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     

Impact of spreading bandwidth on RAKE reception in dense multipathchannels

Spread spectrum (SS) multiple access techniques have been proposed for third generation broadband wireless access. We develop an analytical framework to quantify the effects of spreading bandwidth on SS systems operating in dense multipath environments in terms of the receiver performance, receiver complexity, and multipath channel parameters. In particular, we consider wide-sense stationary uncorrelated scattering (WSSUS) Gaussian channels with frequency-selective fading. The focus of the paper is to characterize the combined signal of the RAKE receiver fingers tracking the strongest multipath components. Closed form expressions for the mean and the variance of the total RAKE receiver output signal-to-noise ratio (SNR) are derived in terms of the number of RAKE fingers, spreading bandwidth, and multipath spread of the channel. The proposed problem is made analytically tractable by transforming the physical RAKE paths into the virtual path domain. A representative result indicates that for SS systems with 5 MHz signal bandwidth operating in a channel with constant power delay profile having 5 μs spread, the average SNR gain from increasing the number of RAKE fingers from one to three is 3.8 dB and from three to five is 1.5 dB. Furthermore, the reduction in the variation of SNR is 1.1 dB and 0.4 dB for the same increments in the number of fingers     

The effects of sequence selection on DS spread spectrum withselective fading and Rake reception

Error probabilities are evaluated for direct-sequence spread-spectrum communications and Rake reception over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, the received signal-to-noise ratio, and the number of taps in the Rake receiver. The focus of the paper is on the effect of the spreading sequence on the performance of each of two systems. One system employs noncoherent detection of differentially-encoded binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver which uses equal-gain combining. The other system employs coherent detection of binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver with perfect gain estimates for the channel. A simple sequence selection criterion is introduced, and the sensitivity of the performance of the system to the choice of the spreading sequence is examined. It is shown that significant performance differences result from different choices of the spreading sequence. It is also shown that, given a moderate range of delay spreads, sequences can be found that yield low bit error probabilities over that range. These are found to be robust with respect to the delay spectrum for the channel, the number of taps in the Rake receiver, the Doppler spread, and the signal-to-noise ratio     

A novel correlation adaptive receiver structure for high speed transmissions in ultra wide band systems with realistic channel estimation

Impulse radio ultra wide band (UWB) communications require robust receivers; typically Rake receivers are required to capture a large number of resolvable paths, (even hundred of paths), so large number of correlators are needed; otherwise, adaptive receivers use complex filters and channel estimation algorithms. Therefore, traditional Impulse radio receivers demand non-practical implementation structures. In this paper we propose a novel correlation-adaptive receiver structure with low complexity for indoor high speed ultra wide band systems. This novel structure combines correlation characteristics from Rake receivers with recursive filters from adaptive receivers. The receiver includes a low complexity recursive channel estimation filter capable of estimating hundreds of channel impulse responses, and a single filter-correlation filter used for coherent bit demodulation. Furthermore, we derive by simulations the bit error rate for high density multipath environments for several impulse radio modulations like TH-PPM, DS-BPSK and TH-BPSK and we compare the performance of the proposed structure with typical Rake receivers.     

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     

Performance of Multicarrier CDMA Rake System over Rayleigh Fading Channel

Based on the theory of multicarrier (MC) technique and the Rake receiver, a multicarrier DS-CDMA Rake system is proposed, where a data sequence multiplied by a spreading sequence modulates multiple carriers. The receiver provides a Rake for each subcarrier, and the outputs of the Rakes are combined by a maximal-ratio combiner. The average probability of error of the system is derived from an uncorrelated subcarrier and frequency-selective fading channel model. The system performances are evaluated over Rayleigh fading channel with an exponential multipath intensity profile(MIP) and with a rectangular MIP, respectively, when multipath interference is present. It is found that this kind of model has larger superiority in an exponential MIP than in a rectangular MIP.     

Increasing the Efficiency of Rake Receivers for Ultra-Wideband Applications

In diversity rich environments, such as in Ultra-Wideband (UWB) applications, the a priori determination of the number of strong diversity branches is difficult, because of the considerably large number of diversity paths, which are characterized by a variety of power delay profiles (PDPs). Several Rake implementations have been proposed in the past, in order to reduce the number of the estimated and combined paths. To this aim, we introduce two adaptive Rake receivers, which combine a subset of the resolvable paths considering simultaneously the quality of both the total combining output signal-to-noise ratio (SNR) and the individual SNR of each path, reducing the number of combined paths, while keeping the desirable performance. These schemes achieve better adaptation to channel conditions compared to other known receivers, without further increasing the complexity. Their performance is evaluated in different practical UWB channels, whose models are based on extensive propagation measurements. The proposed receivers compromise between the power consumption, complexity and performance gain for the additional paths, resulting in important savings in power and computational resources.     

