Performance of RAKE reception in dense multipath channels:implications of spreading bandwidth and selection diversity order

We develop an analytical framework to quantify the effects of the spreading bandwidth (BW) on spread spectrum systems operating in dense multipath environments in terms of the receiver performance, the receiver complexity, and the multipath channel parameters. The focus of the paper is to characterize the symbol error probability (SEP) performance of a RAKE receiver tracking the L strongest multipath components in wide-sense stationary uncorrelated scattering (WSSUS) Gaussian channels with frequency-selective fading. Analytical SEP expressions of the RAKE receiver are derived in terms of the number of combined paths, the spreading BW and the multipath spread of the channel. The proposed problem is made analytically tractable by transforming the physical RAKE paths, which are correlated and ordered, into the domain of a “virtual RAKE” receiver with independent virtual paths. This results in a simple derivation of the SEP for a given spreading BW and an arbitrary number of combined paths     

Optimum spreading bandwidth for selective RAKE reception overRayleigh fading channels

Building on the developments in the performance analysis of generalized selection combining (GSC), this paper examines the optimum spreading bandwidth for a fixed-complexity GSC diversity receiver operating over independent identically distributed Rayleigh paths. For this purpose, the study considers three performance criteria: (1) average combined signal-to-noise ratio (SNR) at the GSC output; (2) average bit error probability (BEP); and (3) outage probability of the instantaneous combined SNR at the GSC output. For the average BEP criterion, results are presented for both coherent and noncoherent combining. For the average combined SNR and some instances of the average BEP optimization problem, an accurate approximate estimate of this optimum bandwidth in the form of a solution of a transcendental equation is provided. In other cases, where the optimization is not easily tractable in an analytic fashion, a numeric-search procedure is used to find this optimum bandwidth for different performance criteria and system parameters of interest. Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a set of system parameters and a particular performance criterion of interest     

Virtual path analysis of selective RAKE receiver in dense multipathchannels

We develop an analytical framework to quantify the effects of spreading bandwidth on spread-spectrum systems operating in dense multipath environments. Closed-form expressions for the mean and variance of the total RAKE receiver output signal-to-noise ratio are derived. The proposed problem is made analytically tractable by transforming the physical RAKE paths into the virtual path domain     

Capacity of RAKE reception with energy randomization

We consider a RAKE receiver for coherent binary orthogonal signaling over a frequency selective multipath Rayleigh fading channel. The receiver uses maximal-ratio combining such that the weight estimation errors are not independent of the additive noise. We find the capacity-achieving energy randomization scheme with two energy levels for the cases of imperfect and perfect channel estimates. We observe that the capacity-achieving probability gets closer to 1/2 with increase in the number of paths. We also show that the capacity is higher if channel estimates are perfect and that the channel estimation errors have more pronounced effect on the capacity at low signal-to-noise ratios.     

Performance of direct-sequence spread-spectrum RAKE receivers withrandom spreading sequences

In this paper, we derive error probability expressions for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) spread direct-sequence spread-spectrum (DSSS) systems employing random spreading sequences with RAKE receivers. The derived expressions accurately take into account the effect of interpath interference which usually has been neglected in previous analyses. Selection, equal gain, and maximal ratio techniques are considered for diversity combining. Two possible finger assignment strategies, one based on the instantaneous amplitudes and another based on the average powers of the multipath components, are considered for the assignment of multipath components to the available demodulating fingers in the RAKE receiver. Also, various simple, and in many cases, closed-form approximations for the error probabilities are derived and their accuracies are assessed     

Impact of filtering on RZ-DPSK reception

We discuss the influence of optical and electrical filtering on the performance of beat-noise limited balanced and single-ended direct detection of return-to-zero differential phase-shift keying (DPSK). Our simulations, supported by 40-Gb/s measurements, show that balanced DPSK detection outperforms both its single-ended equivalent and ON-OFF keying by /spl sim/2.7 dB, with higher gains at narrower optical filter bandwidths.     

