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Probability of Error for Diversity Combining in DS CDMA Systems with Synchronization Errors
Abstract
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. The derived series for probability of error calculations is used to assess the reduction in the system capacity due to different levels of synchronization errors. For all three diversity combining schemes considered, the degradation in the system performance is expressed as an effective reduction in the system processing gain. Systems of 1.25 MHz, 5 MHz and 10 MHz are considered for different number of diversity branches and it is shown that the percentage reduction in the system capacity due to synchronization errors is approximately the same for all these systems.
... The CF method used to evaluate the performance of the DS-SSMA scheme in multipath fading channels with multipath intersymbol interference was applied in [10] without taking into account the MAI effect. An approximate Fourier series technique was utilized in [11,12] to evaluate the BER performance in selective and non-selective Rayleigh fading environments. System degradation caused by an imperfect chip and phase synchronization were also assessed in this technique. ...
... where C n is defined in (59) (see Appendix A) and K μ (z) is the Bessel function for imaginary arguments [24] and it is defined in (67). The PDF of MAI in (12) for the distinct scenario shows that the MAI experienced at any receiving antenna is a sum of Laplacian distributed random variables. It can be easily seen that by setting N = 1 in the above, the PDF of MAI will reduce to a single Laplacian random variable, which is consistent with the result obtained in [16]. ...
... Here, σ 2 z = E z l m 2 and σ 2 η = E η l m 2 represent the MAI power and the noise power, respectively. In order to evaluate the MAI power, we make use of the probability of MAI expression derived in (12). Thus, we can evaluate σ 2 z as ...
A major limiting factor in the performance of multiple-input-multiple-output (MIMO) code division multiple access (CDMA) systems is multiple access interference (MAI) which can reduce the system’s capacity and increase its bit error rate (BER). Thus, a statistical characterization of the MAI is vital in analyzing the performance of such systems. Since the statistical analysis of MAI in MIMO-CDMA systems is quite involved, especially when these systems are fading, existing works in the literature, such as successive interference cancellation (SIC) or parallel interference cancellation (PIC), employ suboptimal approaches to detect the subscriber without involving the need for MAI statistics. The knowledge of both MAI and noise statistics plays a vital role in various applications such as the design of an optimum receiver based on maximum likelihood (ML) detection, evaluation of the probability of bit error, calculation of the system’s capacity, evaluation of the outage probability, estimation of the channel’s impulse response using methods including the minimum mean-square-error (MMSE), the maximum likelihood(ML), and the maximum a posteriori probability (MAP) criterion. To the best of our knowledge, there is no existing work that explicitly evaluates the statistics of the MAI-plus-noise in MIMO fading channels. This constitutes the prime objective of our proposed study here. In this work, we derive the expressions for the probability density function (PDF) of MAI and MAI-plus-noise in MIMO-CDMA systems in the presence of both Rayleigh fading channels and additive white Gaussian noise. Moreover, we evaluate the probability of the bit error rate in the presence of optimum reception using a ML receiver. Our theoretical findings can provide a reliable basis for both system design and various performance analyses of such systems. Our simulation results show that the theoretical findings are very well substantiated.
... However, fast algorithms to compute BEP of Rake receivers in the presence of delay estimation errors and Rayleigh multipath channels, with arbitrarily spaced channel taps and correlated fading are still hard to be found in the existing literature. BEP of a Rake receiver can be derived based on the probability distribution function (pdf) of the signal-to-noise ratio (SNR) at the output of the maximum ratio combiner (MRC) [2], [3], [7], or, equivalently, based on the characteristic function (CF) of SNR at the output of the combiner [8] or on the CF of the quadratic receiver [9], [10], [11]. For Rayleigh fading channels and in the absence of code synchronization errors, the SNR at the output of MRC can be modeled as a quadratic form in complex Gaussian variables [7], [13], [14]. ...
