Cyclic Prefixed Single Carrier Research Articles

Channel Estimation and Multipath Diversity Reception for RIS-Empowered Broadband Wireless Systems Based on Cyclic-Prefixed Single-Carrier Transmission

In this paper, a cyclic-prefixed single-carrier (CPSC) transmission scheme with phase shift keying (PSK) signaling is presented for broadband wireless communications systems empowered by a reconfigurable intelligent surface (RIS). In the proposed CPSC-RIS, the RIS is configured according to the transmitted PSK symbols such that different cyclically delayed versions of the incident signal are created by the RIS to achieve multipath diversity. A practical and efficient channel estimator is developed for CPSC-RIS and the mean square error of the channel estimation is expressed in closed-form. We analyze the bit error rate (BER) performance of CPSC-RIS over frequency-selective Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channels. An upper bound on the BER is derived by assuming maximum-likelihood detection. Furthermore, by applying the concept of index modulation (IM), we propose an extension of CPSC-RIS, termed CPSC-RIS-IM, which enhances the spectral efficiency. In addition to conventional constellation information of PSK symbols, CPSC-RIS-IM uses the full permutations of cyclic delays caused by the RIS to carry information. A sub-optimal receiver is designed for CPSC-RIS-IM to aim at low computational complexity. Our simulation results in terms of BER corroborate the performance analysis and the superiority of CPSC-RIS(-IM) over the conventional CPSC without an RIS and orthogonal frequency division multiplexing with an RIS.

Performance Analysis of Orthogonal Multiplexing Techniques for PLC Systems with Low Cyclic Prefix Length and Symbol Timing Offset.

This paper investigates the degradation caused by interference resulting from cyclic prefix violation and symbol timing offset in narrowband power line communication systems. In this sense, it presents a unified formulation from which Hermitian symmetric orthogonal frequency division multiplexing (HS-OFDM), orthogonal chirp division multiplexing (OCDM), single-carrier cyclic prefix (SCCP), and orthogonal time-frequency division multiplexing (OTFDM) can be easily derived. The paper then provides closed-form expressions for quantifying the aforementioned interference in the presence of a frequency domain equalizer. The numerical analyses exhibit the performances of these schemes under various data communication conditions, such as the availability of channel state information, the presence or absence of interference, modeling of additive noise as a white or colored Gaussian random process, frequency domain equalizer type, and the use of bit and power allocation techniques. The closed-form expressions and performance analyses regarding achievable data rate and bit error probability provide guidance for dealing with distinct constraints in narrowband power line communication (PLC) systems using the HS-OFDM, OCDM, SCCP, or OTFDM scheme. Lastly, the unified formulation and results obtained motivate the design of multi-scheme transceivers.

QR Decomposition-Based Cyclic Prefixed Single-Carrier Transmissions for Cooperative Communications: Concepts and Research Landscape

As an alternative transmission scheme to orthogonal frequency division multiplexing (OFDM), cyclic prefixed single-carrier (CP-SC) transmissions have been widely adopted to overcome the shortcomings of OFDM. How to exploit the achievable full diversity in frequency selective fading channels is the key question in applying CP-SC-based transmissions. Thus, in this tutorial, we focus on recent research in the areas related to CP-SC transmissions for cooperative wireless systems. After explaining the basic concept and operation of CP-SC transmissions, we introduce various types of diversity that are achievable by CP-SC transmissions. To achieve these types of diversity, it is necessary to employ QR decomposition (QRD)-M-based data detection in the receiver. To verify the benefits of CP-SC transmissions in terms of diversity gain, we exemplify various wireless systems for relaying, spectrum sharing, physical layer security, and distributed cyclic delay diversity, and provide link-level simulations. Especially, as alternative metrics of reliability, which is one of the key features of 5G and beyond 5G (B5G) systems, we evaluate the average symbol error rate and outage probability. Finally, we discuss potential research directions involving CP-SC transmissions in emerging wireless communication systems.

