Space-time Line Code Research Articles

Space-Time Line Code Hopping for Physical-Layer Secure Communications

Space-Time Line Code Hopping for Physical-Layer Secure Communications

Full-Rate Space-Time Line Code With Asymptotic SNR Gain

In this letter, we introduce a novel quasi-orthogonal full-rate space-time line code (FR-QSTLC) for an arbitrary number of transmit antennas and four receiver antennas. Its fully analytical examination and the benchmark of full-rate STLCs are provided, and the results are compared in terms of average bit error ratio (ABER) and diversity gain. Due to its quasi-orthogonal properties, the proposed FR-QSTLC exhibits an asymptotic SNR gain of up to 3 dB compared to its orthogonal two-antenna counterpart and outperforms all the other linearly-decoded full-rate STLCs.

Blind symbol and carrier synchronization with carrier frequency offset estimation for space–time line coded systems

In this study, utilizing the structure of the space–time line code (STLC) signals, a blind symbol and carrier synchronization method considering the carrier frequency offset (CFO) is developed. The proposed method can achieve almost perfect synchronization performance with more than three transmit antennas, irrespective of the CFO values. Based on the results, the proposed blind symbol and carrier synchronization method is expected to accelerate the practical deployment and operation of the low-complexity STLC systems that achieve full spatial diversity gain with partial or no channel state information at the receiver.

Cooperative space-time line code for relay-assisted internet of things

We propose a novel cooperative space–time line code (C-STLC) scheme to improve performance of a relay-assisted internet of things (R-IoT). The proposed C-STLC operates with fully distributed manner, where each relay IoT device (RID) attempts to decode the received signal from a source IoT device at the first hop and the RIDs, that succeeded decoding, send the STLC encoded signal based on their local channel state information (CSI) to a single access point (AP) at the second hop. Then, the AP decodes the received signals without CSI. As a main result, we mathematically analyze the outage probability (OP) of the proposed C-STLC scheme. It is shown that the proposed C-STLC significantly outperforms conventional cooperative relaying techniques in terms of the OP.

Intelligent Reconfigurable Surface-Aided Space-Time Line Code for 6G IoT Systems: A Low-Complexity Approach

Intelligent reconfigurable surfaces (IRS) have attracted much attention from both industry and academia due to their performance improving capability and low complexity for 6G wireless communication systems. In this letter, we introduce an IRS-assisted space-time line code (STLC) technique. The STLC was introduced as a promising technique to acquire the optimal diversity gain in 1×2 single-input multiple-output (SIMO) channel without channel state information at receiver (CSIR). Using the cosine similarity theorem, we propose a novel phase-steering technique for the proposed IRS-assisted STLC technique. We also mathematically characterize the proposed IRS-assisted STLC technique in terms of outage probability and bit-error rate (BER). Based on computer simulations, it is shown that the results of analysis shows well match with the computer simulation results for various communication scenarios.

Reconfigurable Intelligent Surface Assisted Space-Time Line Code for SIMO Transmission

In this contribution, we investigate reconfigurable intelligent surface assisted space-time line code (RIS-STLC) transmission for enhancing the signal quality when the direct link between the transmitter and receiver is blocked. In the context of intelligent transmission by RIS, the concept of index modulation (IM) is integrated into the pursuit of higher spectral efficiency, while a two-step detection is developed to improve the performance. Correspondingly, for blind transmission where the channel information at RIS is not available, the phase at RIS not associated with the channel is considered. Subsequently, the bit-error-rate (BER) performances of the proposed RIS-STLC system conditioned on both the intelligent and blind transmission are quantified. Theoretical analysis and simulation results demonstrate the effectiveness of the development of RIS-STLC.

Linear Precoding for Space-Time Line Code-Based Multicast Systems

In this article, a linear precoding weight vector is designed to enhance the minimum signal-to-interference plus noise ratio (SINR) of a space-time line code (STLC)-based multicast users. To solve the intractable minimum SINR maximization problem, the optimal weight vector for each STLC user is derived, and then, the individual optimal weight vectors are linearly combined. The designed linear precoding vector improves the minimum and average SINR of the multicast users as verified by numerical results. Numerical results also verify that the STLC-based multicast is a promising scheme, especially, if a transmitter has a large number of transmit antennas and the additive noises are severe at the users.

