Sufficient Cyclic Prefix Research Articles

Reduced-state maximum-likelihood detection for OFDM systems with insufficient cyclic prefix

Dispersive channels deteriorate the bit error rate (BER) performance of orthogonal frequency-division multiplexing (OFDM) systems with insufficient cyclic prefix (CP). In this paper, we first analyze the intensity of the intersymbol interference (ISI) and intercarrier interference (ICI). For performance enhancement, an effective maximum-likelihood (ML) detection method, named reduced-state maximum-likelihood (RSML), is proposed to detect all target subcarriers parallelly. For each target subcarrier, the proposed RSML detects a few nearby subcarriers jointly, while the remaining subcarriers are directly determined by using pre-detection values. Simulations results show that the proposed RSML achieves a significant performance improvement in terms of BER compared to the existing detection methods and is robust to various channel models and CP lengths. In particular, for certain channel conditions with insufficient CP, the detection performance of RSML is even better than conventional detection with sufficient CP because additional frequency diversity gain is obtained from joint detection at the expense of complexity.

Performance Evaluation of OFDM System with Insufficient CP Using LMS Equalizer under Harsh Multipath Conditions

This paper presents an insufficient cyclic prefix (CP) Orthogonal Frequency Division Multiplexing (OFDM) system with equalizer whose coefficients are calculated using Least Mean Square (LMS) algorithm. The OFDM signal is passed through a channel with four multipath signals which cause the OFDM signal to be under high inter-symbol interference (ISI) and inter-carrier interference (ICI).8-QAM and 16-QAM digital modulation techniques are used to evaluate the performance of the proposed system. The simulation results have accentuated the high performance of the LMS equalizer via comparing its Bit Error Rate (BER) and constellation diagram with those of the Minimum Mean Square Error and Zero Forcing equalizers. Moreover, the results also reveal that the LMS equalizer provides BER performance close to that of the OFDM system with a hypothetical sufficient CP.

CP‐based OFDM radar–communications signal using interval linear phase compression modulation

In this study, a signal design algorithm for radar–communications system is investigated. An arbitrary pulse length orthogonal frequency-division multiplexing with sufficient cyclic prefix (CP-based OFDM) signal is designed as the radar–communications signal, the communication symbols are embedded by proposing an interval linear phase compression (ILPC) modulation. Firstly, the authors construct the model of CP-based OFDM signal, and analyse the impact of the communication symbols embedding. Then, to decrease the impact caused by the communication symbols embedding, the ILPC modulation is proposed. To guarantee the performances of the CP-based OFDM radar–communications signal, a time/frequency domain iterative filtering and clipping method is used. This algorithm can be used to design a CP-based OFDM signal that has a balanced performance in communications and radar. Finally, numerical results are provided to verify the validity of the proposed algorithm.

IRCI-Free CP-OFDM SAR Signal Processing

Recent literature shows that with sufficient cyclic prefix, orthogonal frequency-division multiplexing signals can convert a synthetic aperture radar (SAR) image with interrange cell interference (IRCI) to an IRCI-free SAR image. In this letter, the imaging algorithm is carefully investigated and it is shown that the range reconstruction accuracy can be further improved. By reformulating the system model in a linear model form, the minimum variance unbiased estimator of the range profile is derived, which can attain the Cramer–Rao lower bound, making our algorithm more effective than current algorithms under noisy conditions. Simulation results validate the advantages of the proposed algorithm, especially under low signal-to-noise ratio conditions.

Artificial Intelligence-Aided Receiver for a CP-Free OFDM System: Design, Simulation, and Experimental Test

Orthogonal frequency division multiplexing (OFDM), usually with sufficient cyclic prefix (CP), has been widely applied in various communication systems. The CP in OFDM consumes additional resource and reduces spectrum and energy efficiency. However, channel estimation and signal detection are very challenging for CP-free OFDM systems. In this paper, we propose a novel artificial intelligence (AI)-aided receiver (AI receiver) for a CP-free OFDM system. The AI receiver includes a channel estimation neural network (CE-NET) and a signal detection neural network based on orthogonal approximate message passing (OAMP), called OAMP-NET. The CE-NET is initialized by the least-square channel estimation algorithm and refined by a linear minimum mean-squared error neural network. The OAMP-NET is established by unfolding the iterative OAMP algorithm and adding several trainable parameters to improve the detection performance. We first investigate their performance under different channel models through extensive simulation and then establish a real transmission system using a 5G rapid prototyping system for an over-the-air (OTA) test. Based on our study, the AI receiver can estimate time-varying channels with a single training phase. It also has great robustness to various imperfections and has better performance than those competitive algorithms, especially for high-order modulation. The OTA test further verifies its feasibility to real environments and indicates its potential for future communications systems.

