Large Number Of Subcarriers Research Articles

Pilot Design for MIMO OFDM Systems With Virtual Carriers

We consider the problem of pilot design for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems in the presence of virtual carriers. The design criterion is the average mean-square error (MSE) of the least square (LS) estimates of the channel frequency response over the data carriers. To maximize bandwidth efficiency, the number of pilots is set to its minimum which is equal to the number of unknown channel coefficients. Both the phase shift orthogonal and disjoint pilot schemes are investigated. For a given pilot placement, a closed-form expression for the pilot power distribution for the disjoint scheme is provided. It is found that the optimal power distribution allocates less power to the pilots that are close to the virtual carriers. Pilot placement is obtained using an exhaustive search. The latter is too complex in systems with large number of subcarriers. A suboptimum pilot placement design for the disjoint pilot scheme is presented. It is shown that, unlike fully loaded systems where the two pilot design schemes have similar performance, in the presence of virtual carriers the optimal disjoint scheme not only has lower complexity but also yields more accurate channel estimation and bit error rate performance.

A Performance Comparison of Golay and Reed-Muller Coded OFDM Signal for Peak-to-Average Power Ratio Reduction

Abstract —Multicarrier transmission system such as OrthogonalFrequency Division Multiplexing (OFDM) is a promising techniquefor high bit rate transmission in wireless communication systems.OFDM is a spectrally efficient modulation technique that can achievehigh speed data transmission over multipath fading channels withoutthe need for powerful equalization techniques. A major drawbackof OFDM is the high Peak-to-Average Power Ratio (PAPR) of thetransmit signal which can significantly impact the performance of thepower amplifier. In this paper we have compared the PAPR reductionperformance of Golay and Reed-Muller coded OFDM signal. Fromour simulation it has been found that the PAPR reduction performanceof Golay coded OFDM is better than the Reed-Muller coded OFDMsignal. Moreover, for the optimum PAPR reduction performance, codeconfiguration for Golay and Reed-Muller codes has been identified. Keywords —OFDM, PAPR, Perfect Codes, Golay Codes, Reed-Muller Codes I. I NTRODUCTION Wireless digital communication is rapidly expanding, re-sulting in a demand for portable wireless systems that arereliable and have high spectral efficiency. Orthogonal Fre-quency Division Multiplexing (OFDM) has been consideredto achieve high data rate transmission in mobile environment.OFDM is a method of transmitting data simultaneously overmultiple, equally spaced carrier frequencies using Fouriertransform processing for modulation and demodulation [1].Due to its robustness against the frequency-selective fading,which causes inter symbol interference (ISI) and degrades theperformance [2], OFDM has been adopted in some wirelessstandards such as Digital Audio Broadcasting (DAB), Terres-trial Digital Video Broadcasting (DVB-T), HIPER LAN/2 andIEEE 802.11 standard for WLAN [3] [4]. Moreover, OFDMhas been considered for fourth generation (4G) transmissiontechniques [5].Due to large number of subcarriers, OFDM systems have alarge dynamic signal range with a very high Peak-to-AveragePower Ratio (PAPR). As a result of which, the OFDM signalwill be clipped when passed through a nonlinear power am-plifier at the transmitter end. Clipping degrades the Bit-Error-Rate (BER) performance and causes spectral spreading [6].

Quadrature OFDMA systems based on layered FFT structure

In current OFDMA systems three major problems arise due to the large number of subcarriers, including high peak to average power ratio (PAPR), sensitivity to carrier frequency offset (CFO), and high complexity in users terminals. In this paper, based on an innovative concept of layered FFT structure, we propose novel quadrature OFDMA (Q-OFDMA) systems which can overcome these problems. In particular, the proposed systems can achieve the same guard-interval overhead and same bandwidth occupation to conventional OFDMA systems, while with reduced PAPR and improved CFO robustness and frequency diversity. Q-OFDMA systems also promise low complexity in downlink receivers. Parameter configuration is investigated for both predefined and adaptive users data rates. Theoretical comparison of bit error rate (BER) performance between Q-OFDMA and OFDMA is conducted, and validated by simulation results. It is shown that Q-OFDMA systems could achieve better performance than OFDMA when signal to noise ratio (SNR) is above a threshold depending on the channel condition, and advanced equalizers, such as minimum mean square error equalizer, can significantly decrease this threshold due to the large frequency diversity in Q-OFDMA systems.