Performance analysis of cellular CDMA networks overfrequency-selective fading channel

An effect of multipath fading on the performance of a cellular code-division multiple-access (CDMA) system is analyzed in this paper. A wide-sense stationary uncorrelated scattering (WSSUS) channel model and the coherent binary phase-shift keying (BPSK) with asynchronous direct-sequence (DS) spreading signal are assumed in the analysis. The average error probability for both the forward link and reverse link of a cellular CDMA system over a frequency-selective fading channel using a conventional correlation-type receiver and RAKE receiver are derived. The impact of imperfect power control and channel capacity of a cellular CDMA system is also investigated. The closed forms of average error probability derived in the paper can save a lot of computation time to analyze the performance and channel capacity of a cellular CDMA system. The analytical results show that the performance and maximum transmission rate of cellular CDMA systems degrade with an increase in the number of simultaneous users and the number of interfering cells. The signal-to-interface ratio (SIR) for the reverse link derived in this paper can directly describe the interrelationships among a number of paths, number of users, number of interfering cells, fading factors, and maximum variation of a received unfaded signal     

Rake接收机在超宽带系统中的均衡性能分析

从缩短信道时延扩展的角度出发,研究了Rake接收机的部分信道均衡能力,并推导出了Rake接收机均衡性能与Rake接收机的复杂度和信道衰减系数之间的关系;分析了信道估计误差对Rake接收机合并前后多径信道变化的影响。研究表明当存在估计误差时,Rake接收机仍然能实现均衡的作用,但是性能有所下降;由于低复杂度Rake接收机引入的估计误差较少,在低信噪比条件下其均衡性能甚至会优于高复杂度的Rake接收机。     

MMSE multipath diversity combining for multi-access TH-UWB in the presence of NBI

The performance of asynchronous time-hopping ultra-wideband (TH-UWB) multiple access spread spectrum is analytically investigated in a UWB realistic multipath channel and in the presence of narrowband interference (NBI). In particular, an interference suppression receiver for TH-UWB wireless systems is proposed. It consists of selecting the first strongest multipath components using an appropriate Rake receiver with the path diversity combining being based on the minimum mean square error criterion. Pulse position modulation and pulse amplitude modulation schemes are considered. The expressions of the signal-to-interference and noise ratio at the output of the selective Rake combiner, the system multi-access data rate as well as the conditional bit error rate are also derived. The impact of different parameters, such as the number of selected dominant paths, the NBI power as well as the time hopping sequence code on the system performance are studied. Results reveal that the proposed receiver can almost completely eliminate the effect of NBI.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

Analysis and optimization of pilot symbol-assisted Rake receivers for DS-CDMA systems

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency.     

Low Complexity Rake Receivers in Ultra-Wideband Channels

One of the major issues for the design of ultra-wideband (UWB) receivers is the need to recover the signal energy dispersed over many multipath components, while keeping the receiver complexity low. To this aim we consider two schemes for reduced-complexity UWB Rake receivers, both of which combine a subset of the available resolved multipath components. The first method, called partial Rake (PRake), combines theirs/ arriving multipath components. The second is known as selective Rake (SRake) and combines the instantaneously strongest multipath components. We evaluate and compare the link performance of these Rake receivers in different UWB channels, whose models are based on extensive propagation measurements. We quantify the effect of the channel characteristics on the receiver performance, analyzing in particular the influence of small-scale fading statistics. We find that for dense channels the performance of the simpler PRake receiver is almost as good as that of the SRake receiver, even for a small number of fingers. In sparse channels, however, the SRake outperforms the PRake significantly. We also show that for a fixed transmitted energy there is an optimum transmission bandwidth     

P-order metric UWB receiver structures with superior performance

The generalized Gaussian probability density function is shown to better approximate the probability density function of the multiple access interference in ultra-wide bandwidth systems than the Gaussian approximation and the Laplacian density approximation. Two ultra-wide bandwidth receiver structures based on this new approximation using a p-order metric receiver decision statistic are investigated for the detection of time-hopping ultra-wide bandwidth wireless signals in multiple access interference channels. The first receiver outperforms both the conventional matched filter ultra-wide bandwidth receiver and the soft-limiting ultra-wide bandwidth receiver when only multiple access interference is present in UWB channels. The second new receiver with adaptive limiting threshold outperforms the conventional matched filter ultra-wide bandwidth receiver, the soft-limiting ultra-wide bandwidth receiver, and the adaptive threshold soft limiting ultra-wide bandwidth receiver in all multiple access interference-plus-noise environments. In multipath channels, a new Rake receiver based on the p-order metric receiver is proposed for signal detection. Mathematical analysis and numerical results show that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.     