Channel Estimation and Data Detection for Insufficient Cyclic Prefix MIMO-OFDM

In this paper, we propose an iterative structure for channel estimation and data detection for multiple-input–multiple-output orthogonal frequency-division multiplexing systems (MIMO-OFDM) with insufficient cyclic prefix (CP) and a limited number of pilot subcarriers. Insufficient CP leads to increased intersymbol interference (ISI) and intercarrier interference (ICI). The interference corrupts pilot subcarriers used for channel estimation and affects the detection process. We propose a multistep channel estimation process, which is assisted by a small number of pilot subcarriers. First, the channel covariance matrix and the number of channel paths are acquired from the channel least square estimates at the pilot subcarriers. We then formulate a maximum likelihood process to approximate the time-domain channel. For data detection, a high-performance bidirectional M-algorithm (BDMA) is proposed for trellis-based equalization. Simulation results show that the channel estimate mean square error converges to the Cramer–Rao bound (CRB) after a few iterations. In addition, the achieved bit error rate (BER) can reach that of the sufficient CP case, even when the delay spread is much longer than the CP.1

CP-based MIMO OFDM radar IRCI free range reconstruction using real orthogonal designs

In this paper, we propose a range reconstruction method for a frequency-band shared multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) radar with sufficient cyclic prefix (CP) by using real orthogonal designs. Compared with the application of complex orthogonal designs in our previous work, the application of real orthogonal designs can significantly reduce the number of the all-zero-valued pulses in a coherent processing interval (CPI) for each transmitter and increase the efficiency of radar transmitters. Meanwhile, it still maintains the advantages of full spatial diversity without inter-range-cell interference (IRCI). We also apply the rate-$1$ real orthogonal designs for different numbers of transmitters and pulses for range reconstruction without any idleness of radar transmitters. Simulation results are presented to illustrate the performances of the OFDM pulse design and the CP-based MIMO OFDM radar using real orthogonal designs.

MIMO OFDM radar IRCI free range reconstruction with sufficient cyclic prefix

In this paper, we propose MIMO OFDM radar with sufficient cyclic prefix (CP), where all OFDM pulses transmitted from different transmitters share the same frequency band and are orthogonal to each other for every subcarrier in the discrete frequency domain. The orthogonality is not affected by time delays from transmitters. Thus, our proposed MIMO OFDM radar has the same range resolution as single transmitter radar and achieves full spatial diversity. Orthogonal designs are used to achieve this orthogonality across the transmitters, with which it is only needed to design OFDM pulses for the first transmitter. We also propose a joint pulse compression and pulse coherent integration for range reconstruction. In order to achieve the optimal SNR for the range reconstruction, we apply the paraunitary filterbank theory to design the OFDM pulses. We then propose a modified iterative clipping and filtering (MICF) algorithm for the designs of OFDM pulses jointly, when other important factors, such as peak-to-average power ratio (PAPR) in time domain, are also considered. With our proposed MIMO OFDM radar, there is no interference for the range reconstruction not only across the transmitters but also across the range cells in a swath called inter-range-cell interference (IRCI) free that is similar to our previously proposed CP based OFDM radar for single transmitter. Simulations are presented to illustrate our proposed theory and show that the CP based MIMO OFDM radar outperforms the existing frequency-band shared MIMO radar with polyphase codes and also frequency division MIMO radar.

