's energy, cost and provide desirable quality-of-service (QoS) to the subscribers, this paper proposes an energy-efficient hybrid precoding algorithm for mmWave massive MIMO networks based on the idea of RF chains selection. The sparse digital precoding problem is generated by utilizing the analog precoding codebook. Then, it is jointly solved through iterative fractional programming and successive convex optimization (SCA) techniques. Simulation results show that the proposed scheme outperforms the existing schemes and effectively improves the system performance under different operating conditions.

Energy-Efficient Resource Optimization for Massive MIMO Networks Considering Network Load

This paper investigates the resource optimization problem for a multi-cell massive multiple-input multiple-output (MIMO) network in which each base station (BS) is equipped with a large number of antennas and each base station (BS) adapts the number of antennas to the daily load profile (DLP). This paper takes into consideration user location distribution (ULD) variation and evaluates its impact on the energy efficiency of load adaptive massive MIMO system. ULD variation is modeled by dividing the cell into two coverage areas with different user densities: boundary focused (BF) and center focused (CF) ULD. All cells are assumed identical in terms of BS configurations, cell loading, and ULD variation and each BS is modeled as an M/G/m/m state dependent queue that can serve a maximum number of users at the peak load. Together with energy efficiency (EE) we analyzed deployment and spectrum efficiency in our adaptive massive MIMO system by evaluating the impact of cell size, available bandwidth, output power level of the BS, and maximum output power of the power amplifier (PA) at different cell loading. We also analyzed average energy consumption on an hourly basis per BS for the model proposed for data traffic in Europe and also the model proposed for business, residential, street, and highway areas.

Uplink Spectral Efficiency of Large, Distributed Antenna Systems With MMSE Processing

The spectral efficiency of a representative uplink in a wireless network with spatially distributed antennas and linear minimum-mean-square-error processing is found to approach an asymptote with a simple form as the number of antennas increases. These results generalize prior work which was applicable to systems with small numbers of base stations with large numbers of antennas each, to systems with large numbers of spatially distributed access points with small numbers of antennas each, and systems between these extremes. Additionally, these results are applied to systems where mobiles have multiple transmit antennas, and are used to characterize systems with both disjoint and user-centric clustering of cooperating base stations. Among other conclusions, these results indicate that with the same density and number of antennas cooperating to serve a mobile user, the uplink spectral efficiency with all antennas randomly distributed is several-fold higher than the case when the antennas are concentrated at one base station. These findings help improve our understanding of the tradeoffs involved in distributed antenna systems which have the potential to significantly increase data rates, but at a higher cost.

UHF RFID Indoor Localization Algorithm Based on BP-SVR

With the widespread of Internet of Things (IoT), Radio Frequency Identification (RFID) technology is used in various fields. In the complex indoor environment, the traditional RFID indoor localization algorithm cannot give superior performance. Because a large number of antennas cannot be deployed in practical applications, the dimension of the signal strength feature vector obtained is relatively low, and it is not easy to fully describe the information in the environmental field. Thus, must adopt the appropriate antenna placement structure, the phase difference information can be effectively used as the feature. In this paper, a method of indoor localization algorithm based on Back Propagation–Support Vector Regression (BP-SVR) is proposed, which takes the signal strength and phase difference of the RFID tag as the feature inputs and uses the hidden layer of the neural network to enhance the dimensionality of the data. Moreover, the Sequential Minimal Optimization (SMO) algorithm is used to increase the rate of model learning. The method was valid in a 2D scene. Experimental results show that the method has an average positioning error of 9.5cm in the indoor area of 6m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 8m.

Precoding and Beamforming Techniques in mmWave-Massive MIMO: Performance Assessment