Steady-State Kalman Filtering for Channel Estimation in OFDM Systems for Rayleigh Fading Channels

Kalman filters are effective channel estimators but they have the drawback of having heavy calculations when filtering needs to be done in each sample for a large number of subcarriers. In our paper we obtain the steady-state Kalman gain to estimate the channel state by utilizing the characteristics of pilot subcarriers in OFDM, and thus a larger portion of the calculation burden can be eliminated. Steady-state value is calculated by transforming the vector Kalman filtering in to scalar domain by exploiting the filter charactertics when pilot subcarriers are used for channel estimation. Kalman filters operate optimally in the steady-state condition. Therefore by avoiding the convergence period of the Kalman gain, the proposed scheme is able to perform better than the conventional method. Also, driving noise variance of the channel is difficult to obtain practical situations and accurate knowledge is important for the proper operation of the Kalman filter. Therefore, we extend our scheme to operate in the absence of the knowledge of driving noise variance by utilizing received Signal-to-Noise Ratio (SNR). Simulation results show considerable estimator performance gain can be obtained compared to the conventional Kalman filter.

Uncoordinated orthogonal frequency division multiple access: To spread or not to spread

We study uncoordinated multiple access using the orthogonal frequency division multiple access (OFDMA) technique where multiple users independently and randomly pick a sub-carrier from a set of sub-carriers for transmission in each slot. Signals transmitted on distinct sub-carriers are orthogonal to each other while signals transmitted by different users on the same sub-carrier interfere with each other. We study average throughput and outage probability performance of such a system in the asymptotic limit of large numbers of sub-carriers and users while keeping the ratio of number of users to sub-carriers fixed, for non-fading, flat fading, and frequency-selective fading additive white Gaussian noise channels. The performance is compared to that of a system in which all users spread their signal over all the sub-carriers as in a code division multiple access (CDMA) system. Our results show that at high signal-to-noise ratio (SNR), transmission without spreading results in higher throughput but requires more retransmissions on the average. At low SNRs, the throughput performance is comparable but the system with spreading requires smaller average number of retransmissions.

Blind OFDM Receiver Based on Independent Component Analysis for Multiple-Input Multiple-Output Systems

We propose a novel blind orthogonal frequency division multiplexing (OFDM) receiver structure for multiple- input multiple-output (MIMO) systems based on independent component analysis (ICA), which increases the spectral efficiency effectively compared to training based systems, and provides considerable performance enhancement over previous ICA based methods. To further improve the performance, we also incorporate ICA with iterative layered space-time equalization (LSTE), which provides performance close to the case with perfect channel state information (CSI). The reduced-complexity versions of the two proposed structures, which use channel interpolation, result in similar performance at a substantially lower computational cost. Our receiver structures also have significantly better performance and lower complexity than a previously proposed subspace method when a large number of subcarriers are employed.

Precise BER analysis of π/4-DQPSK OFDM with carrier frequency offset over frequency selective fast fading channels

An exact closed-form bit error rate (BER) expression is derived for an orthogonal frequency-division multiplexing system with π/4-shifted differentially encoded quadrature phase shift keying (π/4-DQPSK) in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Different system configurations, including time domain differential modulation, frequency domain differential modulation, single channel reception, and multi-channel reception with maximal ratio combining diversity, are considered in the exact BER analysis. For a small number of subcarriers, the BER expression can be calculated directly. A Monte Carlo method is designed to evaluate the BER for a large number of subcarriers. The analytical expression can be used to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler spread, on the system BER performance. Particularly, the effect of carrier frequency offset on the system performance, and the differences and opportunities to use frequency domain differential modulation or time domain differential modulation, can be studied in a quantitative way for a more realistic wireless channel environment model. By using the exact closed-form BER expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler spread, and mean delay spread for given operating conditions can be determined.

Pilot-Aided OFDM Channel Estimation in the Presence of the Guard Band

In this letter, pilot design and channel estimation are discussed for orthogonal frequency-division multiplexing (OFDM) systems with guard subcarriers. First, we investigate the effects of guard band on channel estimation errors. From this, we propose pilot placement having a maximum distance between adjacent pilots except for the guard band, and show that it achieves minimum channel estimation errors among partially equispaced pilots using equivalence of the Toeplitz and circulant matrices. Also, an efficient channel estimator is developed by introducing an extended channel and its finite impulse response (FIR) approximation to overcome high numerical complexity caused by the presence of guard subcarriers and the use of a large number of subcarriers. Simulation results are presented for OFDM and orthogonal frequency division multiple access (OFDMA) systems consistent with IEEE 802.16a standards.