Joint Compensation of Transmitter and Receiver IQ Imbalance in OFDM Systems Based on Selective Coefficient Updating

In this paper, a selective coefficient updating (SCU) approach at each branch of the per-tone equalization (PTEQ) structure has been applied for insufficient cyclic prefix (CP) length. Because of the high number of adaptive filters and their complex adaption process in the PTEQ structure, SCU has been proposed. Using this method leads to a reduction in the computational complexity, while the performance remains almost unchanged. Moreover, the use of set-membership filtering with variable step size is proposed for a sufficient CP case to increase convergence speed and decrease the average number of calculations. Simulation results show that despite the aforementioned algorithms having similar performance in comparison with conventional algorithms, they are able to reduce the number of calculations necessary. In addition, compensation of both the channel effect and the transmitter/receiver in-phase/quadrature-phase imbalances are achievable by these algorithms.

OFDM Synthetic Aperture Radar Imaging With Sufficient Cyclic Prefix

The existing linear frequency modulated (LFM) (or step frequency) and random noise synthetic aperture radar (SAR) systems may correspond to the frequency hopping (FH) and direct sequence (DS) spread spectrum systems in the past second and third generation wireless communications. Similar to the current and future wireless communications generations, in this paper, we propose OFDM SAR imaging, where a sufficient cyclic prefix (CP) is added to each OFDM pulse. The sufficient CP insertion converts an inter-symbol interference (ISI) channel from multipaths into multiple ISI-free subchannels as the key in a wireless communications system, and analogously, it provides an inter-range-cell interference (IRCI) free (high range resolution) SAR image in a SAR system. The sufficient CP insertion along with our newly proposed SAR imaging algorithm particularly for the OFDM signals also differentiates this paper from all the existing studies in the literature on OFDM radar signal processing. Simulation results are presented to illustrate the high range resolution performance of our proposed CP based OFDM SAR imaging algorithm.

IRCI Free Range Reconstruction for SAR Imaging With Arbitrary Length OFDM Pulse

Our previously proposed OFDM with sufficient cyclic prefix (CP) synthetic aperture radar (SAR) imaging algorithm is inter-range-cell interference (IRCI) free and achieves ideally zero range sidelobes for range reconstruction. In this OFDM SAR imaging algorithm, the minimum required CP length is almost equal to the number of range cells in a swath, while the number of subcarriers of an OFDM signal needs to be more than the CP length. This makes the length of a transmitted OFDM sequence at least almost twice of the number of range cells in a swath and for a wide swath imaging, the transmitted OFDM pulse length becomes long, which may cause problems in some radar applications. In this paper, we propose a CP based OFDM SAR imaging with arbitrary pulse length, which has IRCI free range reconstruction and its pulse length is independent of a swath width. We then present a novel design method for our proposed arbitrary length OFDM pulses. Simulation results are presented to illustrate the performances of the OFDM pulse design and the arbitrary pulse length CP based OFDM SAR imaging.

Iterative Joint Estimation Procedure for Channel and Frequency Offset in Multi-Antenna OFDM Systems With an Insufficient Cyclic Prefix

This paper addresses a strategy to improve the joint channel and frequency offset (FO) estimation in multi-antenna systems, widely known as multiple-input–multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM), in the presence of intersymbol interference (ISI) and intercarrier interference (ICI) occasioned by an insufficient cyclic prefix (CP). The enhancement is attained by the use of an iterative joint estimation procedure (IJEP) that successively cancels the interferences located in the preamble of the OFDM frame, which is used for the joint estimation and initially contains the interferences due to a CP shorter than the channel length. The IJEP requires at certain steps a proper iterative interference cancellation algorithm, which makes use of an initial FO compensation and channel estimation obtained due to the use of a symmetric sequence in the preamble. After the iterative cancellation of interferences, the procedure performs an additional joint channel and FO estimation whose mean square error converges to the Cramér–Rao bound (CRB). Later on, this subsequent joint estimation permits the removal of the interferences in the data part of the frame, which are also due to an insufficient CP, in the same iterative fashion but saving iterations compared with the use of other estimation strategies. The appraisal of the procedure has been performed by assessing the convergence of the simulated estimators to the CRB as a function of the number of iterations. Additionally, simulations for the evaluation of the bit error rate (BER) have been carried out to probe how the utilization of the proposed IJEP clearly improves the performance of the system. It is concluded that, with a reduced number of iterations in the preamble, the IJEP converges to the theoretical bounds, thus reducing the disturbances caused by a hard wireless channel or a deliberately insufficient CP. Therefore, this eases the interference cancellation in the data part, leading to an improvement in the BER that approximates to the ideal case of a sufficient CP and, consequently, an improvement in the computational cost of the whole procedure that has been analyzed.