Anchor-Aided Channel Estimation for RIS-Assisted Multiuser Broadband Communications

Due to the passive nature of reconfigurable intelligent surface (RIS) and a large number of users, it is very challenging to estimate the cascaded base station (BS)-RIS-user channel directly, especially for multiuser broadband communication systems. In this letter, we propose a novel two-phase method to estimate multiuser broadband cascaded channels with the assistance of two anchor nodes. Specifically, in the first phase, the cascaded channel from the two anchors to the BS and that between two anchors are estimated to acquire the BS-RIS channel state information (CSI) with sign ambiguities. It is accomplished based on cyclic-prefixed single-carrier transmission and phase configuration at the RIS, which creates multiple cyclic delayed versions of transmitted signals for isolating all broadband channel taps. In the second phase, the RIS-user channel and subsequently the cascaded BS-RIS-user channel are estimated in the frequency domain using the knowledge of the partial BS-RIS CSI. Simulation results verify the superiority of the proposed scheme over the state-of-the-art methods in terms of estimation overhead, normalized mean-squared error and bit error rate.

New Statistical Results of Partial Sums of Ordered Gamma-Distributed RVs for Performance Evaluation of Wireless Communication Systems

With the increase in the complexity of communication systems, order statistics have become increasingly significant in performance evaluation, especially for advanced diversity techniques over fading channels. However, existing analytical approaches are not useful owing to their high complexity. In this paper, we present novel and insightful statistical results of the partial sums of ordered Gamma-distributed random variables. By adopting a unified analytical framework to obtain the desired joint probability density function from the joint moment-generating function, we redefine and derive the common key functions specialized for the Gamma distribution. The derived formula is presented in the form of either general closed-form expressions or at least a single integral form instead of the originally complicated multiple-integral form. In terms of a feasible application of our results, we present a complete and general closed-form analysis of the statistics of the combined received signal-to-noise ratio of the distributed cyclic delay diversity with the cyclic prefix single-carrier scheme. We also show that our analytical results can provide potential mathematical solutions for other wireless communication systems. Selected numerical examples are presented and discussed to illustrate the effectiveness of the applied approach and related results. All the derived analytical results were compared and verified by using Monte Carlo simulations to verify the accuracy of our analysis.

Cyclic Delay Diversity With Index Modulation for Green Internet of Things

Cyclic delay diversity (CDD) is a simple and yet effective transmit diversity technique. Thanks to its strong power saving capability, CDD is very promising for green Internet of Things (IoT) networks. However, the reduced degrees of freedom in data transmission and the overhead of cyclic prefix lead to unsatisfactory spectral efficiency (SE), hindering the direct application of CDD to IoT networks where short-packet communication prevails. To tackle this problem, in this article, we propose to convey additional information via the varying cyclic delays for improving the SE of the CDD system based on the concept of index modulation (IM), which applies to both OFDM and cyclic-prefixed single-carrier (CPSC) signals. The methods to generate all possible cyclic delays and the optimal receivers are designed for both proposed systems. To aim at low computational complexity, we further propose a suboptimal receiver for the CDD-CPSC-IM system. Moreover, a closed-form upper bound on the bit error rate (BER) of the CDD-OFDM-IM system is derived, from which the coding gain is characterized. Simulation results in terms of BER corroborate the analysis and the superiority of the proposed systems over the pure CDD-OFDM and CDD-CPSC systems, uncovering the potential of CDD in the application to green IoT networks.