UWB Impulse Radio Receiver Based on Single Bit Quantization

Impulse Radio (IR) modulation is perceived to be a practical means of exploiting the multi-gigahertz bandwidth available for UWB links. However, the RMS delay spreading of indoor channels relative to the transmitted pulse width is typically very large such that several hundred signal samples are required to be quantized and processed for each received pulse. To realize a relatively low power low-complexity receiver of satisfactory performance in low signal to noise ratio environments, signal sampling based on single bit quantization is proposed which is readily realizable at gigahertz rates with modest power consumption. In this paper, the architecture and performance of a coherent IR receiver based on single bit quantization will be analyzed from the perspectives of Rake receiver processing, channel estimation and signal detection. This paper demonstrates that single bit quantization results in a modest manageable performance penalty relative to linear multi-bit sampling. This penalty is readily justifiable in light of the significant reduction in overall receiver complexity.     

时间选择性衰落信道DS-CDMA系统的联合时空频3D-Rake

针对Rake接收结构由于快衰落导致多普勒散布，导致系统性能下降的问题，在时频Rake、时空Rake接收机设计基础上，提出一种联合时空频3D-Rake接收结构。利用自适应天线在空间形成定向波束和利用联合时频处理技术，将频域多普勒频率分集的分析方法应用到时空二维处理中，实现基于天线阵列的时空频三维信号处理。通过接收合并具有不同时延、多普勒频移和来自不同方向的信号，实现最大信噪比准则下的最优接收，提高系统分集增益，和时频Rake、时空Rake相比，其系统性能得到进一步提高，数值仿真表明，联合时空频3D-Rake比时空Rake平均信干噪比提高了3dB。     

Differential space–time modulation for DS‐CDMA systems

Differential space–time modulation (DSTM) schemes were recently proposed to fully exploit the transmit and receive antenna diversities without the need for channel state information. DSTM is attractive in fast flat fading channels since accurate channel estimation is difficult to achieve. In this paper, we propose a new modulation scheme to improve the performance of DS‐CDMA systems in fast time‐dispersive fading channels. This scheme is referred to as the differential space–time modulation for DS‐CDMA (DST‐CDMA) systems. The new modulation and demodulation schemes are especially studied for the fast fading down‐link transmission in DS‐CDMA systems employing multiple transmit antennas and one receive antenna. We present three demodulation schemes, referred to as the differential space–time Rake (DSTR) receiver, differential space–time deterministic (DSTD) receiver, and differential space–time deterministic de‐prefix (DSTDD) receiver, respectively. The DSTD receiver exploits the known information of the spreading sequences and their delayed paths deterministically besides the Rake‐type combination; consequently, it can outperform the DSTR receiver, which employs the Rake‐type combination only, especially for moderate‐to‐high SNR. The DSTDD receiver avoids the effect of intersymbol interference and hence can offer better performance than the DSTD receiver. Copyright © 2001 John Wiley & Sons, Ltd.     

Récepteurs en râteau pour les systèmes à étalement de spectre par séquences directes

This paper investigates the structure of a continuous and a discrete time Rake receivers. The former receiver is the most used and consists on combining the output of correlators locked on the most significant paths. Since the conventional synchronisation module of this receiver is not able to distinguish closer paths, we propose a maximum likelihood acquisition algorithm and an enhanced tracking loop. The latter receiver was recently suggested and works without the knowledge of path delays and their number. It is based on a global estimation of the impulse response of the multipath channel convolutionned with the shaping filter. Performance comparison of the two receivers is established for the fdd mode of the umts interface.     

BER performance analysis of the discrete time and the continuous time Rake receivers for the UMTS downlink

The paper gives the bit error rate (BER) expressions of the continuous time and discrete time Rake receivers (CTR and DTR) for the UMTS downlink. The former receiver is the most used and consists in combining the output of correlators locked on the most significant paths. Since the conventional synchronization module of the CTR is hot able to distinguish close paths, a discrete time implementation of the Rake receiver which circumvents the problem of path delay estimation was proposed in previous papers. The DTR consists in a matched filter to the discrete time equivalent model of the global channel resulting from the convolution of the impulse response of the transmitter shaping filter and the multipath channel. Using the assumption of Gaussian noise on the receiver output, we derive the BER expressions of both the CTR and DTR. The obtained expressions are valid for any multipath channel and take simultaneously into account path gain estimation noise, the intersymbol interference and the multiuser interference which is a realistic scenario for the UMTS downlink. Based on this theoretical study, a power control policy is also formulated.     

Code hopping - direct sequence spread spectrum to compensate for intersymbol interference in an ultra-wideband system

We propose code hopping - direct sequence spread spectrum (CH-DSSS) with binary phase shift-keying (BPSK) modulation to compensate for intersymbol interference (ISI) in an Ultra-wideband system. The central idea is that code hopping (CH) affects ISI amplitudes that are produced by both the cross- and the auto-correlation properties of spreading codes for codewords; not just by the latter as occurs without CH. We also propose a low complexity CH pattern search algorithm to find good CH patterns. To evaluate the performance of the CH-DSSS system, a bit error rate (BER) expression is derived for a Rake receiver by applying the Beaulieu series method. Computational results show that significant gains can be obtained by CH for both the average BER and the outage probability (e.g. a 6 dB gain in outage probability for a non-line of sight channel).