... If both fading and code synchronization errors are present, the statistics of SNR are changed compared to the case with no delay errors, and closed form formulas of its pdf are not easy to be derived. The solution usually adopted to deal with multipath fading channels and code synchronization errors is to assume flat fading channels, whose pdf over the observation interval is approximatively constant [2], [3]. Alternatively, characteristic function-based methods can be employed, but they have a large computational complexity, especially when channel imperfections, such as code synchronization errors, are taken into account [11]. ...
... One important question when dealing with Rake receivers is how much diversity can be gained if closely-spaced paths are used in the combiner. Usually, it is assumed that the paths are at least one chip apart [2], [3], [7]. However, some diversity might be achieved even if the paths are closely-spaced, and our theoretical model allows us to study this effect. ...
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.
... Many of these techniques are based on extensions of previous studies of intersymbol interference (ISI) systems. These methods include the moment space technique [13], characteristic function method [14], method of moments [15], [16], and an approximate Fourier series method [17], [18]. Generally, these techniques can achieve more accurate BER estimate than CLT-based approximations at the expense of much higher computational complexity. ...
... The characteristic function method was used in studying the performance of DS-SS systems on specular multipath fading channels with multipath ISI; however, MAI was not considered in this paper [20]. In [17] and [18], Sunay and McLane used an approximate Fourier series method to study BER performance under both frequency nonselective and selective Rayleigh fading. Additionally, the system degradations due to imperfect chip and phase synchronization were assessed. ...
... Averaging over in (17) with respect to the Rayleigh distribution (5) and using the integral identity [24, p. 101, eq. 3.61], we approximate the average BER in Rayleigh fading using the SGA as (18) ...
A binary direct-sequence spread-spectrum multiple-access system
with random sequences in flat Rayleigh fading is considered. A new
explicit closed-form expression is obtained for the characteristic
function of the multiple-access interference signals. It is shown that
the overall error rate can be expressed by a single integral whose
integrand is nonnegative and exponentially decaying. Bit-error rates
(BERs) are obtained with this expression to any desired accuracy with
minimal computational complexity. The dependence of the system BER on
the number of transitions in the target user signature chip sequence is
explicitly derived. The results are used to examine definitively the
validity of three Gaussian approximations and to compare the
performances of synchronous systems to asynchronous systems
... We can now set or to obtain useful formulas for the integral. Suppose (11) then using the identity in (3), we have (12) Substituting (11) and (12) in (10), setting in (10), and letting , we obtain (4b). The error term in (5b) is obtained by combining and in (10). ...
... When deriving (4b), we set in the LHS of (10). However, if instead we set (a variable parameter) and use (11) and (12) in (10), then we get a slightly more general infinite series for the cdf (17) where (18) This series depends on the sampling rate parameter and an additional parameter . Note that if , then this reduces to (4b), the Beaulieu series. ...
A frequent problem in digital communications is the computation of the probability density function (PDF) and cumulative distribution function (CDF), given the characteristic function (CHF) of a random variable (RV). This problem arises in signal detection, equalizer performance, equal-gain diversity combining, intersymbol interference, and elsewhere. Often, it is impossible to analytically invert the CHF to get the PDF and CDF in closed form. Beaulieu (1990, 1991) has derived an infinite series for the CDF of a sum of RVs that has been widely used. We rederive his series using the Gil-Pelaez (1951) inversion formula and the Poisson sum formula. This derivation has several advantages including both the bridging of the well-known sampling theorem with Beaulieu's series and yielding a simple expression for calculating the truncation error term. It is also shown that the PDF and CDF can be computed directly using a discrete Fourier transform.
... Performance of rake combining 1536-1276/06$20.00 c 2006 IEEE techniques (selection, equal gain and maximal ratio diversity) in the presence of chip and phase synchronization errors is reported in [17]. As expected, the maximal ratio combiner outperforms other combiners and quite drastic capacity losses are seen due to synchronization errors and fading. ...