A dCDD-Based Transmit Diversity Scheme for Downlink Pseudo-NOMA Systems

In this paper, a new transmit diversity scheme is proposed for cooperative pseudo-non-orthogonal multiple access (Pseudo-NOMA) without assuming full channel state information at the transmitter (CSIT). To support two users under the near-far user pairing constraint, a distributed cyclic delay diversity (dCDD) scheme is adapted into NOMA by dividing a set of remote radio heads (RRHs) into two groups for multiple cyclic-prefixed single carrier transmissions. To maximize a far user's rate and two users' sum rate over independently but non-identically distributed frequency selective fading channels and under a near-far user pairing constraint, we first derive closed-form expressions for the rates of the two users with full CSIT. Considering that only partial CSIT is available, a new RRH assignment and power allocation scheme is proposed for dCDD-Pseudo-NOMA. For various simulation scenarios, the provided link-level simulations verify that higher rates can be achieved by dCDD-Pseudo-NOMA compared with the traditional orthogonal multiple access with dCDD and dCDD-Conventional-NOMA that uses the superimposed signals. Furthermore, the proposed RRH assignment and power allocation scheme makes dCDD-Pseudo-NOMA achieve almost the same rate as that of ideal dCDD-Pseudo-NOMA which requires full CSIT.

Diversity Gain Analysis of Distributed CDD Systems in Non-Identical Fading Channels

This paper investigates the diversity gain of a distributed cyclic delay diversity (dCDD) scheme for cyclic-prefixed single carrier systems in non-identical fading channels. Non-identical small-scale fading is assumed in the environment, in which non-identical line-of-sight and non-line-of-sight fading coexist. A condition for dCDD resulting in intersymbol interference free reception at the receiver, is extended to this new channel environment. For an overpopulated system setup, a generalized performance analysis, is not available from existing works, is conducted after developing closed-form expressions for the distribution of the signal-to-noise ratio (SNR) realized at the receiver. Since the order statistics are involved in the statistical properties of the SNR, the corresponding spacing statistics are utilized to derive feasible closed-form expressions. The finalized closed-form expressions are shown to provide very reliable outage probability and spectral efficiency of dCDD for underpopulated and overpopulated systems. An asymptotic performance analysis verifies the maximum achievable diversity of the dCDD even in the overpopulated case within the considered channel environment. Link-level simulations are conducted and these verify the maximum achievable diversity gain.

Joint Radar-Communication With Cyclic Prefixed Single Carrier Waveforms

In recent years, software defined radio and digital signal processing have been widely used in communication and radar. As a result, the hardware and RF front-end for radar and wireless communication tends to be similar. Thus, using the same RF and hardware platform for joint radar-communication becomes viable. Joint radar-communication would bring more efficient plan and usage for the radio spectral resource. Furthermore, it could enable new applications that require information exchange and precise localization at the same time. In this paper, cyclic prefixed single carrier (CP-SC) and its variations are chosen as the waveforms for joint radar-communication. CP-SC waveform and its variations are popular in wireless communication and have been chosen by a few standards like IEEE 802.11ad and LTE-advanced. Efficient algorithms are proposed to use such waveforms for range and speed detection/estimation of targets. The proposed algorithms are derived from the maximum likelihood (ML) principle and have low computational complexity. Simulations show that the estimation performance of the proposed method is almost the same as that of ML and is much better than that of the channel estimation based method.

BER Performance of Signal Detection for Massive Multi User Spatial Modulation Systems

Massive spatial modulation (MSM) is considered as an attractive technique for multi antenna wireless communications. That is because, it gives higher energy efficiency and spectral efficiency than small scale multiple-input multiple-output (MIMO) systems. Massive SM-MIMO utilizes multiple transmit antennas for each user with only one transmit radio frequency (RF) chain and hundreds of receive antennas at base station (BS) with small number of RF chain. Where, each user can activate any one of its transmit antennas and the index of active transmit antenna (TA) can convey to information bits in addition to the information bits conveyed through classical modulation symbols (e.g. 16QAM). Owing to large number of TAs at the user and small number of RF chains at BS, multi user signal detection becomes challenging problem. To solve this matter, a joint grouped SM transmission scheme at users and group subspace pursuit (GSP) based signal detection at BS can be proposed to improve the signal detection performance. Owing to joint transmission scheme, SM signals in same transmission group exhibit group sparsity. Also, spatial signal composed of multiple users’ SM signals exhibits distributed sparsity. By utilizing these sparse features, the proposed GSP based signal detection can detect SM signals more reliability than other detection techniques. Additionally, the cyclic prefix single carrier (CPSC) is utilized to withstand the multipath channels. Simulation results prove that BER performance of the proposed GSP based signal detection outperforms classical SP based signal detection by 8 dB SNR gain at BER = 10−2. This gain can be improved by 2 dB by increasing the number of transmit antenna.