Analysis of RAKE reception with MRC and imperfect weight estimationfor binary coherent orthogonal signaling

We consider a RAKE receiver for coherent binary orthogonal signaling employing predetection maximal-ratio combining (MRC), in which the tap weights are estimated by adding two matched filtered outputs using the two reference signals. The weight estimation errors here are not independent of the additive channel noise, and therefore do not fit into the Gaussian error model for MRC. Instead of analyzing the distribution of the weight estimation errors, we find the characteristic function of the decision variable, and from it we obtain a formula for the symbol error probability     

Performance evaluation of DS-CDMA systems on multipath propagationchannels with multilevel spreading sequences and RAKE receivers

Performance of small-cell wireless direct sequence code-division multiple access (DS-CDMA) systems with multilevel spreading sequences is investigated. An analytical methodology to evaluate both outage probability and mean bit error probability is presented; and its results are compared to those obtained with a semianalytical Monte Carlo based approach. Multipath propagation, the exact correlation properties of spreading codes, and both the simple correlator and RAKE receivers are taken into account in the analysis, which is oriented to asynchronous and synchronous environments. The spreading sequences investigated include multilevel sequences with complex isomorphic mapping, as well as some well-known two-level sequences. The numerical results show the impact of multilevel sequences on system performance, the improvements found in the absence of multiple access interference by using them rather than binary sequences, and the agreement between analytical and semianalytical evaluation     

Geometric model for DSPN satellite reception in the dense scatterermobile environment

A geometric propagation model is developed for simulating the reception of direct sequence pseudonoise (DSPN) satellite signals by a directional or omni directional antenna in the dense scatterer mobile environment. The model is used to predict fading statistics. As expected, the mitigation of fading is closely related to the ratio of DSPN chip duration to delay spread of the scatterer medium for both the omni and directional antennas. The results suggest a general, frequency domain interpretation for the value of DSPN in mitigating multipath fading     

Performance of DS-UWB multiple-access systems with diversity reception in dense multipath environments

Ultrawideband (UWB) technology is characterized by transmitting extremely short duration radio impulses. To improve its multiple-access capability, the UWB technology can be combined with traditional spread-spectrum techniques. This paper demonstrates the influence of spatial and temporal diversities on the performance of direct-sequence (DS) UWB multiple-access systems in dense multipath environments. Numerical results show that the bit error rate performance of the DS-UWB system can be improved significantly by increasing the number of antenna array elements and/or by adding more multipaths coherently at the receiver. Furthermore, this paper studies the impact of array geometry on system performance and shows that a rectangular array can capture more energy and thus can offer better performance than a uniform linear array.     

Effective bandwidth of DSPN signalling for mitigation of fading in dense scatterers

The use of direct sequence pseudonoise (DSPN) signalling to mitigate the fading caused by very dense scatterers in the mobile communication environment is explored for the specific case of a rectangular signal spectrum. A very simple and revealing relationship emerges between the variability of the signal strength and the signal bandwidth.<>     

Optimal bandwidth allocation to coding and spreading in DS-CDMA systems using LMMSE front-end detector

In code-division multiple-access (CDMA) systems, it is interesting to study the optimal bandwidth allocation to coding and spreading in order to maximize the number of users that the system can accommodate. This optimal bandwidth allocation is referred to as the optimal allocation point (OAP). In this brief, a practical CDMA system with a fixed total-bandwidth expansion factor that employs convolutional codes and random spreading is considered. The receiver consists of a multiuser linear-minimum-mean-square-error (lmmse) detector front end followed by autonomous single-user decoders. Intuitive reasoning is applied for the existence of an OAP in such a system. Also, we present a theoretical formulation to estimate the OAP in the aforementioned system. Simulations confirm the correctness of results obtained. Further, the paper investigates system behavior at different values of information-bit signal-to-noise ratio (SNR). At high values of SNR, within the range considered, the system favors spreading only. However, at relatively lower SNRs, channel coding is required to improve the system performance, and it is important that we operate at the OAP obtained.     