Modified Block Coordinate Descent Method for Intelligent Reflecting Surface-Aided Space-Time Line Coded Systems

The intelligent reflecting surface (IRS) technology can be combined with the space-time line code (STLC) to reduce the channel estimation overhead for adjusting the IRS phase shifts. However, the computational complexity to design the phase shift values of IRS elements can increase prohibitively with the increment of IRS elements. To reduce the design complexity for the IRS-aided STLC system, we propose a modified block coordinate descent (MBCD) algorithm that can simply design the phase shift values of the IRS. The proposed MBCD algorithm can dramatically reduce the computational complexity with no compromise of performance compared to the various existing methods, such as a semidefinite relaxation method, an alternating direction method of multipliers, an analytic constant modulus algorithm, and a complex unit-modulus constraint relaxation method.

Ergodic Capacity of Space–Time Line Code Systems With Transmit Antenna Selection

Since a novel diversity technique called a space–time line code (STLC) was invented, previous studies have focused on the analysis of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate-1</i> STLC assuming <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two</i> receive antennas. For the state-of-the-art STLCs with transmit antenna selection (TAS), in this study, the ergodic capacities of TAS-STLC systems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">various code rates</i> are mathematically derived, not only for a TAS-STLC system with two receive antennas but also for those with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">three</i> or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">four</i> . To this end, the probability density function of the instantaneous signal-to-noise ratio was characterized. The accuracy of the mathematical analysis was validated by a numerical simulation. This study is significant for investigating the fundamental performance of TAS-STLC systems.

Artificial-Noise-Aided Space–Time Line Code for Enhancing Physical Layer Security of Multiuser MIMO Downlink Transmission

We consider secure downlink multiple-input–multiple-output (MIMO) communications between a transmitter and multiple users when there exists a passive eavesdropper. A downlink main channel between the transmitter and a user is estimated through uplink pilot symbols in a time-division duplex mode. On the other hand, to hinder an eavesdropper from estimating the eavesdropper channel between the transmitter and the eavesdropper, the transmitter does not send any pilot symbols. The main channel is hence available at the transmitter only, while the eavesdropper channel is unavailable at any node. Assuming these channel state information (CSI) conditions, we propose a MIMO transmission method using space–time line code (STLC) with artificial noise (AN) for enhancing the physical layer security. The STLC enables noncoherent detection at the receiver, i.e., a user, without CSI and achieves full spatial diversity. We derive the lower bound of the secrecy sum rate for the proposed STLC transmission method without AN, with AN, and with AN and imperfect CSI. Moreover, numerical results verify that the proposed STLC scheme outperforms the conventional eigen-beamforming and the precoding space-time block code in terms of secrecy sum rate regardless of the signal-to-noise ratio, the number of transmit antennas, and the CSI uncertainty.

Full-Rate Space–Time Line Code for Four Receive Antennas

For multiple-input multiple-output systems with four receive antennas, conventional space–time line codes (STLCs) have supported code rates of 3/4, 4/7, and 1/2. To provide a wider range of transmission rates, we herein propose a rate-1 STLC for four-receive-antenna systems. We present an encoding method to achieve full rate and devise a simple decoding scheme that does not require full channel state information at the receiver. Assuming a large number of transmit antennas, we analyze the bit error rate performance and demonstrate that the proposed STLC can achieve full spatial diversity.

Intelligent Reflecting Surface-Aided Space–Time Line Coded Systems

In this study, an intelligent reflecting surface (IRS)-aided space–time line code (STLC) system is examined to efficiently extend its coverage area. The IRS phase-shift values of each element can be designed using a semidefinite relaxation (SDR) method to maximize the received signal-to-noise ratio of the IRS-STLC systems. A unit-modulus constraint relaxation (UCR) method is proposed to reduce the computational complexity of the SDR method. The numerical results verify that the proposed UCR-based IRS can achieve comparable bit-error-rate performance to the SDR-based IRS, albeit with significantly reduced computational complexity. Owing to the proposed IRS, the coverage area can be significantly extended.

