Frequency-selective Rayleigh Fading Research Articles

A Gaussian Mixture Approach to Blind Equalization of Block-Oriented Wireless Communications

We consider blind equalization for block transmissions over the frequency selective Rayleigh fading channel. In the absence of pilot symbols, the receiver must be able to perform joint equalization and blind channel identification. Relying on a mixed discretecontinuous state-space representation of the communication system, we introduce a blind Bayesian equalization algorithm based on a Gaussian mixture parameterization of the a posteriori probability density function (pdf) of the transmitted data and the channel. The performances of the proposed algorithm are compared with existing blind equalization techniques using numerical simulations for quasi-static and time-varying frequency selective wireless channels.

Adaptation of ASTC in a Correlated Rayleigh Frequency-Selective Fading Channels in OFDM systems with PAPR Reduction

In this paper we suggest to use the ASTC (Algebraic Space Time Codes) as powerful coding technique for IEEE 802.11x OFDM standard combined with PAPR reduction scheme. ASTC with their very Algebraic- construction based on Quaternionic algebra, have a full rate, full divers ity, non-vanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitt ed energy per antenna and good shaping, readily lend themselves to high data rate situations. However, by their c they require a nonselective flat fading channels belonging to narrow-band systems. In fact, such sy stems are not readily found in airs interfaces. In open air we have what are commonly called frequency-selecti

Soft demodulation algorithms for orthogonally modulated and convolutionally coded DS-CDMA systems

A convolutionally coded M-ary orthogonal direct sequence code division multiple access (DS-CDMA) system in time-varying frequency-selective Rayleigh fading channels is considered in this work. We propose several novel soft demodulation algorithms based on interference cancellation and suppression techniques that can be coupled with soft decoding to improve the system performance in an iterative manner. The performance of the proposed demodulation algorithms is evaluated numerically and proved to achieve substantial bit error rate (BER) performance gain compared with the conventional detection schemes.

An average Cramer-Rao bound for frequency offset estimation in frequency-selective fading channels

Several variations of Cramer-Rao bounds for carrier frequency offset (CFO) estimation in frequency-selective fading channels have been used to benchmark practical estimators' performance or to design training signals for CFO estimation. Among them, the extended Miller-Chang bound (EMCB) provides a tighter bound than the CRB for locally unbiased estimators. However, there is no closed-form expression of the EMCB for the CFO estimation in frequency-selective fading channels with an arbitrary training signal. In this letter, we derive a closed-form exact average CRB (the EMCB) valid for any training signal and any signal structure for the CFO estimation over frequency-selective Rayleigh fading channels with uncorrelated or arbitrarily correlated taps. The accuracy and generality of the proposed average CRB expression, and its advantages over the existing expressions are corroborated by numerical and simulation results.

BER Analysis of OFDM Systems Impaired by Phase Noise in Frequency-Selective Fading Channels

In this paper, we study the effect of finite-power, phase-locked loop based phase noise on the bit-error-rate (BER) performance of orthogonal frequency division multiplexing (OFDM) systems in frequency-selective fading channels. It is well known the impact of phase noise on the performance of an OFDM system can be divided into a multiplicative term called common phase error (CPE) and an additive term called intercarrier interference (ICI). Based on the conditional Gaussian approximation technique, we first derive the BER formulas for BPSK, QPSK, 16-QAM, and 64-QAM modulated OFDM signals in frequency-selective Rayleigh fading channels. To further quantify the individual influence of the CPE and the ICI on system performance for different phase noise spectra, we derive the BER expressions for perfect CPE compensation cases. The analytical results obtained for frequency-selective Rayleigh fading channels are then generalized to frequency-selective Rician fading channels. Simulation results not only validate the accuracy of our analysis but also show the dependency of BERs on the shapes of phase noise spectra.