Impact of channel-state information on coded transmission overfading channels with diversity reception

We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian     

Impact of cache interferences on usual numerical dense loop nests

In numerical codes, the regular interleaved accesses that occur within do-loop nests induce cache interference phenomena that can severely degrade program performance. The authors identify cache interference phenomena and determine their causes and the conditions under which they occur. Based on these results, a methodology is derived for computing an analytical expression of cache misses for most classic loop nests, which can be used for precise performance analysis and prediction. It is shown that cache performance is unstable, because some unexpected parameters, such as arrays base address, can play a significant role in interference phenomena. It is also shown that the impact of cache interferences can be so high that the benefits of current data locality optimization techniques can be partially, if not totally, eradicated     

Impact of frequency offsets and IQ imbalance on MC-CDMA reception based on channel tracking

New air interfaces are currently being developed to meet the high spectral efficiency requirements of the emerging wireless communication systems. Multicarrier code-division multiple access (MC-CDMA) is seen as a promising candidate for the fourth-generation (4G) cellular communication systems because it can interestingly deal with the multipath propagation at a low processing complexity. Besides spectral efficiency and power consumption, the production cost of the transceiver should also be optimized. Direct conversion radio frequency (RF) receivers are appealing because they avoid costly intermediate frequency (IF) filters. However, they imply RF IQ separation, introducing a phase and amplitude mismatch between the I and Q branches. A communication system based on MC-CDMA is sensitive to synchronization errors and front-end non-idealities because it uses a long symbol duration. The goal of this paper is to evaluate the impact of the carrier frequency offset, the sampling clock offset, and the IQ imbalance on the MC-CDMA downlink system performance, considering a receiver based on channel tracking designed to cope with high mobility conditions. It is demonstrated that part of the effects is compensated by the channel estimation and an expression of the variance of the remaining symbol estimation error is provided. For the cellular system and the target performance considered in this paper, specifications are defined on the non-idealities. The results are validated with bit-error rate simulations.     

Optimal allocation of bandwidth for source coding, channel coding, and spreading in CDMA systems

This paper investigates the tradeoffs between source coding, channel coding, and spreading in code-division multiple-access systems, operating under a fixed total bandwidth constraint. We consider two systems, each consisting of a uniform source with a uniform quantizer, a channel coder, an interleaver, and a direct-sequence spreading module. System A is quadrature phase-shift keyed modulated and has a linear block channel coder. A minimum mean-squared error receiver is also employed in this system. System B is binary phase-shift keyed modulated. Rate-compatible punctured convolutional codes and soft-decision Viterbi decoding are used for channel coding in system B. The two systems are analyzed for both an additive white Gaussian noise channel and a flat Rayleigh fading channel. The performances of the systems are evaluated using the end-to-end mean squared error. A tight upper bound for frame-error rate is derived for nonterminated convolutional codes for ease of analysis of system B. We show that, for a given bandwidth, an optimal allocation of that bandwidth can be found using the proposed method.     

Impact of diversity reception on fading channels with codedmodulation. I. Coherent detection

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system)     

Impact of diversity reception on fading channels with codedmodulation. III. Co-channel interference

For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions     

Modelling direct sequence pseudonoise(dspn) satellite reception with directional antennas in the dense scatterer mobile environment

A geometric propagation model is developed for simulating the reception of direct sequence pseudonoise (DSPN) satellite signals by a directional or omni antenna in the dense scatterer mobile environment. The model is first validated for narrowband signals by a direct comparison of both simulated cumulative signal strength statistics and simulated diffuse Doppler spectra with classical theory. The model is then used to predict fading statistics for DSPN signaling, either with omni or directional antennas. As expected, the mitigation of fading is closely related to the ratio of DSPN chip duration to delay spread of the scatterer medium for both the omni and directional antennas.     

Impact of diversity reception on fading channels with codedmodulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M⩾2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown