Level crossing rate and average fade duration of MRC and EGC diversity in Ricean fading

The average level crossing rate and average fade duration of the output signal of a maximal ratio combiner (MRC) and equal gain combiner (EGC), operating on independent Ricean fading input branch signals, are derived. Exact, closed-form results are obtained for MRC diversity, while precise expressions for EGC diversity are presented with an infinite series method. The results are valid for an arbitrary number of independent, identically distributed diversity branches, isotropic scattering, and a specular component perpendicular to the line of motion of the mobile.     

Level crossing rate and average fade duration of the select-and-hold policy of selection diversity combining in a Rayleigh fading channel

The select-and-hold policy (SAH) is a general form of selection diversity combining (SDC). In this letter, we provide closed-form expressions for average level crossing rate and average fade duration for Nth-order SAH-SDC. The diversity branches are assumed to be independent and identical Rayleigh fading channels. A useful guideline for choice of the holding time is also obtained.     

Useful approximation for the characteristic function of weakly fading signals

A simple approximation is presented for the characteristic function of a signal subject to shallow fading. It is shown that the multiplicative perturbation due to the fading can be viewed as an additive noise due to a random component having an envelope distribution identical to a shifted version of the distribution representing the original fading process.     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

The diversity gain of transmit diversity in wireless systems withRayleigh fading

In this paper, we study the ability of transmit diversity to provide diversity benefit to a receiver in a Rayleigh fading environment. With transmit diversity, multiple antennas transmit delayed versions of a signal to create frequency-selective fading at a single antenna at the receiver, which uses equalization to obtain diversity gain against fading. We use Monte Carlo simulation to study transmit diversity for the case of independent Rayleigh fading from each transmit antenna to the receive antenna and maximum likelihood sequence estimation for equalization at the receiver. Our results show that transmit diversity with M transmit antennas provides a diversity gain within 0.1 dB of that with M receive antennas for any number of antennas. Thus, we can obtain the same diversity benefit at the remotes and base stations using multiple base-station antennas only     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

MC-CDMA performance evaluation over a multipath fading channelusing the characteristic function method

This letter presents an efficient and accurate performance evaluation method for binary MC-CDMA systems with deterministic signature sequences. This method is based on a formulation of the characteristic function, and does not resort to any assumption on the statistical or spectral behavior of the interference. The accuracy of the Gaussian approximation method is also considered     

Antenna diversity combining schemes for WCDMA systems in fading multipath channels

In this paper, we analyze the performance of various receive antenna diversity schemes for use in combination with transmit diversity on the downlink of wideband code-division multiple-access third-generation systems. We consider open loop and closed loop versions of both maximal ratio combining and selection diversity, and study the impact of channel correlation on the performance of these schemes. We also present an analysis of the asymptotic performance of coded systems. The analytical results are compared with simulation results obtained in typical channels.     

Autocorrelation functions arising in analysis of narrowband systems and their representation in terms of characteristic function

Three expressions of closely similar form are derived for the autocorrelation functions of the envelope, the result of hard limiting, and the instantaneous frequency of a general narrow-band signal. The characteristic function of probability theory links the analysis, and the result that pertains to the instantaneous frequency is thought to be new.     

Outage probability comparisons for diversity systems with cochannel interference in Rayleigh fading

Space diversity is an effective method to combat fading and cochannel interference (CCI) in wireless systems. In this paper, outage performances of several diversity schemes, including a practical variation of maximal-ratio combining that does not require signal-to-noise ratios at different antennas, equal-gain combining, and selection combining, are compared analytically for an interference-limited environment in a Rayleigh fading channel. Our analysis provides insight into the performance of diversity schemes in the presence of CCI as well as assesses the impact of cochannel interferer power distributions.     

