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Performance Analysis of the RAKE Receiver in the Presence of Multipath Delay Estimation Errors and Rician Fading Channels
Abstract
We derive here a novel unified framework for computing the average bit-error-ratio (BER) of a direct-sequence spread spectrum receiver using maximum ratio combiner (MRC), in the presence of code synchronization errors and multipath Rayleigh or Rician fading channels. Traditionally, for single-user systems, the signal-to-noise ratio at the output of MRC is modeled as a quadratic form in complex Gaussian variables. We show that this model does not hold when delay errors are present and we propose an improved generic model incorporating the multipath delay estimation errors. We also discuss the case when the RAKE receiver is employed in the presence of multiple users. Based on our theoretical model, BER can be easily derived in a semi-analytical fashion, for any type of pulse shaping and any spacing between multipaths. Very fast results can be obtained for high spreading factors, when inter-chip (ICI) and inter-symbol interference (ISI) may be neglected. These results also give the lower bounds on BER for low spreading factors. Theoretical BER curves with QPSK modulation are validated by link level simulations for different downlink Rayleigh and Rician fading channels. Moreover, we discuss the impact of the delay error distribution on BER and we emphasize some practical applications of our generic technique. Copyright © 2003 AEI.
... Nous pouvons constater que le profil de célérité de l'onde acoustique dans l'eau agit sur les trajectoires des rayons et par la suite sur le retard de propagation des trajets multiples induits au cours de la propagation du signal dans le canal. Le retard de propagation des différents trajets multiples est un paramètre important dans la caractérisation du canal sous marin [LR03a], ainsi que les atténuations que subit l'onde acoustique dans sa propagation sous l'eau. L'estimation de 1. Caractérisation du canal sous-marin ces deux paramètres est cruciale lors de la réception du signal, dite asynchrone et dans la reconstitution du signal émis, comme nous allons voir par la suite. ...
For some applications the need for stealth and covert communications is crucial, especially for military purposes. The underwater acoustic channel is very noisy environment. It is subjected to multiple noise sources, reflections and refractions of acoustic waves, which creates multipath. Considering the multipath nature of the underwater acoustic channel and the transmission of acoustic waveforms at very low signal to noise ratio (SNR) as the need for low probability of intercept (LPI) is essential for our application, we propose a transmission scheme based on direct sequence spreading spectrum and code division multiple access (DS-CDMA). We present the receivers structures for this transmission method and we evaluate their performance. We study the performance of the proposed receivers for Rayleigh fading multipath channels in presence of multiuser access interference. The receivers structures allow both the channel parameters estimation by using a bench of matching filters to the spread code sequences of each user and to exploit the spatial diversity of the underwater acoustic channel by the mean of a coherent recombination of the different paths energy contributions, after the channel estimation (MRC : maximum ratio combining). The channel parameters, paths time delays and channel coefficients, are estimated at the output of matched filters at symbol rate. We show that we can potentially improve the system performance by implementing a successive interference cancellation method. The results obtained establish that the proposed system achieves excellent and robust performance at very signal to noise ratio. The convergence of the successive interference cancellation structure is achieved with no more than three iterations. At last, we introduce channel coding that allows us to improve the overall system performance along with its robustness by using error-correcting codes. Some of the developed algorithms were implemented and tested on real data procured by a sea trials campaign conducted off the coast of Brittany at Rade de Brest and in the Mediterranean Sea. ¿¿¿
... The focus here is on the correlated channels. The detailed theoretical framework for Rayleigh and Rician uncorrelated fading channels has been developed by the authors in [12]. Although the starting point is based on the traditional expression of the instantaneous SNR [7], [14], the consequent derivations are structured into a novel framework, taking into consideration the errors in the delay estimates, the pulse shaping function and the possible correlations between MRC branches. ...
We derive here a simple and accurate theoretical method for computing the bit-error-probability (BEP) of a direct-sequence spread spectrum (DS-SS) receiver using maximum ratio com-biner (MRC), in the presence of code synchronization errors, root raised cosine (RRC) pulse shaping, and Rayleigh fading channels with correlated paths. Theoretical BEP curves with QPSK modulation are validated by link level simulations for different downlink Rayleigh fading channels. The impact of the delay estimation errors on the performance of Rake receiver is analyzed for both closely-spaced and distant channel taps, and for different path correlation coefficients.