Massive MIMO and mmWave communication are the technologies for achieving 5G design goals. Fortunately, these two technologies share a symbiotic integration. As a result, amalgamating mmWave communications with massive MIMO forms,mmWave-massive MIMO,” which significantly improves spectral and energy efficiency. It also achieves high multiplexing gains and increases mobile network capacity. However, massive MIMO, mmWave communications, and mmWave-massive MIMO systems have been studied independently. Consequently, this article explores the ideas, performances, comparisons, and discussions of these three 5G technologies jointly, considering their precoding and beamforming methods. On the other hand, the complexity of these technologies increases when a large number of antennas and radio frequencies (RFs) are used. Thus, several investigations are going on to search for the appropriate precoding and beamforming strategies with low cost, power, and complexity. Therefore, massive MIMO linear precoding techniques such as zero-forcing, maximum ratio transmission, regularized zero-forcing, truncated polynomial expansion and phased zero forcing are addressed in this work. In addition, the most common non-linear precoding schemes: dirty-paper coding, Tomlinson-Harashima, and vector perturbation, are presented. Furthermore, a detailed discussion of the beamforming techniques called analog, digital, and hybrid analog-digital beamforming schemes is included. We also examine the potential of hybrid analog-digital beamforming with its fully-connected and sub-connected architecture approaches in making mmWave massive MIMO a reality. We evaluate their performance with the parameters: bit error rate, signal to noise ratio, complexity, spectral efficiency, and energy efficiency. According to the analytical and simulation results, the partially-connected hybrid analog/digital beamforming architecture offers better all-over performance for mmWave-Massive MIMO communications by compromising: power consumption, cost, complexity, and performance. Finally, the potential future directions in mmWave-massive MIMO precoding and beamforming challenges are addressed.

An Efficient Machine Learning Based Precoding Algorithm for Millimeter-Wave Massive MIMO

Millimeter wave communication works in the 30–300 GHz frequency range, and can obtain a very high bandwidth, which greatly improves the transmission rate of the communication system and becomes one of the key technologies of fifth-generation (5G). The smaller wavelength of the millimeter wave makes it possible to assemble a large number of antennas in a small aperture. The resulting array gain can compensate for the path loss of the millimeter wave. Utilizing this feature, the millimeter wave massive multiple-input multiple-output (MIMO) system uses a large antenna array at the base station. It enables the transmission of multiple data streams, making the system have a higher data transmission rate. In the millimeter wave massive MIMO system, the precoding technology uses the state information of the channel to adjust the transmission strategy at the transmitting end, and the receiving end performs equalization, so that users can better obtain the antenna multiplexing gain and improve the system capacity. This paper proposes an efficient algorithm based on machine learning (ML) for effective system performance in mmwave massive MIMO systems. The main idea is to optimize the adaptive connection structure to maximize the received signal power of each user and correlate the RF chain and base station antenna. Simulation results show that, the proposed algorithm effectively improved the system performance in terms of spectral efficiency and complexity as compared with existing algorithms.

Attacker Detection in Massive MIMO Systems Over Spatially Uncorrelated Rician Fading Channels

Physical security is a potentially promising research direction for the fifth-generation and beyond networks. This paper investigates the physical layer security of massive multiple-input multiple-output (MIMO) spatially-uncorrelated Rician fading channels in time-division duplex mode. Relying on the fact that the propagation channels need to be estimated in practice to detect the desired signals in the uplink and construct the precoding vectors in the downlink, an active attack on the pilot training phase is potentially harmful to the wireless networks.We demonstrate how a jammer can attack in the training phase of Massive MIMO with spatially-uncorrelated Rician fading channels and show the scheme for detecting the presence of a jammer. Based on the fundamental properties of Massive MIMO communication, the network can treat the jamming effects as additive white Gaussian noise. A threshold to detect the existence of the active jammer is, therefore, computed in closed-form expression with a sufficiently large number of antennas at the base station. The key merit of our proposed method is that it only requires partial channel information and two training time slots to detect the jammer activity. Numerical results manifest the effectiveness of our proposed active jamming detection over various system parameter settings. Furthermore, the benefits of the dominant line-of-sight (LoS) components have been testified. In particular, the detection probability is improved by about 1.5 times with the presence of the LoS components, while the false-alarm probability gets improved by more than ten folds.

Performance Analysis of MIMO-NOMA Iterative Receivers for Massive Connectivity

The Fifth Generation (5G) of wireless networks introduced support to Machine-Type Communications (MTC), which is the wireless connectivity solution for Internet of Things (IoT) applications. MTC is split into two different categories: massive MTC (mMTC) and critical MTC (cMTC). Current 5G standards and technologies are not capable of fully satisfying the requirements of both mMTC and cMTC use cases, thus industry and academia have already started developing solutions for MTC in beyond-5G and 6G networks. In some mMTC use cases, receivers might not be equipped with a large number of antennas owing to cost, size or power limitations, thus the number of active devices in a time slot may surpass the number of antennas. Due to the limited spatial multiplexing capabilities, only multi-antenna techniques are not enough to provide connectivity to a massive number of devices in such scenarios. In this paper, we propose and evaluate the performance of iterative linear receivers that can address this issue. By combining Multiple-Input Multiple-Output (MIMO) techniques with Non-Orthogonal Multiple Access (NOMA) exploiting Successive Interference Cancellation (SIC) or Parallel Interference Cancellation (PIC) decoding, the proposed novel receivers are capable of performing dynamic ordering SIC/PIC decoding of multiple overlapping signals even when the number of active devices surpasses that of receive antennas. The performance of the receivers is studied in terms of outage probability and computational complexity. Simulation results show that, among all the receivers studied in this paper, the PIC-based Minimum Mean Square Error (MMSE) receiver presents the best performance while at the same time reducing the number of complex signal operations such as matrix inversions.