Optimal Pilot Design and Error Rate Analysis of Block Transmission Systems in the Presence of Channel State Information (CSI) Estimation Error

This work proposes novel techniques toward the design of optimal pilot sequences to perform channel estimation in block transmission systems over wideband frequency selective wireless fading channels. The framework developed is based on minimization of the Bayesian Cramer-Rao bound (BCRB) for the mean squared error (MSE) of the channel state information (CSI) estimate. Optimal pilot signals are determined for the four predominant classes of block transmission systems, viz. single carrier zero padding (SC-ZP), multi-carrier zero padding (MC-ZP), single carrier cyclic prefix (SC-CP) and multi-carrier cyclic prefix (MC-CP) systems. This makes the techniques developed general in nature and thus applicable in a wide variety of block transmission systems. As part of this study, succinct expressions and results are also derived to characterize the error rate performance, incorporating also the effect of CSI estimation error resulting due to the proposed algorithms. Finally, numerical results obtained via Monte-Carlo simulation are presented to illustrate and compare the CSI acquisition performance of optimal pilot designs with that of conventional designs and also validate the theoretical analysis for the error rate performance.

OTFS Performance on Static Multipath Channels

Orthogonal time frequency space (OTFS) modulation is known to achieve excellent error performance in delay–Doppler channels. However, its performance over static multipath channels has never been fully investigated. In this letter, we show that, in static multipath channels, the system structure of OTFS is equivalent to the asymmetric orthogonal frequency division multiplexing (A-OFDM), a scheme proposed by Zhang et al. , bridging between cyclic prefix single carrier (CPSC) and traditional OFDM. We derive a condition on the parameters of OTFS to guarantee that all the transmitted symbols experience uniform channel gains, as in CPSC. Finally, we apply a low-complexity message passing detection to OTFS/A-OFDM and show a significant performance improvement over ZF and MMSE detection originally proposed for A-OFDM.

Secrecy Analysis of Distributed CDD-Based Cooperative Systems With Deliberate Interference

In this paper, a cooperative cyclic-prefixed single carrier (CP-SC) system is studied and a scheme to improve its physical layer security is proposed. In particular, a distributed cyclic delay diversity (dCDD) scheme is employed and a deliberate interfering method is introduced, which degrades the signal-to-interference-plus-noise ratio (SINR) over the channels from a group of remote radio heads (RRHs) to an eavesdropper, while minimizing the signal-to-noise ratio loss over the channels from the RRHs to an intended user. This is obtained by selecting one RRH that acts as an interfering RRH and transmits an interfering artificial noise sequence to the eavesdropper. Through the use of the dCDD scheme, a channel that minimizes the receive SINR at the eavesdropper is selected for the interfering RRH. This choice enhances the secrecy rate of the CP-SC system. The system performance is evaluated by considering the secrecy outage probability and the probability of non-zero achievable secrecy rate, which are formulated in closed-form analytical expressions for the case of identically and non-identically distributed frequency selective fading channels. Based on the proposed analytical framework, the diversity order of the system is studied. Monte Carlo simulations are employed to verify the analytical derivations for numerous system scenarios.

Secrecy Performance of Finite-Sized In-Band Selective Relaying Systems With Unreliable Backhaul and Cooperative Eavesdroppers