In this paper we analyze the impact of system imperfections on the overall cellular code-division multiple access (CDMA) radio network performance. The theory is general and some examples of practical sets of channel and system parameters are used as illustration. A flexible signal model, based on the complex signal format, is used enabling us to model all wideband CDMA standards. For such a signal, we first derive a complex decorrelator structure. In the next step imperfections in the operation of a decorrelating space-time Rake combiner are modeled and analyzed. Relative capacity losses and the network sensitivity function are used as performance measures. Simulations are also performed to confirm some of the key assumptions made in the analysis. Numerical results show that the user capacity varies significantly depending on the multipath profile, diversity order, fading rate, and code crosscorrelations. It is shown that up to 97 % of the system capacity can be lost due to the system imperfections. More, advanced and robust parameter estimators and/or multiuser detectors are needed to alleviate these degradations at the cost of increased complexity
As larger diversity and coding gains are introduced into
spread-spectrum systems to mitigate the effects of multipath fading and
thermal noise, system performance is increasingly being limited by
channel estimation error. To properly design these systems, performance
measures incorporating the effects of estimation errors are needed. A
lower bound on the probability of bit error for a RAKE receiver
operating with imperfect phase estimates is presented along with a
method to obtain a closed-form expression for its evaluation. Further,
this lower bound is compared to an upper bound so that an accurate
assessment of system performance can be obtained
In this paper, we investigate the impact of mistiming on the performance of Rake receivers in direct-sequence ultra-wideband (DS-UWB) systems from the perspective of the achievable information rate. A generalized expression for the performance degradation due to mistiming is derived. Monte Carlo simulations based on this expression are then conducted, which demonstrate that the performance loss has little relationship with the target achievable information rate, but varies significantly with the system bandwidth and the multipath diversity order, which reflects design trade-offs among the system timing requirement, the bandwidth and the implementation complexity. In addition, the performance degradations of Rake receivers with different multipath component selection schemes and combining techniques are compared. Among these receivers, the widely used maximal ratio combining (MRC) selective-Rake (S-Rake) suffers the largest performance loss in the presence of mistiming. Comment: 5 pages, 7 figures, submitted to IEEE VTC 2011 spring in Sept.2010
The average bit error rate of an asynchronous bandlimited binary DS-CDMA system with three diversity combining receiver schemes over Nakagami-m fading channels is studied. Maximal ratio combining, predetection equal gain combining and predetection selection combining are considered. Random spreading and flat slow fading are assumed. The spectrum raised cosine and Beaulieu-Tan-Damen pulse shapes are employed. The standard Gaussian approximation for the multiple access interference is used for the performance analysis giving a closed-form expression for the BER of maximal ratio combining. Characteristic function and approximate Fourier series methods are used for the performance analysis of equal gain and selection combining schemes, respectively. Our results are valid for arbitrary diversity orders and arbitrary Nakagami fading parameters. The Beaulieu-Tan-Damen pulse outperforms the spectrum raised-cosine pulse in all situations considered.
Accurate average bit error rate analysis of diversity receivers for asynchronous bandlimited binary DS-CDMA systems operating over Nakagami-m fading channels is studied. Predetection equal gain combining (EGC) and selection combining (SC) are considered. The fading is assumed to be flat and slow, and random spreading sequences are considered. The spectrum raised cosine (SRC) and Beaulieu-Tan-Damen (BTD) pulse shapes are employed. The improved Gaussian approximation for multiple access interference is employed with characteristic function and Fourier series methods for the performance analysis. Our results are valid for arbitrary diversity order and arbitrary Nakagami fading parameter and the computational complexity does not grow with the diversity order. The new Beaulieu-Tan-Damen pulse outperforms the spectrum raised-cosine pulse in all situations examined.