A Study on the Basics Processes of Massive MIMO

Massive Multiple Input Multiple Output (MIMO) is a key technique used in 5G mobile communication systems; it aims to efficiently increase the spectral efficiency of the communication systems. Massive MIMO is a MIMO system with a massive number of antennas in the base station, it uses its large number of antennas to efficiently transmit and receive the signals between the base stations and the user equipment and maximize the spectral efficiency of the system. Massive MIMO is mainly composed of three important processes: channel estimation, uplink transmission (receive beamforming), and downlink transmission (transmit beamforming). Based on the effective channel estimation methods, the base station can process the signal to make efficient transmit and receive beamforming and provide good transmission and reception quality, which is measured by the spectral efficiency of the system. Many references present the basics of massive MIMO processes, including channel estimation, transmit beamforming and receive beamforming. This paper aims to present a cleared and concluded study on these basics massive MIMO processes. It presents different channel estimation methods and evaluates its performance based on the normalized mean square error. It also presents different receive and transmit beamforming techniques and evaluates its performance based on spectral efficiency.

Power Allocation and Energy Cooperation for UAV-Enabled MmWave Networks: A Multi-Agent Deep Reinforcement Learning Approach.

Unmanned Aerial Vehicle (UAV)-assisted cellular networks over the millimeter-wave (mmWave) frequency band can meet the requirements of a high data rate and flexible coverage in next-generation communication networks. However, higher propagation loss and the use of a large number of antennas in mmWave networks give rise to high energy consumption and UAVs are constrained by their low-capacity onboard battery. Energy harvesting (EH) is a viable solution to reduce the energy cost of UAV-enabled mmWave networks. However, the random nature of renewable energy makes it challenging to maintain robust connectivity in UAV-assisted terrestrial cellular networks. Energy cooperation allows UAVs to send their excessive energy to other UAVs with reduced energy. In this paper, we propose a power allocation algorithm based on energy harvesting and energy cooperation to maximize the throughput of a UAV-assisted mmWave cellular network. Since there is channel-state uncertainty and the amount of harvested energy can be treated as a stochastic process, we propose an optimal multi-agent deep reinforcement learning algorithm (DRL) named Multi-Agent Deep Deterministic Policy Gradient (MADDPG) to solve the renewable energy resource allocation problem for throughput maximization. The simulation results show that the proposed algorithm outperforms the Random Power (RP), Maximal Power (MP) and value-based Deep Q-Learning (DQL) algorithms in terms of network throughput.

Low‐rank matrix fitting based channel estimation for full‐dimensional massive MIMO systems

Full-dimensional (FD) massive MIMO can overcome the limitation of the physical space at the base station (BS) and meet the increasing capacity requirement for future wireless communications. However, the pilot overhead for the acquisition of the channel state information (CSI) at the BS could be prohibitively high due to the large number of antennas. In this letter, exploiting the Kronecker property of the channel, we propose a low-rank matrix fitting based channel estimation (LMFCE) scheme to reduce the pilot overhead in FD massive MIMO systems. The simulation results illustrate that the proposed LMFCE scheme can significantly reduce the pilot overhead for the channel estimation.

Codebook-Based Hybrid Beamforming Using Combined Phase Shifters of High and Low Resolutions

The hybrid beamforming architecture where a combination of analog and digital precoders is employed has attracted much attention recently for its flexible trade-off between power consumption and performance. A codebook-based beamforming scheme is generally considered as a more practical solution rather than the adaptive beamforming schemes due to the large number of antennas. However, the constant amplitude constraint brought by the phase shifters (PSs) in the analog precoder always makes the codebook design problem a tricky and complicated one. In this work, we consider a novel combined PS (CPS) architecture where one high-resolution PS is connected to each RF chain in parallel with low-resolution PSs to each antenna. The corresponding codebook design aiming for ideal flat beam gains is then proposed for the CPS architecture. Simulation results reveal that the proposed scheme achieves a good trade-off between performance and energy efficiency compared with conventional single PS (SPS) and the recently proposed double PS (DPS) architecture.