Reduced Feedback MIMO-OFDM Precoding and Antenna Selection

Transmitter precoding for multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) is an effective way of leveraging the diversity gains afforded by a multiple-transmit multiple-receive antenna system in a frequency selective environment. In the limited feedback scenario, optimal precoder representation for narrowband MIMO systems using moderately sized codebooks designed on the Grassmann manifold has been shown to perform remarkably well. In MIMO-OFDM systems, precoder matrices have to be designed for all subcarriers and the amount of feedback can get prohibitively large. This is especially true for next generation wireless local area networks and wireless metropolitan area networks which have a large number of subcarriers. In this paper, we present techniques to reduce this feedback requirement and the performance of these algorithms is numerically shown to provide improvement over existing schemes

Low-Complexity Orthogonal Spectral Signal Construction for Generalized OFDMA Uplink With Frequency Synchronization Errors

In orthogonal frequency-division multiplexing, the total spectral resource is partitioned into multiple orthogonal subcarriers. These subcarriers are assigned to different users for simultaneous transmission in orthogonal frequency-division multiple access (OFDMA). In an unsynchronized OFDMA uplink, each user has a different carrier frequency offset (CFO) relative to the common uplink receiver, which results in the loss of orthogonality among subcarriers and thereby multiple access interference. Hence, OFDMA is very sensitive to frequency synchronization errors. In this paper, we construct the received signals in frequency domain that would have been received if all users were frequency synchronized. A generalized OFDMA framework for arbitrary subcarrier assignments is proposed. The interference in the generalized OFDMA uplink due to frequency synchronization errors is characterized in a multiuser signal model. Least squares and minimum mean square error criteria are proposed to construct the orthogonal spectral signals from one OFDMA block contaminated with interference that was caused by the CFOs of multiple users. For OFDMA with a large number of subcarriers, a low-complexity implementation of the proposed algorithms is developed based on a banded matrix approximation. Numerical results illustrate that the proposed algorithms improve the system performance significantly and are computationally affordable using the banded system implementation

Distribution of the ICI Term in Phase Noise Impaired OFDM Systems

Orthogonality between the subcarriers of an orthogonal frequency division multiplexing (OFDM) system is affected by phase noise, which causes inter-carrier interference (ICI). The distribution of this interference term is studied in this paper. The distribution of the ICI for large number of carriers is derived and it is shown that the complex Gaussian approximation, generally applied in previous literature, is not valid and that the ICI term exhibits thicker tails. An analysis of the tail probabilities confirms these finding and shows that bit-error probabilities are severely underestimated when the Gaussian approximation for the ICI term is used, leading to too optimistic design criteria. Results from a simulation study confirm the analytical findings and show the validity of the limit distribution, obtained under the assumption of a large number of subcarriers, already for a modest number of subcarriers.

Analytical evaluation of nonlinear effects in MC-CDMA signals

The MC-CDMA signals (multicarrier coded division multiple access) have strong envelope fluctuations which make them very prone to nonlinear effects. These effects can be both intentional (such as the ones inherent to a nonlinear signal processing for reducing the envelope fluctuations) or not (such as the ones inherent to a nonlinear power amplification). In this paper we present an analytical tool for the performance evaluation of nonlinear effects in MC-CDMA signals which takes advantage of the Gaussian-like behavior of MC-CDMA signals with a large number of subcarriers and employs results on memoryless nonlinear devices with Gaussian inputs so as to characterize statistically the signals at the output of the nonlinear device. This characterization is then used for an analytical computation of the SIR levels (signal-to-interference ratio) and the BER performance (bit error rate). A set of numerical results is presented and discussed, showing the accuracy of the analytical BER performance analysis in the presence of nonlinear effects

Analysis of Asynchronous Long-Code Multicarrier CDMA Systems With Correlated Fading