Performance Analysis of a Complex Multicode Tracking Loop in Bandlimited Rayleigh Fading Channels

This paper presents the root-mean-squared tracking error performance analysis of a class of coherent digital delay-locked loops for multicode direct sequence spread spectrum signals in bandlimited correlated Rayleigh fading channels. In the transmit side, multiple independent PSK-modulated data streams in the in-phase and qudrature phase branches are spread by short mutually orthogonal codes before being further complex spread by a long complex PN code. We assume that the system employs a pilot code channel to assist the receiver's synchronization and channel estimation. The proposed code tracking loop incorporates the pilot-aided channel estimator and derives the timing error from all short-code-spread subchannels. Our analysis takes into account the effects of imperfect channel estimate, correlated frequency selective Rayleigh fading and band-limiting. Numerical results are presented to quantify the impact of the resulting multipath interference within the same code channel and amongst different code channels.

Effects of asynchronous MAI on average SEP performance of OFDMA uplink systems over frequency-selective Rayleigh fading channels

This paper investigates the effects of asynchronous multiple access interference (MAI) on the performance of orthogonal frequency-division multiple access (OFDMA) uplink systems in frequency-selective Rayleigh fading environments. We first analyze the MAI and its statistical characteristics using the Gaussian approximation. Then the analytical expression for the uncoded average symbol error probability (SEP) is obtained with various modulation schemes. Comparison with simulation results shows a tight agreement of the proposed analysis over a wide range of asynchronous timing errors and for various numbers of asynchronous users. Numerical examples show that when asynchronous timing errors reside within the guard interval, a performance of uncoded SEP- 10-3 can be feasible even in high dispersive environments. Furthermore, the effect of the Gaussian approximation is examined, and the performance comparison between interleaved- and block-type subcarrier allocation schemes is provided.

Interference Management for DS-CDMA Systems through Closed-Loop Power Control, Base Station Assignment, and Beamforming

In this paper, we propose a smart step closed-loop power control (SSPC) algorithm and a base station assignment method based on minimizing the transmitter power (BSA-MTP) technique in a direct sequence-code division multiple access (DS-CDMA) receiver with frequency-selective Rayleigh fading. This receiver consists of three stages. In the first stage, with constrained least mean squared (CLMS) algorithm, the desired users’ signal in an arbitrary path is passed and the inter-path interference (IPI) is reduced in other paths in each RAKE finger. Also in this stage, the multiple access interference (MAI) from other users is reduced. Thus, the matched filter (MF) can use for more reduction of the IPI and MAI in each RAKE finger in the second stage. Also in the third stage, the output signals from the matched filters are combined according to the conventional maximal ratio combining (MRC) principle and then are fed into the decision circuit of the desired user. The simulation results indicate that the SSPC algorithm and the BSA-MTP technique can significantly reduce the network bit error rate (BER) compared to the other methods. Also, we observe that significant savings in total transmit power (TTP) are possible with our methods.

On the Construction of Orthogonal Spreading Code Groups for MC-CDMA with FDE in a Frequency Selective Channel

The bit error rate (BER) performance of multicode multi-carrier code division multiple access (MC-CDMA) severely degrades due to the inter-code interference (ICI) in a strong frequency-selective channel. Recently a spreading code group construction method was proposed for MC-CDMA. The Walsh-Hadmard (WH) codes are divided into a number of code groups such that the code orthogonality can be maintained within each group even in a strong frequency-selective channel; any code pair taken from different groups is not orthogonal. The number of spreading codes in each group is determined by the maximum time delay difference of the channel. In this paper, we point out that the number of codes in each group is determined by the distribution of time delay differences among the propagation paths of the channel, not the maximum time delay difference. Based on that observation, we show that more orthogonal spreading codes can exist in each code group. The conditional BER is derived taking into account the interference from other code groups and the achievable downlink BER performance using the proposed spreading code group construction is numerically evaluated in a frequency-selective Rayleigh fading channel.