In this paper, we investigate the performance of conventional RAKE
receivers using maximum ratio combining (MRC) for a UMTS terrestrial
radio wideband code division multiple access (UTRA-WCDMA) downlink. Both
perfect and non-perfect multipath slowly Rayleigh fading channel
estimations are considered. Exact bit error probabilities (BER) are
derived, using quadratic forms and characteristic functions, for BPSK
modulation. The users may have different bit rates. Then, the
mean-squared estimation error (MSEE) of the channel tap weights is
computed and compared to the Cramer-Rao lower bound (CRLB)
Accurate bit error rate calculation is considered for a binary,
direct sequence spread spectrum multiple access system using
conventional matched filter receivers and long code sequences in flat
fading Nakagami channels. To this end, a closed-form expression for the
characteristic function of a sum of multiple interfering signals is
found. The exact average bit error rate is expressed as a single
integral with a well-behaved integrand function. Numerical results
obtained from the new accurate bit error rate expression are compared
with the standard Gaussian approximation
An accurate bit-error-rate (BER) calculation method is derived for a binary direct-sequence (DS) spread-spectrum multiple-access (SSMA) system using conventional matched filter receivers and random sequences on flat-fading Nakagami channels. A closed-form expression for the characteristic function of a sum of multiple Nakagami interfering signals is found. The accuracy of the standard Gaussian approximation (SGA) is assessed for DS code-division multiple-access (CDMA) systems operating on Nakagami fading channels.
In wideband code-division multiple-access (CDMA) systems, where
large diversity gains are used to mitigate the effects of multipath
fading, system performance is increasingly limited by channel estimation
error. In a packet-based system, the estimation error can be reduced by
increasing the header length; however this, for a fixed bandwidth,
reduces the amount of transmit energy available to the data symbols and
reduces the processing gain of the system. To determine the allocation
of the transmit energy between the data and estimation symbols in order
to minimize the probability of bit error, we use an approximate upper
bound on the probability of bit error for a RAKE receiver operating with
imperfect phase estimates
The effect of imperfect timing is analyzed in equal gain combining (EGC) and maximal ratio combining (MRC) techniques over Rayleigh and Nakagami-m fading channels with binary phase-shift keying modulation. In the case of EGC, the bit-error probability is derived, while in the case of MRC, error rate bounds are presented. Theoretical results are justified by computer simulation. Numerical results demonstrate that both EGC and MRC are fairly sensitive to timing errors, and comparatively, MRC is more sensitive.
The authors propose and analyze a direct-sequence spread-spectrum
multiaccess (DS/SSMA) receiver that employs a cascade of cochannel
interference (CCl) cancellers for communication over multipath fading
channels. The receiver first coherently demodulates and despreads the
received signal to produce correlator outputs and initial data
estimates. Based on these estimates, the cancellation scheme essentially
creates replicas of the contributions of the CCl embedded in the
correlator outputs and removes them for a second improved hard data
decision. By repeating this operation over and over, a cascade of CCl
cancellers is derived. Through theoretical analysis and simulation, the
authors investigate the canceller's bit error rate (BER) performance in
both the absence and presence of errors in the amplitude and phase
estimates of each user's received signal. Numerical results show the
considerably large improvement in performance that can be attained by
the cancellation scheme, even under partially degraded estimates
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The application of selection diversity in conjunction with simple channel coding is considered for a multiuser, slowly fading, Spread-Spectrum Multiple Access (SSMA), digital radio system. For the most part, the index of performance for our study is the average bit error probability; we also give some consideration to multipath outage as a performance measure. All subscribers are assumed to communicate to a central station; that is, a star network architecture is assumed. Average power control is also assumed. The average mentioned in this context includes averaging over the channel fading statistics. The modulation is direct-sequence, spread-spectrum, binary phase-shift keying. We assume perfect timing and carrier recovery in our coherent receiver, and a slowly varying, Rayleigh fading, discrete multipath model is used. Previous analyses have found that SSMA can tolerate few simultaneous users for fading radio channels. We find that the combination of spread-spectrum modulation with low-complexity diversity and/or channel coding can restore fading-channel user levels to an acceptable figure. In addition, selection diversity plus channel coding is more effective than either method by itself. Finally, it turns out that SSMA is less sensitive to a change in the value of delay spread of a fading channel than, say, time-division multiple access. The method of moments is used to accurately assess the system error probability. Using this technique, we also assess the accuracy of assuming that the multiuser interference has a Gaussian distribution, which allows it to be analyzed by a simple method. Using this assumption, we compare selection diversity plus channel coding with the maximal-ratio-combining technique for diversity reception. Except for a high order of diversity, the former is more efficient and is always less complex than the latter.