The effects of inter-carrier interference (ICI) and aperiodic random spreading sequences on the performance of asynchronous multicarrier code-division multiple-access (CDMA) systems with correlated fading between sub-carriers are investigated in this research. To conduct theoretical analysis for the maximal ratio combining (MRC) receiver, random parameters including asynchronous delays, correlated Rayleigh fading, and spreading sequences are averaged to find the unconditional covariance matrix of the interference-plus-noise vector. We demonstrate that the ICI in the system proposed by Kondo and Milstein (1996) can be mitigated by assigning a common random spreading sequence over all sub-carriers for each user, rather than using a set of distinct spreading sequences, where code sequences are assumed perfectly time-synchronized. Moreover, the analytic expression for the bit error probability (BEP) can be obtained with the Gaussian approximation. Simulation results are used to demonstrate the accuracy of our analysis. Various design tradeoffs including the number of sub-carriers, fading correlations, ICI and multipath effect are presented in simulation. We conclude that, when properly choosing a sufficiently large number of sub-carriers, the benefit of mitigating multipath interference and exploiting potential hidden frequency diversity shall prevail the impairment brought by increased ICI.

Block coding scheme for reducing PAPR in OFDM systems with large number of subcarriers

The major drawback in Orthogonal Frequency Division Multiplexing (OFDM) system is due to the high Peak-to-Average Power Ratio (PAPR), so the performance of the system is significantly degraded by the nonlinearity of a High Power Amplifier (HPA) in the transmitter. In order to mitigate distortion, a block coding scheme for reducing PAPR in OFDM systems with large number of subcarriers based on complementary sequences and predistortion is proposed, which is capable of both error correction and PAPR reduction. Computer simulation results show that the proposed scheme significantly improves Bit Error Rate(BER) performance as compared to an uncoded system when an HPA is employed or a coded system without predistortion.

On the peak-to-average power of ofdm signals based on oversampling

Orthogonal frequency-division multiplexing (OFDM) introduces large amplitude variations in time, which can result in significant signal distortion in the presence of nonlinear amplifiers. We introduce a new bound for the peak of the continuous envelope of an OFDM signal, based on the maximum of its corresponding oversampled sequence; it is shown to be very tight as the oversampling rate increases. The bound is then used to derive a closed-form probability upper bound for the complementary cumulative distribution function of the peak-to-mean envelope power ratio of uncoded OFDM signals for sufficiently large numbers of subcarriers. As another application of the bound for oversampled sequences, we propose tight relative error bounds for computation of the peak power using two main methods: the oversampled inverse fast Fourier transform and the method introduced for coded systems based on minimum distance decoding of the code.

A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions

Presents a hybrid analytical-simulation procedure for performance evaluation in M-ary quadrature amplitude modulation (M-QAM) orthogonal frequency-division multiplexing (OFDM) digital radio systems in the presence of distortions caused by high-power amplifiers (HPAs). The present analysis is carried out considering an additive white (AWGN) transmission channel. It is shown that, in the case of an OFDM system with a large number of subcarriers, the distortion on the received symbol caused by the amplifier can be modeled, with good approximation, as a Gaussian noise added to the received symbol. This important result allows a hybrid analytical-simulation approach to solve the problem of performance evaluation. In practice, the simulation aspect is only used to estimate means and variances of the nonlinear noise. Such estimated parameters are subsequently used to evaluate analytically the system bit-error rate (BER) using an expression, which takes into account both AWGN and nonlinear noise effects. The advantage of the proposed method lies in the strongly reduced computational time. In fact, an accurate estimate of the nonlinear noise parameters requires only few iterations when compared with a classical semianalytical approach. This is especially true when low BER values (<10/sup -4/) have to be estimated. The proposed procedure is applied to evaluate M-QAM-OFDM performance in the presence of distortions caused by traveling-wave tube (TWT) and solid-state-power (SSP) amplifiers.

The effect of nonlinearity on a QPSK-OFDM-QAM signal

The effect of nonlinearity on a QPSK-OFDM-QAM signal is analyzed. One of the characteristics of an OFDM-QAM signal is its wide range of envelope fluctuation: its crest factor, defined as the ratio of the peak instantaneous power to the average (rms) power in dB, is typically greater than 10. When an OFDM-QAM signal drives a nonlinear device, nonlinearity will result in signal compression and intermodulation among the sub-carriers at the output. An analytical method is used to predict the input back-off needed to keep the intermodulation below an acceptable level. For sufficient large number of sub-carriers, we show that to keep the intermodulation power 30 dB below the signal power, we need to back-off the input power by 6.5 dB. However, from the BER point of view, the degradation is less than 2 dB at BER=0.01% even for 1 dB input back-off.