Precise SER Analysis and Performance Results of OSTBC MIMO-OFDM Systems over Uncorrelated Nakagami-m Fading Channels

Although the topic of multiple-input multiple-output (MIMO) based orthogonal frequency division multiplexing (OFDM) over different fading channels is well investigated, its closed form symbol error rate (SER) expressions and performance results employing orthogonal space time block codes (OSTBCs) over uncorrelated frequency-selective Nakagami-m fading channels are still not available. The closed form expressions are extremely useful for evaluating system's performance without carrying out time consuming simulations. Similarly, the performance results are also quite beneficial for determining the system's performance in the sense that many practical wireless standards extensively employ MIMO-OFDM systems in conjunction with M-ary quadrature amplitude modulation (M-QAM) constellation. This paper thus, derives exact closed form expressions for the SER of M-ary Gray-coded one and two dimensional constellations when an OSTBC is employed and Nt transmit antennas are selected for transmission over frequency-selective Nakagami-m fading channels. For this purpose, first an exact closed-form of average SER expression of OSTBC based MIMO-OFDM system for M-ary phase shift keying (M-PSK) using traditional probability density function (PDF) approach is derived. We then compute exact closed form average SER expressions for M-ary pulse amplitude modulation (M-PAM) and M-QAM schemes by utilizing this generalized result. These expressions are valid over both frequency-flat and frequency-selective Nakagami-m fading MIMO channels and can easily be evaluated without using any numerical integration methods. We also show that average SER of MIMO-OFDM system using OSTBC in case of frequency-selective Rayleigh fading channels remains independent to the number of taps, L of that fading channel and the performance of the same system for two-tap un-correlated Rayleigh and Nakagami-m fading channels is better than that of the correlated one. Moreover, Monte Carlo simulation of MIMO-OFDM system using multiple transmit and receive antennas for different modulations is presented to validate our theoretical results. Finally, due to availability of closed form expressions, we further provide the performance results of MIMO-OFDM system over frequency-selective Nakagami-m fading channels employing (M-QAM) using OSTBCs under the transmission rate equal to 1, 2 and 3 bit(s)/s/Hz, respectively.

Distributed space-time-frequency coding for cooperative OFDM systems

A distributed space-time-frequency (STF) coding scheme is proposed for cooperative OFDM (C-OFDM) systems with three terminals over quasi-static frequency-selective Rayleigh fading channels. The outage probability is derived and its tight closed-form lower bound is presented. Asymptotic analysis indicates that the proposed scheme can achieve both spatial and multipath (frequency) diversity. The theoretical analysis of the proposed STF coded scheme is further implemented by the distributed group STF block coding (D-GSTFBC) scheme based on the subcarrier grouping technique. Simulation results confirm the previously introduced theoretical analysis.

Doppler Spread Estimation for Broadband Wireless OFDM Systems Over Rician Fading Channels

In this paper, we present a new Doppler spread estimation algorithm for broadband wireless orthogonal frequency division multiplexing (OFDM) systems with fast time-varying and frequency-selective Rayleigh or Rician fading channels. The new algorithm is developed by analyzing the statistical properties of the power of the received OFDM signal in the time domain, thus it is not affected by the influence of frequency-domain inter-carrier interference (ICI) introduced by channel variation within one OFDM symbol. The operation of the algorithm doesn’t require the knowledge of fading channel coefficients, transmitted data, or signal-to-noise ratio (SNR) at the receiver. It is robust against additive noise, and can provide accurate Doppler spread estimation with SNR as low as 0 dB. Moreover, unlike existing algorithms, the proposed algorithm takes into account the inter-tap correlation of the discrete-time channel representation, as is the case in practical systems. Simulation results demonstrate that this new algorithm can accurately estimate a wide range of Doppler spread with low estimation latency and high computational efficiency.