An Interference Nulling Based Channel Independent Precoding for MIMO-OFDM Systems with Insufficient Cyclic Prefix

In this paper, a new interference nulling based channel independent precoding for MIMO-OFDM systems of nt transmit and nr receive antennas with insufficient cyclic prefix (CP) is proposed. By employing the notion of interference nulling, we show that our proposed channel independent precoding scheme can eliminate the inter-block interference (IBI) caused by the insufficient CP with higher bandwidth efficiency than the conventional zero-padded or a sufficient CP added block transmission system when nr ≤ nt. It is also shown that when nr >; nt, the IBI can be eliminated without the need of any zero-padding or adding CP or precoding when the OFDM block length is not too small.

Efficient Time-Domain Residual ISI Cancellation for OFDM-Based WLAN Systems

In orthogonal frequency-division multiplexing (OFDM) systems, the multipath components whose delays exceed cyclic prefix (CP) cause intersymbol interference (ISI) and intercarrier interference (ICI), which may degrade system performance severely. In this paper, we propose two novel iterative cyclicity restoration (CR) schemes to efficiently cancel these interferences for OFDM-based wireless local area network (WLAN) systems. The time-domain parallel CR (PCR) scheme is introduced first. Using time-domain iterative solution, PCR provides much lower computational complexity than conventional CR. Furthermore, in order to improve the performance of PCR, we present successive CR (SCR) method based on Gauss-Seidel iteration. SCR offers faster convergence speed than PCR without increasing the computational cost. It is shown that both PCR and SCR need only a few iterations to approach the system performance with sufficient CP. SCR has approximately the same performance as conventional CR with much lower computational complexity for WLAN applications.

A Novel Zero-Order FIR Zero-Forcing Filterbanks Equalizer Using Oblique Projector Approach for OFDM Systems

In conventional OFDM systems, the effect of inter-block-interference (IBI) can be completely removed by inserting sufficient redundant symbols between successive transmission blocks. In this paper, based on the reformulated received block symbols of the discrete multirate filterbanks model, a new transceiver model for the cyclic prefix (CP) OFDM systems is proposed, associated with the oblique projector technique (view as the pre-processor for achieving IBI-free). Consequently, a novel ISI-free receiver with the zero-order FIR zero-forcing (ZF) filterbanks equalizer can be devised, under noise-free environment. For performance comparison the bit-error-rate (BER) is investigated for the cases of noisy and noise-free channels. In all cases, viz., the length of CP is shorter or longer than the order of the channel impulse response, we show that the same BER performance compared with the one suggested in [3] can be achieved, under the same assumptions and conditions. Since a simple cascade configuration of the IBI cancellation using the oblique projector followed by the ISI cancellation using the zero-order FIR ZF filterbanks equalizer can be realized for OFDM systems with sufficient or insufficient CP, the complexity of transceiver design can be reduced.

Performance Analysis of Two-Branch Transmit Diversity Block-Coded OFDM Systems in Time-Varying Multipath Rayleigh-Fading Channels

Based on Alamouti code, Lee and Williams proposed two-branch transmit diversity block-coded orthogonal frequency-division multiplexing (TDBC-OFDM) systems, namely, space-time block-coded OFDM (STBC-OFDM) and space-frequency block-coded OFDM (SFBC-OFDM). However, they employed the simple maximum-likelihood (SML) detector, which was designed under the assumption that the channel is static over the duration of a space-time/frequency codeword. Therefore, STBC-OFDM/SFBC-OFDM suffers from the high time/frequency selectivity of the wireless mobile fading channel. In this paper, besides the original SML detector, three detectors proposed by Vielmon et al. are applied to improve the two-branch TDBC-OFDM systems. Additionally, assuming sufficient cyclic prefix, the performances of all systems in spatially uncorrelated time-varying multipath Rayleigh-fading channels are evaluated by theoretical derivation and computer simulation, as well. According to the derived bit-error rate (BER), we further derive the bit-error outage (BEO) to provide a more object judgment on the transmission quality within a fading environment. Numerical results have revealed that significant performance improvement can be achieved even when the systems are operated in highly selective channels.