Rotated Golden Codewords Based Space-Time Line Code Systems

The space-time line code (STLC) has been recently proposed in the literature. In STLC systems, the channel state information is assumed to be known at the transmitter, but not at the receiver. In the conventional STLC systems, the inputs of the STLC encoder are either M-ary phase shift keying symbols or M-ary quadrature amplitude modulation symbols and can achieve diversity order with very low detection complexity. In order to further improve the error performance of the STLC systems, in this paper, rotated Golden codewords based STLC (RGC-STLC) systems are proposed.We extend the 1&#x00D7;2 and 2 &#x00D7; 2 transmit-receive antenna structure in the conventional STLC into 1 &#x00D7; 4 and 2 &#x00D7; 4 transmit-receive antenna structures in the proposed RGC-STLC system. The inputs of the proposed RGC-STLC encoder are the rotated Golden codewords. Compared to the conventional 1 &#x00D7; 2 and 2 &#x00D7; 2 STLC systems, the 1 &#x00D7; 4 and 2 &#x00D7; 4 RGC-STLC systems achieve a higher diversity order. Based on the feature of the rotated Golden codewords, low complexity detection schemes for the 1 &#x00D7; 4 and 2 &#x00D7; 4 RGC-STLC systems are further proposed. Finally, the union bounds on the average symbol error probability for the 1 &#x00D7; 4 and 2 &#x00D7; 4 RGC-STLC systems are derived and shown to match the simulation results very well at high signal-to-noise ratios.

Performance Analysis of Uplink NOMA With Constellation–Rotated STLC for IoT Networks

We investigate the uplink non-orthogonal multiple access (NOMA)-based Internet-of-Things (IoT) networks, where each IoT device (station: STA) equipped with a single antenna exploits the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constellation-rotated</i> space-time line code (CR-STLC) to send signals to an access point (AP) equipped with two receive antennas. The AP decodes the signals transmitted from the STAs with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimal</i> joint maximum-likelihood (JML) detector. As a main result, we mathematically analyze both the bit-error-rate (BER) performance and the spatial diversity order of each STA in the two-user uplink CR-STLC NOMA system. In particular, it is shown that the two-user uplink CR-STLC NOMA system achieves the optimal diversity order regardless of the constellation rotation angle in the high signal-to-noise ratio (SNR) regime. We also consider two different rotation angle optimization techniques (dynamic rotation & fixed rotation) to improve the BER performance in the practical SNR regime, and found that the fixed rotation approach is simple but yields almost the same performance as the dynamic approach. Finally, we show that the uplink CR-STLC NOMA system achieves the spatial diversity order of 1 even when more than two STAs send packets simultaneously. It is worth noting that all STAs obtain an improved spatial diversity gain compared to that without constellation rotation.

Efficient User Subset Selection for Multiuser Space-Time Line Code Systems

This paper considers the problem of user subset (US) selection for minimizing the bit error rate (BER) of multi-user space-time line code (MU-STLC) multiple-input multiple-output systems with fairness-aware per-user power allocation. The optimal selection criterion suitable for MU-STLC transmissions based on zero forcing (ZF) precoding is given and two efficient algorithms are then proposed. First, an incremental search approach is presented for US selection in the MU-STLC systems. The proposed suboptimal solution to BER minimization starts an empty US and adds users one by one, where the low-complexity recursive computation of the block matrix inverse is further performed. Second, by avoiding recurring matrix computations in each incremental procedure of the first algorithm, a more efficient algorithm is developed. It is observed through simulation results that the proposed incremental-based algorithms achieve most US selection gains with very low complexity. In addition, it is demonstrated that when there are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{T} $ </tex-math></inline-formula> transmit antennas, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> users (each user has 2 receive antennas), and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> selected users, the achievable upper diversity order of the ZF precoding-based MU-STLC systems with optimal US selection is given as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2(N_{T} -K+1)(U-K+1)$ </tex-math></inline-formula> . The analytical diversity order is well-matched with simulation results.

Performance Analysis of Space-Time Line Code in Correlated Fading Channels

Recently, the idea of space-time line code (STLC) was developed in [1] as an efficient way to increase the diversity of multiple-input multiple-output (MIMO) communications, with a special code structure that exploits the channel state information (CSI) at the transmitter. In this paper, in order to evaluate the performance of STLC in practical transmission environment, we analyse the bit-error rate (BER) performance of STLC in the context of correlated Rayleigh and Rician fading MIMO channels. Finally, simulation results validate the accuracy of the above theoretical analysis.