MRC in the Presence of Asynchronous Cochannel Interference Over Frequency-Selective Rayleigh Fading Channels

This paper studies the performance of Rake receivers with maximal ratio combining (MRC) in the presence of cochannel interference over slowly varying frequency-selective fading channels with combined spatial receive antenna diversity and temporal multipath diversity. Two models for the instantaneous powers of the residual multipath components and the resolved cochannel interfering signals, which represent the overall interfering signals, are employed. The first model considers the phase asynchronism between the desired signal replicas and interfering signals, whereas the second model assumes that the instantaneous powers of interfering signals incoherently add up. The desired signal replicas and interfering signals are assumed to experience statistically independent Rayleigh fading processes with arbitrary statistics. For the system model previously described, new closed-form expressions for the probability density function (pdf) of the combined signal-to-interference-plus-noise ratio (SINR) are derived. These expressions are then used to obtain formulas for various performance measures. The case study under consideration and the corresponding derived expressions for the statistical measures generalize many previous results and can usefully be employed to investigate the impact of various system and channel parameters on the performance of Rake receivers with MRC in the presence of cochannel interference.

Analysis and Compensation of DC Offset in OFDM Systems Over Frequency-Selective Rayleigh Fading Channels

Direct-conversion receivers have become popular in radio-frequency (RF) circuit design for their advantages of low cost, low power consumption, and fewer chip components over other architectures such as heterodyne receivers. However, the direct-conversion receiver architecture often suffers from direct current (dc) offset, which is a consequence of the imperfect direct-conversion process. In this paper, we study the effects of dc offset on the symbol error rate (SER) performance of orthogonal frequency-division multiplexing (OFDM) systems in multipath Rayleigh fading channels. Since OFDM system performance is sensitive to carrier frequency offset (CFO), the CFO must be estimated and compensated at the receiver. Due to CFO compensation, the dc offset caused by direct-conversion receivers and/or mixed-signal circuits no longer only affects the dc subcarrier and is spread over all subcarriers. By deriving the analytical SER formulas for OFDM systems with various modulation formats, the dependency of SER on dc offset and CFO is clearly quantified. These SER formulas can help system designers determine suitable specifications of RF components and understand whether digital DC offset compensation is necessary or not. Finally, we propose and analyze a simple DC offset estimation and cancellation scheme under the assumption that DC offset holds constant in one OFDM symbol duration. Numerical results demonstrate the effectiveness of the proposed DC offset-cancellation scheme.

BER analysis of space–time diversity in CDMA systems over frequency-selective fading channels

The performance of direct-sequence code division multiple access (DS-CDMA) using space-time spreading system, over frequency-selective fading channels, is investigated. The underlying transmit diversity scheme, previously introduced in the literature, is based on two transmit and one receive antenna. It was shown that when employed in flat fast-fading channels, the received signal quality can be improved by utilising the spatial and temporal diversities at the receiver side. We study the problem of multiuser interference in asynchronous CDMA systems that employ transmit/receive diversity using space-time spreading. To overcome the effects of interference, a decorrelator detector is used at the base station. Considering binary phase-shift keying transmission, we analyse the system performance in terms of its probability of bit error. In particular, we derive the probability of error over frequency-selective Rayleigh fading channels for both fast and slow-fading channels. For the fast-fading channel, both simulations and analytical results show that the full system diversity is achieved. On the other hand, when considering a slow-fading channel, we show that the scheme reduces to conventional space-time spreading schemes where the diversity order is half of that of fast-fading.