This paper investigates the secrecy performance of a finite-sized in-band selective relaying system with $M$ transmitters connected via unreliable backhaul links, $N$ decode-and-forward relays, and $K$ collaborative eavesdroppers. To send the source message to the destination, a transmitter-relay pair that achieves the highest end-to-end signal-to-noise ratio is selected for transmissions, while the $K$ eavesdroppers combine all the received signals from the selected transmitter and relay using maximal ratio combining. The proposed model introduces backhaul reliability and eavesdropping probability parameters to investigate practical constraints on the transmitter-relay cooperation and eavesdropper collaboration, respectively. Closed-form expressions are derived for the secrecy outage probability, probability of non-zero achievable secrecy rate, and ergodic secrecy rate for non-identical frequency-selective fading channels with robust cyclic-prefixed single carrier transmissions. These results show that the asymptotic secrecy outage probability and probability of non-zero achievable secrecy rate are exclusively determined by the number of transmitters $M$ and their corresponding set of backhaul reliability levels. Under unreliable backhaul connections, it is found that the secrecy diversity gain is determined by $M$ , $N$ , and the number of multipath components in the frequency selective fading channels. Link-level simulations are conducted to verify the derived impacts of backhaul reliability and collaborative eavesdropping on the secrecy performance.

Performance Analysis of Distributed Single Carrier Systems With Distributed Cyclic Delay Diversity

This paper investigates a distributed cyclic delay diversity (CDD) transmission scheme for cyclic-prefixed single carrier systems in non-identically and identically distributed frequency selective fading channels. The distinguishable feature of the proposed scheme lies in providing a transmit diversity gain while reducing the burden of estimating the channel state information, which is a challenging task in distributed and cooperative systems. To effectively use the distributed CDD scheme at the transmitters, two sufficient conditions are derived to eliminate the intersymbol interference at the receiver and leveraged to convert the multi-input single-output channel into a single-input single-output channel. These conditions allow the system to achieve the maximum diversity for frequency selective fading channels at a full rate. To achieve this maximum diversity, a fixed number of CDD transmitters are selected based on the channel conditions, symbol block size, and maximum time dispersion of the channel, and a new two-stage transmission mode is proposed. Based on the distributed CDD and the proposed selection schemes, a new expression for the signal-to-noise ratio at the receiver is obtained with the aid of order statistics, and then closed-form expressions for the outage probability and average symbol error rate (ASER) are derived. As far as the identically distributed frequency selective fading channel model is concerned, the achievable maximum diversity gain is proved, with the aid of asymptotic analysis, to be equal to the product of the total number of transmitters in the system and the number of multipath components. Link-level simulations are also conducted to validate the analytical expressions for outage probability, ASER, and maximum achievable diversity gain.

Decision Directed Multiple-Relay Diversity Detector in Asynchronous Cooperative Communication Systems

In this paper, decision directed spatial diversity combining algorithm is presented for asynchronous cooperative communication systems with amply-and-forward relays in frequency flat fading channels. Cyclic prefix assisted single carrier transmission combined with joint frequency domain equalization is carried out to obtain the initial detection solution. Based on that, spatial diversity is employed to improve the performance, where every relayed component in the received signal is decoupled using linear interference cancellation technique, and then the components are synchronized and combined together, so the diversities supplied by the asynchronous relays are acquired. Numerical simulations show the effectiveness of the proposed algorithm.

Orthogonal Time/Frequency Multiplexed Modulation Families for Software Defined Radio

The uplink and downlink transmissions in Long-Term Evolution (LTE) systems are performed using single-carrier and multicarrier modulation schemes, respectively. To respond such trend, orthogonal time-multiplexed modulation (OTMM) is proposed as several new single-carrier modulation families originated from the orthogonal multiplexed modulation (OMM) families to provide low peak-to-average power ratio and versatile modulations with different degrees in power and bandwidth efficiencies. To further facilitate a software defined radio (SDR) implementation, the proposed OTMM families are incorporated into the original OMM family in a unified signal structure. Typical basis sets are also unified to suit an SDR implementation. To establish a unified modulation platform, the present study therefore proposes a set of orthogonal time-multiplexed modulation (OTMM) families to complement the existing set of orthogonal multiplexed modulation (OMM) schemes. The OTMM and OMM families are integrated in a software defined radio (SDR) modulation structure by means of a common signal model and five unified basis sets. The resulting structure supports both time multiplexing and frequency multiplexing, and therefore offers greater flexibility in improving the power and bandwidth efficiencies of the LTE system. The proposed structure thus attends throughput and signal robustness simultaneously in hostile environments and also provides versatile choices in modulations with low peak-to-average power ratio. Keywords: Bandwidth efficiency, cyclic-prefixed single-carrier modulation, LTE system, orthogonally multiplexed modulation, software defined radio, time multiplexing.