Efficient Transmit Antenna Subset Selection for Multiuser Space-Time Line Code Systems.

We consider the problem of the efficient transmit antenna subset (TAS) selection for maximizing the signal-to-interference-plus-noise ratio (SINR) of multiuser space–time line code (MU–STLC) systems. The exhaustive search for optimal TAS selection is impractical since the total number of transmit antennas increases. We propose two efficient TAS selection schemes based on the Woodbury formula. The first is to incrementally select active transmit antennas among the available transmit antennas. To reduce the complexity of the incremental selection scheme, the Woodbury formula is employed in the optimization process. The second is to perform the decremental strategy in which the Woodbury formula is also applied to develop the low-complexity TAS selection procedure for the MU–STLC systems. Simulation results show that the proposed incremental and decremental TAS selection algorithms offer better alternatives than the existing greedy TAS selection algorithm for the MU–STLC systems. Furthermore, in terms of bit error rate, the proposed minimum mean square error decremental TAS selection algorithm turns out to outperform the existing greedy algorithm with significantly lower computational complexity. Finally, we analyze the detection SINR penalty experienced from TAS selection and the analytical quantity is shown to be well matched with simulation results.

Generalized Space–Time Line Code With Receive Combining for MIMO Systems

In this article, a generalized space–time line code (GSTLC) is proposed. The proposed GSTLC concurrently transmits multiple data streams obtained by space–time line code encoding and precoding to provide spatial multiplexing and diversity. When full channel state information (CSI) is available to the transmitter and limited CSI is available to the receiver, an optimal precoding matrix is derived for GSTLC with linear combining that is based on the minimum mean square error (MMSE) criterion. Moreover, the detection signal-to-interference-plus-noise ratio (SINR) is derived corresponding to the optimal MMSE precoder. Using the SINR, we propose a receiver combining scheme that selects the best combining matrix, thereby minimizing the bit error rate (BER) from a codebook that includes candidate combining matrices. Through numerical simulations, we demonstrate that the proposed GSTLC with the optimal combiner achieves the theoretical lower bound of BER. In addition, we show that the GSTLC with combiner selection performs better than conventional precoded spatial multiplexing methods in terms of the BER.

Over-the-Air Computation Strategy Using Space–Time Line Code for Data Collection by Multiple Unmanned Aerial Vehicles

In this study, we investigated a data collection system for multiple unmanned aerial vehicles (UAVs) in the sky. To reduce the required data collection time for a time-division multiple access (TDMA)-based protocol, an over-the-air computation (OAC) strategy was employed, and the average values of data computed. In this method, multiple single-antenna sensing UAVs (sUAVs) report the sensing data to a two-antenna data-collection UAV (dUAV) through the OAC strategy. To this end, we propose an efficient OAC strategy using a space-time line code (STLC) scheme that can achieve a full spatial diversity gain. Using the efficient data collection protocol of the proposed STLC-OAC strategy, the overall operation time for data collection can be significantly reduced relative to s TDMA-based strategy. Furthermore, the proposed STLC-OAC strategy can reduce the normalized mean square error (NMSE) of the estimated average value of the data relative to that of the TDMA-based method. As the gap in the NMSEs between TDMA- and STLC-OAC-based strategies was observed to increase as the number of sUAVs increased, it can be concluded that the proposed STLC-OAC strategy is advantageous for UAV-based data collection systems, especially when a large number of sUAVs report the sensing data.

Bandwidth Design for Energy-Efficient Unmanned Aerial Vehicle Using Space–Time Line Code

In this paper, considering a seamless control of an unmanned aerial vehicle (UAV) by a ground base station (GBS), the energy consumption of the UAV is minimized in the downlink communication from the GBS with multiple antennas to the UAV with two antennas. By exploiting the benefit of a space–time line code (STLC) scheme that does not require training for full channel estimation at the receiver, i.e., the UAV, we employ the STLC scheme and design the passband bandwidth. Precisely, the number of symbols within the given frame duration is designed to reduce the total energy consumption at the UAV for the given data volume. With the designed frame, we numerically verify that the proposed STLC-based UAV consumes less energy than a UAV employing the maximum eigen beamforming scheme when optimized in terms of the received signal-to-noise ratio.