This article presents a study of Global Navigation Satellite System (GNSS) receiver correlation performance in the presence of phase noise (PN) originating from the radio front-end's phase-locked loop (PLL). Various constituent PLL sub-blocks, such as the reference oscillator (RO), phase and frequency detector (PFD), voltage controlled oscillator (VCO), loop filter and frequency dividers contribute to the overall PN of the PLL. The PLL phase noise modeling is covered in detail. Correlation performance of GNSS baseband tracking loops is then calculated as a function of several PLL design parameters, such as the VCO thermal PN, loop filter bandwidth (BW), frequency division ratio (FDR), and the receiver correlator's pre-detection integration times (PIT). The effects of these parameters on the signal to noise ratio (SNR) of the correlation product are described and simulated. Based on the results of these simulations, we present guidelines for radio front-end PLL circuit design in order to maintain a minimum baseband correlation performance within the GNSS receiver. Copyright © 2014 Institute of Navigation.
The purpose of this introductory chapter is to provide several measures of performance related to practical communication system design and to begin exploring the analytical methods by which they may be evaluated. While the deeper meaning of these measures will be truly understood only after their more formal definitions are presented in the chapters that follow, the introduction of these terms here serves to illustrate the various possibilities that exist, depending on both need and relative ease of evaluation.
Multiuser demodulation algorithms for centralized receivers of asynchronousdirect-sequence (DS) spread-spectrum code-division multiple-access (CDMA) systems infrequency-selective fading channels are studied. Both DS-CDMA systems with short (onesymbol interval) and long (several symbol intervals) spreading sequences are considered.Linear multiuser receivers process ideally the complete received data block. The approximationof ideal infinite memory-length (IIR) linear multiuser detectors by...
Carrier frequency, carrier phase, multipath profile, delay values
as well as fading characteristics are important for coherent detection.
Several DS-CDMA receivers have been investigated, but mainly with the
assumption of perfect estimation of those parameters. This paper deals
with the impact of channel phase and path delay estimation errors to the
performance of pre and post-combining blind adaptive linear minimum mean
square error (LMMSE) receivers. Comparisons are made also with the
conventional RAKE receiver. The results show that channel phase
estimation errors degrade almost equally the performance of blind
adaptive LMMSE and RAKE receivers. Delay estimation errors by over 20%
of chip time cause the loss of advantages of LMMSE detection
Wideband CDMA systems employ pilot symbols for coherent detection.
When the pilot symbols are time-multiplexed with data symbols, their
number is usually limited, due to overhead considerations and rate
matching requirements. Therefore, channel estimation based only on the
pilot symbols is usually not accurate enough. It was shown previously
that, in the absence of code synchronization errors, a pilot-aided
decision-directed (PADD) approach exhibits better BER performance than
pilot-aided estimation over fading channels, because it uses both pilot
and data symbols for channel estimation. This paper shows the impact of
the delay estimation errors on the PADD algorithm. The multipath delays
are estimated using pilot-aided (PA), non-data aided (NDA), or
decision-directed (DD) algorithms, and the comparison with ideal channel
estimation case is done via simulation. The PADD algorithm in the
presence of multipath delay errors is also compared with the pilot-aided
plus linear interpolation channel estimation. The simulation results
show that the PADD algorithm is not very sensitive to the delay
estimation errors when the delays are estimated via an NDA or DD
approach, and it exhibits better performance than the traditional
pilot-aided methods also when the delay estimation errors are present
Performance bounds for a UMTS RAKE receiver with imperfect timing
synchronisation are presented. Firstly, an analytical expression for the
bit error probability (Pe) performance of the RAKE receiver
is derived. This analysis establishes that the bit error probability
performance of the RAKE receiver is less sensitive to timing errors for
higher spreading factors. However, significant performance degradations
for all spreading factors confirm the need for timing synchronisation in
the RAKE receiver. An extension of the analysis is presented for a
multipath environment, allowing the derivation of an upper and a lower
performance bound. The results indicate that a very simple interpolator
providing 4 samples within a chip period results in a performance loss
smaller than 0.15 dB
We develop an analytical framework to study the performance of
wireless systems using maximal ratio combining (MRC) with an arbitrary
number of diversity branches in correlated multipath fading. We consider
the coherent detection of digital signals received over correlated
Nakagami (1960) fading channels, where the instantaneous signal-to-noise
ratios (SNRs) of the diversity branches are not necessarily independent
or identically distributed. Specifically: (1) these SNRs can be
arbitrarily correlated; (2) the SNR distributions can be from different