We consider a cellular satellite system conceived to enhance the capabilities of the pan-European terrestrial system (GSM). This adopts EHF band and highly-inclined orbits. We present a preliminary assessment of system capacity based on asynchronous direct-sequence spread-spectrum multiple access (DS-SSMA). Performance is measured in terms of error probability achieved by K users simultaneously accessing the system with a given signal-to-noise ratio.
An analysis of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. The results of this analysis reveal which code parameters have the greatest impact on communication performance and provide analytical tools for use in preliminary system design. Emphasis is placed on average performance rather than worst-case performance and on code parameters which can be computed easily.
The full derivation of an upper bound previously given by the
authors (see Proc. IEEE Veh. Tech. Conf., St. Louis, USA, p.362-7, 1991)
is provided, and comparisons are made between the authors' bound and
other similar bounds, as well as to simulations on the Rician channel.
The Rician channel results were used to test the robustness of the
Gaussian assumption. Although not originally intended for this
application, the authors' bound is found to be accurate when compared to
simulations and to other analytical bounds in certain parameter regions
In this paper we determine the performance of a direct sequence spread spectrum multiple access system where the users utilize different carrier frequencies. This scheme is applicable to a system, such as an indoor wireless communication system utilizing very high frequencies, where the available bandwidth is so large that it is not feasible to spread the signal over the whole band. The multi-user interference is modeled as a compound Gaussian random variable and expressions are found for the variance of the interference as a function of relative phase and frequency parameters. In addition to different carrier frequencies the analysis also accounts for offsets in the chip clock frequencies, general chip pulse shaping function, and different received signal powers. We give results for the error probability in a multiple access system utilizing BPSK, QPSK, and OQPSK modulation.
Error probabilities for various unbalanced DS-CDMA systems are
calculated using the standard Gaussian approximation, improved Gaussian
approximation and the Fourier series based schemes. A scarcely populated
system, a system with a dominant interferer, a system in a fading
channel and a multimedia system with a single high processing gain user
are considered. It is seen that the standard Gaussian approximation in
all of these cases gives inaccurate results, especially when the number
of users active in the system is low. The improved Gaussian
approximation on the other hand, gives more accurate results for a
scarcely populated system and a system with a dominant interferer. For
systems in fading channels and multimedia systems, neither of the
Gaussian approximations are accurate. For all of these cases, the
Fourier series based scheme gives very accurate results without
computational complexity
Direct sequence spread spectrum CDMA systems is receiving
considerable attention in the field of mobile communication. The bit
error rate performance of a code division multiple access correlator
type receiver with imperfections in power control, carrier phase
estimate and spreading code phase estimate is analyzed. Imperfection in
power control is taken into account by modeling the received signal
power as a log normally distributed random variable. The phase 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, standard deviation
of the code phase error is above 0.01 and mean square error of carrier
phase estimate is above 0.01. The communication system considered is a
microcellular system operating in an indoor environment where K
transmission stations are asynchronously transmitting over their
individual multipath fading channels to the base station receiver
Use of direct sequence code division multiple access (DS CDMA) has
been the object of much attention in the research and development of a
multi-service personal communications network. The performance of such a
system is usually given in terms of the bit error rate as a function of
the number of active users for a given signal to noise ratio. We have
investigated the degradation in the performance of a BPSK modulated,
bi-phase spread DS CDMA system due to synchronization errors. A Fourier
series approach has been used to find an infinite series representation
for the probability of error when both chip timing and carrier phase
errors are present. The analysis requires the characteristic functions
of both the multiple access interference and self interference and these
functions have been expressed in terms of the special functions of
mathematical physics. Computation of the infinite series is very fast as
a whole bit error curve can be generated in minutes on a Sparc IPX
workstation. The infinite series is also compared with the standard
Gaussian approximation and an alternative Gaussian approximation found
in the literature. The series is then used to assess the reduction in
system capacity when synchronization errors are present in the system.