RCSA Protocol with Rayleigh Channel Fading in Massive-MIMO System

Introduction: Massive MIMO is a process where cellular BSs a large number of antennas. In this study, we concern about the end-to-end massive-MIMO system under the Rayleigh channel fading effect. Also, it includes both inter-channel interference and intra channel interference in an m-MIMO network system. Method: The major aim is to increase the throughput and network capacity as well as minimizing the channel collision in between the associated pilots. Here, we proposed an RCSA protocol with Rayleigh channel fading effect in the m-MIMO network to create a network like a real-time scenario. Here we have focused on the deployment of urban scenarios with the small timing variation and provided our novel RAP for the UEs, where the UEs want to access the network. To validate the performance of our proposed scheme we are going to compare with the state-of-art technique in the result analysis section. Result: We provide the analysis based upon the two considered scenarios; such as scenario-A considered at intra-channel interference and whereas in scenario-B considered both intra-cell channel interference as well as inter-cell channel interference. Where our RCSA approach is proposed with uncorrelated Rayleigh fading channels (URFC) that used to increase the capacity of network and decrease the collision probability. Conclusion: Here, we proposed the RCSA approach and it consist of four major steps such as; system initialization and querying; response queuing; resource contention and channel state analysis and, resource allocation. The system performs in the TDD mode of operation and the resources of time-frequency are divided into the coherent blocks of channel Discussion: In order to compare our RCSA-URFC approach, here we consider the state-of-art technique such as vertex graph-coloring-based pilot assignment (VGCPA) [35] under URFC. In addition we also consider the bias term randomly to make decision on particular UE. It very difficult to guess the strong probability of UE, therefore as per information obtained via

Surveying on MIMO Technology for Future Wireless Communication

Massive MIMO is an extension of traditional MIMO with the exception that the BSs in massive MIMO are equipped with large number of antennas, usually hundred or more. This large number of antennas provide several positive advantages towards wireless communication with respect to increasing volume of data traffic. Each antenna is capable of serving multiple users simultaneously leading to reduction in power consumption as well as data rate amplification. Additionally, narrow and more focused beams are pointed to individual user devices located at the cell edge thereby upgrading of downlink signal quality. Using massive MIMO technique also increases reliability of the links, reduces noise effects, and mitigates and interference. With increasing number of users gets service, the throughput of the system also increases.

Manifold Discriminative Learning Inspired Hybrid Beamforming for Millimeter-Wave Massive MIMO Systems

Millimeter-wave (mmWave) massive MIMO (multiple-input multiple-output) is a promising technology as it provides significant beamforming gains and interference reduction capabilities due to the large number of antennas. However, mmWave massive MIMO is computationally demanding, as the high antenna count results in high-dimensional matrix operations when conventional MIMO processing is applied. Hybrid precoding is an effective solution for the mmWave massive MIMO systems to significantly decrease the number of radio frequency (RF) chains without an apparent sum-rate loss. In this paper, we propose user clustering hybrid precoding to enable efficient and low-complexity operation in high-dimensional mmWave massive MIMO, where a large number of antennas are used in low-dimensional manifolds. By modeling each user set as a manifold, we formulate the problem as clustering-oriented multi-manifolds learning. The manifold discriminative learning seek to learn the embedding low-dimensional manifolds, where manifolds with different user cluster labels are better separated, and the local spatial correlation of the high-dimensional channels within each manifold is enhanced. Most of the high-dimensional channels are embedded in the low-dimensional manifolds by manifold discriminative learning, while retaining the potential spatial correlation of the high-dimensional channels. The nonlinearity of high-dimensional channel is transformed into global and local nonlinearity to achieve dimensionality reduction. Through proper user clustering, the hybrid precoding is investigated for the sum-rate maximization problem by manifold quasi conjugate gradient methods. The high signal to interference plus noise ratio (SINR) is achieved and the computational complexity is reduced by avoiding the conventional schemes to deal with high-dimensional channel parameters. Performance evaluations show that the proposed scheme can obtain near-optimal sum-rate and considerably higher spectral efficiency than some existing solutions

Efficient Technique for PAPR and BER Reduction in Downlink Large Scale MU-MIMO-OFDM System