Nakagami families, i.e., fading parameters (ms) are not necessarily
equal; and (3) the average SNRs (averaged over the fading) of the
branches are not necessarily equal. We derive closed-form expressions
for three performance measures of a MRC diversity system: (1)
probability density function (p.d.f.) of the combiner output SNR; (2)
symbol error probability (SEP) for coherent detection; and (3) outage
probability. We obtain a canonical structure for these performance
measures as a weighted sum of the corresponding expressions for a
non-diversity (single-branch) system with appropriately-defined
parameters. This result is fundamental: the canonical structure depends
only on the properties of the channel and diversity combiner, and not on
the specific modulation technique. Calculations of the SEP for specific
modulation techniques are illustrated through examples
This paper presents the impact of timing error on the performance
of multirate direct sequence code division multiple access (DS-CDMA)
systems based on variable spreading factor (VSF) using multiuser
detection techniques such as the parallel interference cancellation
(PIC) detector. The performance is evaluated for a single-rate and a
three-rate system using Monte-Carlo simulation in the additive white
Gaussian noise (AWGN) channel without multipath fading. The bit error
probability (BEP) of the matched filter (MF) and the PIC detector with
and without timing errors are compared
The parallel interference cancellation (PIC) multiuser receiver is
among the most interesting multiuser demodulators for practical mobile
communication systems. Thus, the performance of the PIC multiuser
receivers operating in frequency selective fading channels is evaluated
in this paper. A decision-directed (DD) multiuser complex channel gain
estimation based both on prediction and smoothing is applied. The impact
of delay estimation errors on the bit error rate (BER) of the receiver
in both channel coded and uncoded CDMA systems is evaluated. It is
observed that a rather low standard deviation of delay estimation errors
(⩽0.1) is required to obtain a robust receiver performance. If that
is the case the performance of the PIC receiver is close to the known
delay case, and superior performance can be obtained
A majority of multiuser detectors for CDMA are based on coherent
detection where carrier frequency, carrier phase, transmission delays
and channel characteristics are assumed known at the receiver. In a real
system, these parameters must however be estimated based on the received
signal. In this paper we investigate the impact of delay and channel
estimation errors on the performance of multi-stage successive
interference cancellation and limited tree-search detection. The
estimation errors are modelled as zero-mean Gaussian random variables
with the variance being a measure of the accuracy of the
estimation
An efficient series that is used to calculate the probability of
error for a BPSK modulated DS CDMA system with chip timing and carrier
phase errors in a slowly fading multipath channel is derived. The
receiver is assumed to be a coherent RAKE receiver. Three types of
diversity schemes are considered: selection diversity, equal gain
diversity combining and maximal ratio diversity combining. The error
probability derivation does not resort to the widely used Gaussian
approximation for the intersymbol interference and multiple access
interference and is very accurate. Systems of 1.25 MHz and 5 MHz are
considered for different numbers of diversity branches
The bit error rate performance of a multipath combining type code division multiple access receiver with imperfections in power control, channel parameter estimation and spreading code phase estimation is analyzed. Imperfection in power control is taken into account by modeling the received signal power as a log normally distributed random variable. The estimate errors are modeled as zero mean Gaussian random variables. It is shown that the performance of such a receiver significantly degrades when variance of power control imperfection is above 0 dB, mean square error in channel parameter estimation is above 0.01 and standard deviation of the code phase error is above 0.1
An approximated probability density function is presented for the
SNR in maximal ratio combining diversity systems with an arbitrary
number of diversity branches in an arbitrarily correlated Nakagami
fading environment. Comparisons between the exact and approximated
distribution show good agreement over wide ranges of correlation
coefficients
The exact performance of optimal and suboptimal quadratic receivers in a binary hypothesis test between jointly distributed zero mean complex Gaussian variates is derived. The probability of error is given as a function of the characteristic values of a generalized eigenvalue problem set up in terms of the covariance matrix of the received signal-plus-noise and in the matrix of the quadratic form of the receiver. The results include the exact performance of various types of suboptimal receivers including those previously derived for the envelope matched filter for MFSK and the noncoherent DBPSK receiver in rapid Rayleigh fading, nonfrequency-selective channels. Also, the performance of near-optimal stationary process-long observation time [SPLOT] receivers, "energy detectors," and other approximately optimal receivers may be calculated for noncoherent signaling in the same channel.