We have expressed this degradation in the system performance as an
effective processing gain reduction
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
Efficient series that are used to calculate the probability of
error for quadriphase spread, BPSK modulated, synchronous,
quasi-synchronous and asynchronous DS-CDMA systems in the presence of
chip timing and carrier phase errors are derived. The derivations
require the characteristic functions of the multiple access interference
and of the self interference. These series are then used to assess the
capacity of the systems at different levels of synchronization errors.
The derivations are performed for both constant and random
synchronization errors. Using the series, the asynchronous quadriphase
spread system capacity is compared to that of an asynchronous binary
spread system
The effects of the `near-far' problem on the Direct Sequence Code
Division Multiple Access (DS/CDMA) system performance is investigated,
for nonfading and Rayleigh faded channels, for spread spectrum mobile
communication, respectively. For this purpose, the near-far situation is
considered for various values of the interference to desired signal
power ratios (αi), and for different number of users
(K). Results obtained in this study show that the error probability
degrades substantially as the number of users in the system grows, or as
the interfering signals' strength increases. It is also noticed that the
performance deteriorates in the Rayleigh fading channel as compared to
the nonfading case due to the near far problem, which results in a
severe reduction in the multiple access capability of the DS/CDMA system
The performance of a microcellular radio system is evaluated by
assuming the desired and cochannel interfering signals by shadowed
Rician and uncorrelated shadowed Rayleigh distributions, respectively.
Performance is measured in terms of cochannel interference probability
and spectrum efficiency. The effects of protection ratio, carried
traffic (blocking probability), Rician parameter, and standard deviation
of log-normal shadowed local mean on the performance parameters are
investigated. The performance is mathematially analyzed by modeling the
power-law with distance by a dual path-loss law with a turning point
The ideal probability-computing M -ary receiver is derived for a fading, noisy, multidiversity channel, in which the link fadings may be mutually correlated, as may the link noises. The results are interpreted in terms of block diagrams involving various filtering operations. Two special cases, those of very fast and very slow fading, are considered in detail.
This paper provides analyses of three types of diversity combining systems in practical use. These are: selection diversity, maximal-ratio diversity, and equal-gain diversity systems. Quantitative measures of the relative performance (under realistic conditions) of the three systems are provided. The effects of various departures from ideal conditions, such as non-Rayleigh fading and partially coherent signal or noise voltages, are considered. Some discussion is also included of the relative merits of predetection and postdetection combining and of the problems in determining and using long-term distributions. The principal results are given in graphs and tables, useful in system design. It is seen that the simplest possible combiner, the equal-gain system, will generally yield performance essentially equivalent to the maximum obtainable from any quasi-linear system. The principal application of the results is to diversity communication systems and the discussion is set in that context, but many of the results are also applicable to certain radar and navigation systems.
We evaluate the capacity and bandwidth efficiency of microcellular
CDMA systems. Power control, multipath diversity system bandwidth, and
path loss exponent are seen to have a major impact on the capacity. The
CDMA system considered uses convolutional codes, orthogonal signalling,
multipath/antenna diversity with noncoherent combining, and fast
closed-loop power control on the uplink (portable-to-base) direction. On
the downlink (base-to-portable), convolutional codes, BPSK modulation
with pilot-signal-assisted coherent reception, and multipath diversity
are employed. Both fast and slow power control are considered for the
downlink. The capacity of the CDMA system is evaluated in a multicell
environment taking into account shadow fading, path loss, fast fading,
and closed-loop power control. Fast power control on the downlink
increases the capacity significantly. Capacity is also significantly
impacted by the path loss exponent. Narrowband CDMA (system bandwidth of
1.25 MHz) requires artificial multipath generation on the downlink to
achieve adequate capacity. For smaller path loss exponents, which are
more likely in microcellular environments, artificial multipath
diversity of an order of as high as 4 may be needed. Wideband CDMA
systems (10 MHz bandwidth) achieve greater efficiencies in terms of
capacity per MHz
A performance analysis of direct-sequence systems with long
pseudonoise sequences is presented. The assessment of the symbol error
probability in the presence of multiple-access interference is stressed,
but other types of interference are also considered for completeness.