Compressive-Sensing-Based Multiuser Detector for the Large-Scale SM-MIMO Uplink

Conventional spatial modulation (SM) is typically considered for transmission in the downlink of small-scale MIMO systems, where a single one of a set of antenna elements (AEs) is activated for implicitly conveying extra bits. By contrast, inspired by the compelling benefits of large-scale MIMO (LS- MIMO) systems, here we propose a LS-SM-MIMO scheme for the uplink (UL), where each user having multiple AEs but only a single radio frequency (RF) chain invokes SM for increasing the UL-throughput. At the same time, by relying on hundreds of AEs but a small number of RF chains, the base station (BS) can simultaneously serve multiple users whilst reducing the power consumption. Due to the large number of AEs of the UL-users and the comparably small number of RF chains at the BS, the UL multi-user signal detection becomes a challenging large-scale under-determined problem. To solve this problem, we propose a joint SM transmission scheme and a carefully designed structured compressive sensing (SCS)-based multi-user detector (MUD) to be used at the users and BS, respectively. Additionally, the cyclic- prefix single-carrier (CPSC) is used to combat the multipath channels, and a simple receive AE selection is used for the improved performance over correlated Rayleigh-fading MIMO channels. We demonstrate that the aggregate SM signal consisting of SM signals of multiple UL-users in one CPSC block appears the distributed sparsity. Moreover, due to the joint SM transmission scheme, aggregate SM signals in the same transmission group exhibit the group sparsity. By exploiting these intrinsically sparse features, the proposed SCS-based MUD can reliably detect the resultant SM signals with low complexity. Simulation results demonstrate that the proposed SCS-based MUD achieves a better signal detection performance than its counterparts even with higher UL-throughtput.

Secrecy Performance of Finite-Sized Cooperative Single Carrier Systems With Unreliable Backhaul Connections

In this paper, the secrecy performance of finite-sized cooperative cyclic prefixed single carrier systems with multiple eavesdroppers and unreliable wireless backhaul connections across multiple transmitters is investigated. For nonidentical frequency-selective fading channels between the relay and destination nodes, secrecy performance metrics including the secrecy outage probability, ergodic secrecy rate, and probability of nonzero achievable secrecy rate are derived. Furthermore, the existence of performance limits on the secrecy outage probability and probability of non-zero achievable secrecy rate are verified for various backhaul scenarios. These limits are found to be exclusively determined by the backhaul reliability. For imperfect backhaul connections, it is found that the diversity gain promised by cooperative cyclic prefixed single-carrier systems cannot be achieved in the conventional asymptotic high signal-to-noise ratio region. Link-level simulations are conducted to verify the derived impact of backhaul reliability on the secrecy performance.

Broadband PLC‐channel equalisation in the frequency domain based on complementary sequences

Multipath channels, like power lines, have a periodic time-variant response that impacts on data transmission. Power Line Communications (PLC) performance, in the context of a cyclic-prefix single carrier modulation scheme, can benefit from frequency domain equalisation techniques. This study proposes a frequency-domain dynamic characterisation and equalisation algorithm based on the properties of complementary sequences (CSs). This proposal takes advantage of CS properties to reduce the complexity of the algorithm by performing all the operations in the frequency domain, and without the necessity of noise/variance estimators. The proposal is compared to some well-known methods like zero forcing and minimum mean-square error (MMSE) through the transmission of data under different PLC channels. Bit error rate (BER) is also measured using Middleton Class A impulse noise (IN) model and the performance of all methods is finally evaluated under a time-variant PLC channel model showing the importance of dynamic equalisation on PLC systems. Reported computational resources and simulations show that the proposal is four time faster than MMSE and improves the BER performance by up to 4 dB. In addition, the proposed identification algorithms shows to work properly even in PLC channels with attenuations higher than 40 dB and severe IN scenarios.