Turbo Code with Modified LLR and Performance Analysis for Bluetooth Packets in Indoor Environments

Most of the restrictions in indoor environments do not exist for outdoor sites. The main limitations for indoors are the attenuation of walls and the multipath fading effects. The signal propagation is limited by the standard free space path loss in outdoor environments or free space. The loss in free space is usually equal to the range squared whereas the loss exponent for indoors is more like the 4th power. This study investigates the performance of turbo codes with modified Maximum-A-Posteriori (MAP) decoding algorithm for Bluetooth data packets in indoor environments over the frequency selective Rayleigh fading channels; which are also called as indoor wireless communication channels. In order to reduce the computational complexity of turbo decoders, MAP algorithm is modified in this study. Bit error rate (BER) versus energy of bit-to-noise ratio (E b /N o ) of modified MAP algorithms for Bluetooth data packets at 2.4 GHz industrial-scientific-medical (ISM) band are evaluated by means of computer simulations. Thus, modified logarithmic likelihood ratio (LLR) method can significantly reduce the computational complexity of the MAP algorithm. Furthermore, the performances of different types of forward error correction (FEC) coding for Bluetooth data packets are compared in the study.

Interference cancellation enhancement through generalized widely linear equalization in QAM systems

In this paper, we introduce a generalized widely linear (WL) equalizer for quadrature amplitude modulation (QAM) systems with single/multiple antennas. In our proposed implementation, the WL receiver first separates the in-phase (I) and quadrature (Q) parts of the complex-valued baseband received signal and jointly filters the two branches for signal detection. Infinite length WL minimum mean-square error (WL-MMSE) linear, and WL decision-feedback-equalizer (WL-DFE) settings are derived and performance is analyzed in co-channel interference limited channels. It is shown that, in frequency selective Rayleigh fading channels, the interference cancellation (IC) gain depends mainly on the rank (r) of the interference correlation matrix (ICM) which is defined as the covariance of the vector-valued signal which consists of the real and imaginary parts of the noise-plus-interference signal collected at multiple antenna branches. Assuming that the DFE feedback path is error free, we show that a WL QAM receiver with N antennas exhibits full IC capability (that is complete interference removal) when the ICM is rank deficient i.e., when: r < 2N. This condition implies that a WL-DFE receiver can reject any combination of M1 pulse-amplitude-modulation (PAM) and M2 QAM interferers satisfying the constraint: M1 + 2M2 < 2N. Simulation results show that, in the presence of PAM-type interference, the gain of WL-DFE is reduced by decision feedback errors while the IC benefit of WL-MMSE is limited by the noise enhancement problem. Nevertheless, the proposed receivers are shown to be useful in cellular systems that employ a combination of PAM and QAM schemes.

On the sum capacity of a T‐user N‐frequency multiple access channel with noise

AbstractIn this paper, we investigate the sum capacity of a noisy multiple access channel (MAC): the T‐user N‐frequency noiseless MAC in cascade with a noisy channel. The noisy channel includes frequency‐selective Rayleigh fading and Additive White Gaussian Noise (AWGN). The receiver may use multiuser detection (MUD) or single user detection (SUD). We show that when using SUD, the uniform distribution achieves sum capacity. Considering MUD and assuming that all users have the same input distribution, we show through numerical optimisation, that, for most relevant values of T and N, a product of uniform input distributions maximises a tight upper bound on sum capacity. Numerical results were obtained and it was observed that, for fixed N, there is a value of T which maximises sum capacity. As expected, the results also show that there is a significant gain in sum capacity when MUD is used. Copyright © 2009 John Wiley &amp; Sons, Ltd.

RLS Channel Estimation with Adaptive Forgetting Factor for DS-CDMA Frequency-Domain Equalization

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can increase the downlink bit error rate (BER) performance of DS-CDMA beyond that possible with conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. Recently, we proposed a pilot-assisted channel estimation (CE) based on the MMSE criterion. Using MMSE-CE, the channel estimation accuracy is almost insensitive to the pilot chip sequence, and a good BER performance is achieved. In this paper, we propose a channel estimation scheme using one-tap recursive least square (RLS) algorithm, where the forgetting factor is adapted to the changing channel condition by the least mean square (LMS)algorithm, for DS-CDMA with FDE. We evaluate the BER performance using RLS-CE with adaptive forgetting factor in a frequency-selective fast Rayleigh fading channel by computer simulation.

An exact error probability analysis of OFDM systems with frequency offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.