Both binary and quaternary spreading waveforms are treated. The
analysis, which uses a nonstandard Gaussian approximation, makes
transparent the answers to a number of technical issues. Approximate
error probabilities that are relatively simple computationally are
derived. The approximations are accurate to within at least one decibel
and, more typically, a few tenths of a decibel
The performance of a multiple-cell direct-sequence code division
multiple-access cellular radio system is evaluated. Approximate
expressions are obtained for the area-averaged bit error probability and
the area-averaged outage probability for both the uplink and downlink
channels. The analysis accounts for the effects of path loss, multipath
fading, multiple-access interference, and background noise. Two types of
differentially coherent receivers are considered: a multipath rejection
receiver and a RAKE receiver with predetection selective combining.
Macroscopic base station diversity techniques and uplink and downlink
power control are also topics of discussion
The authors consider the performance of a cellular radio,
direct-sequence code-division multiple access, (CDMA) system. The
base-to-mobile link is modeled as a flat Rayleigh fading channel, with
all signals transmitted from a given base station fading in unison. For
the mobile-to-base link, the authors use a similar model, except that
the waveforms from all users are assumed to experience independent
fading. The effects of imperfect power control are shown
The performance of a spread-spectrum CDMA (code-division multiple
access) system in a mobile satellite environment is analyzed.
Comparisons to single-channel-per-carrier FDMA systems are presented
which show that the CDMA approach provides greater capacity. Results
from computer simulations, laboratory tests, and field tests of a
prototype modem are also presented. The tests results show excellent
performance of the modem in the mobile environment and also the
feasibility of the spread-spectrum approach to satellite mobile
communications
The exact calculation of error probabilities for direct-sequence
spread-spectrum multiple-access (DS/SSMA) systems has been addressed in
the literature. The exact calculation is computationally difficult, so
emphasis has been on approximations and bounds. One particularly
attractive approximation is to just use a signal-to-noise ratio in a
Gaussian approximation, the `standard approximation'. Unfortunately,
that approximation is not generally accurate enough. An improved
Gaussian approximation with good accuracy has recently been presented.
The author derives an accurate Gaussian approximation which is also
computationally very simple
An efficient series that can be used to calculate the probability
of error in a binary symmetric channel with intersymbol interference and
additive noise is derived. The series is derived by representing the
noise complementary probability distribution function by an exact or
approximate Fourier series. Bounds on the accuracy of the estimate are
derived for Gaussian noise. Examples show that only a small numerical
effort may be required to compute error probabilities of interest using
the series. Applications to both finite and infinite intersymbol
interference systems are discussed. A similar technique is used to
derive series representations for the probability of error of additive
noise channels with cochannel interference or with combined intersymbol
and cochannel interferences. The accuracy of the results is bounded for
Gaussian noise
Averaged diversity combining is applied to an asynchronous DS/CDMA
system using convolutional encoding and Viterbi decoding. A cyclic
redundancy check (CRC) code is included in the scheme to trigger
retransmission requests. Multiple received packets are combined on a bit
by bit basis to form a single, more reliable packet. The error
correcting decoder operates on the combined packet, as opposed to the
most recently received individual packet (e.g., as in a type-I hybrid
ARQ protocol), substantially increasing the probability of acceptance
with each additional transmission. We show that the proposed technique
allows a significant increase in the CDMA system capacity, throughput,
and reliability
It is shown that, particularly for terrestrial cellular telephony,
the interference-suppression feature of CDMA (code division multiple
access) can result in a many-fold increase in capacity over analog and
even over competing digital techniques. A single-cell system, such as a
hubbed satellite network, is addressed, and the basic expression for
capacity is developed. The corresponding expressions for a multiple-cell
system are derived. and the distribution on the number of users
supportable per cell is determined. It is concluded that properly
augmented and power-controlled multiple-cell CDMA promises a quantum
increase in current cellular capacity
On optimal diversity reception IRE Transactions on Information Theory Imai: A spread s p e c t m multiaccess I ] F. Simpson. J. Holtzman: On calculating bit error probability : for convolutional coding over the ricean fading channel
- G L Turin
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