We consider the downlink of a Universal Mobile Telecommunication
System terrestrial radio access-wideband code division multiple access
(UTRA-WCDMA) system and we investigate the performance of the
conventional RAKE receiver. A multipath slowly Rayleigh fading channel
is assumed. For the purpose of channel tap weight estimation, a common
control physical channel, that is either serial or parallel multiplexed
with the dedicated physical channels, is used. The receiver sensitivity
to imperfect knowledge of the path delays, to the number of pilot
symbols, and to the power ratio of pilot to data channels is also
investigated. The system performance is evaluated by means of bit-error
rates (BERs) derived using quadratic forms and characteristic functions
for a BPSK modulation. The mean-squared estimation error (MSEE) of the
channel tap weights is also computed and compared to the classical
Cramer-Rao lower bound (CRLB). The mutual interference between pilot and
data symbols is taken into account
In this paper, we analyze the bit error probability (BEP) of
binary and quaternary differential phase shift keying (2/4 DPSK) and
noncoherent frequency shift keying (NCFSK) with postdetection diversity
combining in arbitrary Rician fading channels. The model is quite
general in that it accommodates fading correlation and noise correlation
between different diversity branches as well as between adjacent symbol
intervals. We show that the relevant decision statistic can be expressed
in a noncentral Gaussian quadratic form, and its moment generating
function (MGF) is derived. Using the MGF and the saddle point technique,
we give an efficient numerical quadrature scheme to compute the BEP. The
most significant contribution of the paper, however, lies in the
derivation of a closed-form cumulative distribution function (cdf) for
the decision statistic. As a result, a closed-form BEP expression in the
form of an infinite series of elementary functions is developed, which
is general and unifies previous published BEP results for 2/4 DPSK and
NCFSK for multichannel reception in Rician fading. Specialization to
some important cases are discussed and, as a byproduct, a new and
general finite-series expression for the BEP in arbitrarily correlated
Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and
NCFSK performance for independent and correlated Rician fading channels;
and some interesting findings are presented
We consider the use of multistage parallel interference
cancellation at the base station of a code-division multiple-access
(CDMA) wireless system. Previous work in this area has demonstrated the
potential for significant improvements in capacity and near-far
resistance. However, most previous work has assumed perfect
synchronization with the signals of interest. Practical systems will
experience phase jitter and timing errors. We undertake an analysis of
the effects of phase and timing errors, obtaining a closed form result
for bit-error rate (BER) performance after an arbitrary number of stages
of cancellation in an additive white Gaussian noise (AWGN) channel. This
result is shown to agree well with simulations. Simulation results are
also presented for the important case of frequency selective Rayleigh
fading. The results from both analysis and simulations demonstrate that
interference cancellation is fairly robust to phase and timing errors
The performance of the MUSIC and ML methods is studied, and their
statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the
estimation problems is derived, and some useful properties of the CRB
covariance matrix are established. The relationship between the MUSIC
and ML estimators is investigated as well. A numerical study is reported
of the statistical efficiency of the MUSIC estimator for the problem of
finding the directions of two plane waves using a uniform linear array.
An exact description of the results is included
The linear minimum mean-squared-error (LMMSE) criterion can be
used to obtain near-far resistant receivers in direct-sequence
code-division multiple-access systems. The standard version of the LMMSE
receiver (postcombining LMMSE) minimizes the mean-squared error between
the filter output and the true transmitted data sequence. Since the
detector depends on the channel coefficients of all users, it cannot be
implemented adaptively in fading channels due to severe tracking
problems. A modified criterion for deriving LMMSE receivers
(precombining LMMSE) in fading channels is presented. The precombining
LMMSE receiver is independent of the users' complex channel
coefficients, and it effectively converts the time-varying Rayleigh
fading channel to an equivalent fixed additive white Gaussian noise
channel from the point of view of updating the detector. The performance
of the LMMSE receivers in fading channels is studied via computer
simulations and numerical analysis. The results show that the
postcombining LMMSE receiver has potentially larger capacity, but it
cannot be used in fast fading channels. The precombining LMMSE receiver
has slightly worse capacity than the postcombining LMMSE receiver, but
remarkably larger capacity than the conventional RAKE receiver at the
signal-to-noise ratios of practical interest
The bit-error probability of a linear receiver for code-division
multiple-access communications is analyzed. The analysis is presented
for the additive white Gaussian noise and fading multipath channels also
with data-aided channel estimation. Two ways to approximate the
averaging over the interfering data symbol combinations are considered
and compared. Numerical examples are presented to demonstrate the
usefulness of the analysis methods
The matched filter bound (MFB) for the two-path channel derived in
Mazo (1991) is extended to Rayleigh fading channels with an arbitrary
number of time-discrete paths. General results on antenna diversity
reception and communication over correlated-path fading channels are
presented. Examples of the MFB for several practically useful channels
are given
The bit error rate performance of a high chip rate, indoor code
division multiple access multipath combining receiver with imperfections
in power control, estimation of channel parameters (path amplitude and
phase), and estimation of spreading code phase is analyzed. Imperfection
in power control is taken into account by modeling the received signal
power as a log normally distributed random variable. The estimate errors
are modeled as zero mean Gaussian random variables. It is shown that the
performance of such a receiver degrades when the variance of power
control imperfection is above 0 dB, mean square error in channel
parameter estimation is above 0.01, or standard deviation of the code
phase error is above 0.1
Physical Layer-General Description
3GPP. Physical Layer-General Description. 3GPP Technical
Report TS 25.201 V3.0.0, Oct. 1999.