Background &amp; Objective: The Orthogonal Frequency Division Multiplexing (OFDM) based large scale multiuser multiple input multiple output (LS-MU-MIMO) system is a preferred choice for signal transmission because it can substantially enhance the spectral and energy efficiency of the next-generation wireless systems. However, there are several practical issues in implementing large multiuser-MIMO-OFDM systems and one of the critical issues is the high Peak-to-Average- Power Ratio (PAPR). Due to the use of a large number of antennas at the Base Station (BS) of an LSMU- MIMO-OFDM system, it requires a large number of Power Amplifiers (PAs) which are needed to be connected to each antenna element. The high PAPR in an OFDM based LS-MU-MIMO system results in the decrease in the efficiency of PAs and enhancement in nonlinear signal distortions. This work is concerned with the reduction in PAPR of LS-MU-MIMO-OFDM systems using the SCFDMA scheme for the downlink transmission. The reduction in PAPR is achieved on the basis of discrete Fourier transform spreading (DFT-S) scheme known as DFT-SC-FDMA. The SC-FDMA scheme can achieve the reduction in PAPR of MIMO-OFDM signal up to the level of single-carrier transmission. Further, the reduction in PAPR is achieved with the sub mapping schemes such as localized FDMA (LFDMA) and distributed FDMA (DFDMA), Interleaved FDMA (IFDMA). Result: In this work, we propose to perform jointly multiuser MMSE precoding, SC-IFDMA and antenna reservation technique to reduce the PAPR and Bit Error Rate (BER) of the large MU-MIMO system. To show the effectiveness of the proposed scheme in the reduction of PAPR with different modulation techniques, subcarriers, and subcarrier mapping schemes, the results are compared with the existing OFDM based large MU-MIMO system. Conclusion: The MATLAB simulation results confirm that our proposed combination of MMSE MUprecoding, SC-IFDMA and antenna reservation technique is able to reduce PAPR and BER to a significant extent for LS-MU-MIMO-OFDM systems.

Planar Array Failed Element(s) Radiation Pattern Correction: A Comparison

Phased arrays are widely used in different fields, such as broadcasting, radar, optics, and space communications. The principle of phased arrays is to generate a directed signal from a large number of antennas to be steered at any desired angle. This, however, increases the probability of defective elements in an array. Faulty elements in an array cause asymmetry and result in increased sidelobe levels which rigorously distort the radiation pattern. Increased sidelobe radiation wastes energy and can cause interference by radiating and receiving signals in unintended directions. Therefore, it is necessary to find a method that can provide accuracy in the radiation pattern transmitted or received in the presence of failed element(s) in an array. This paper compares the few available optimization methods, namely, simulated annealing (SA), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Pattern Search (PS) methods. For each method, various types of failures were examined, and the most suitable techniques to recover the far-field radiation are recommended. The optimization is then carried out by selecting the optimal weights of the remaining working elements in the planar array. The optimized radiation pattern’s efficiency was evaluated by comparing the Signal to Noise Ratio (SNR) value of the optimized radiation with reference and failed radiation patterns. The PSO method showed a better performance compared to all the other methods in reducing the failed radiation pattern’s SNR value. In various types of failure tests, this method reduced the failed radiation pattern’s SNR from 1 to 10 dB. This method also successfully produced a radiation pattern that closely matches the reference pattern before any failed element(s) are presented in the array. The life cycle of a planar array system with faulty elements can be increased by optimizing the remaining active elements in the array with the PSO method. It also reduces the cost of restoring and replacing the failed elements in an array regularly. This approach also prevents near-field measurement that requires complicated processes using costly equipment.

Application of Deep Learning to Sphere Decoding for Large MIMO Systems

Although the sphere decoder (SD) is a powerful detector for multiple-input multiple-output (MIMO) systems, it has become computationally prohibitive in massive MIMO systems, where a large number of antennas are employed. To overcome this challenge, we propose fast deep learning (DL)-aided SD (FDL-SD) and fast DL-aided $K$-best SD (KSD, FDL-KSD) algorithms. Therein, the major application of DL is to generate a highly reliable initial candidate to accelerate the search in SD and KSD in conjunction with candidate/layer ordering and early rejection. Compared to existing DL-aided SD schemes, our proposed schemes are more advantageous in both offline training and online application phases. Specifically, unlike existing DL-aided SD schemes, they do not require performing the conventional SD in the training phase. For a $24 \times 24$ MIMO system with QPSK, the proposed FDL-SD achieves a complexity reduction of more than $90\%$ without any performance loss compared to conventional SD schemes. For a $32 \times 32$ MIMO system with QPSK, the proposed FDL-KSD only requires $K = 32$ to attain the performance of the conventional KSD with $K=256$, where $K$ is the number of survival paths in KSD. This implies a dramatic improvement in the performance--complexity tradeoff of the proposed FDL-KSD scheme.