A unified approach for calculating error rates of linearlymodulated signals over generalized fading channels

We present a unified analytical framework to determine the exact average symbol-error rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths, which are not necessarily identically distributed. In all cases, the proposed approach leads to an expression of the average SER involving a single finite-range integral, which can be easily computed numerically. In addition, as special cases, SER expressions for single-channel reception are obtained. These expressions reduce to well-known solutions, give alternative (often simpler) expressions for previous results, or provide new formulas that are either closed-form expressions or simple to compute numerically     

Channel capacity of OFDM systems employing diversity in fading environments

This paper derives capacity of a fading channel with orthogonal frequency division multiplexing (OFDM) transmission employing diversity techniques and adaptive policies involving (i) power and rate, (ii) optimal rate and (iii) channel inversion with fixed rate. Two major diversity techniques are considered (i) maximal ratio combining (MRC) and (ii) selective combining (SC). Closed‐form expressions and/or bounds on various channel capacity with OFDM transmission under different scenarios are derived. Simulation results are given. Copyright © 2011 John Wiley & Sons, Ltd.     

Level crossing rate and average fade duration for pure selection and threshold selection diversity‐combining systems

Exact and closed‐form expressions for the level crossing rate and average fade duration are presented for the M‐branch Pure Selection Combining and for the two‐branch Threshold Selection Combining schemes, assuming independent branches in a Rayleigh environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The plots presented here are also compared with those of the general solution recently published for the Equal Gain and Maximal Ratio Combining and an agreeable coherence is found. Copyright © 2001 John Wiley & Sons, Ltd.     

Outage probabilities of diversity cellular systems with cochannelinterference in Nakagami fading

Analytical, closed-form expressions for cellular outage probabilities in generalized Nakagami fading are derived for three practical diversity combining schemes. The outage is defined as the probability that the signal-to-interference power ratio (SIR) is less than a power protection ratio. The analysis considers L-branch equal gain (EG), selection (SC), and switched (SW) diversity combining schemes. The analyses are not limited to a single interferer, but rather assume the presence of multiple independent cochannel interferers. Previous results have used some approximations to study the performance of the EG combiner. A precise method is used to analyze the performance of an L-branch EG combiner. Selection diversity combining using the total power algorithm, the desired power algorithm, and the signal-to-interference power algorithm is analyzed. The effects of diversity on the reuse factor and on the spectrum efficiency of cellular mobile radio systems are considered in detail. The results for the Rayleigh fading channel are obtained and presented as a special case of the generalized Nakagami fading model     

Unified analysis of switched diversity systems in independent andcorrelated fading channels

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed     

Moments-based approach to the performance analysis of equal gain diversity in Nakagami-m fading

In this letter, an alternative moments-based approach for the performance analysis of an L-branch predetection equal gain combiner (EGC) over independent or correlated Nakagami-m fading channels is presented. Exact closed-form expressions are derived for the moments of the EGC output signal-to-noise ratio (SNR), while the corresponding moment-generating function (MGF) is accurately approximated with the aid of Pade/spl acute/ approximants theory. Important performance criteria are studied; the average output SNR, which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters, the average symbol-error probability for several coherent, noncoherent, and multilevel modulation schemes, and the outage probability, which are both accurately approximated using the well-known MGF approach. The proposed mathematical analysis is illustrated by various numerical results, and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach.     

Approximation of SNR statistics for MRC diversity systems inarbitrarily correlated Nakagami fading channels

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     

一种高效的计算Mie级数的新方法

介绍了一种在高频情况下高效计算Mie级数的新方法,利用这种方法,通过一系列变换将传统的Mie级数变换成一个新的留数序列并给出一个全新的推导过程.推导结论表明,这种方法同传统的Mie级数以及Sommerfeld-Waston变换的解相比物理概念更加清晰,同传统Mie级数解相比极大地减少计算所需的求和项的数目.仿真结果证实这种方法得到的结果同传统方法的结果一致吻合.     

Signal space diversity: a power- and bandwidth-efficient diversitytechnique for the Rayleigh fading channel

The increasing need for high data-rate transmissions over time- or frequency-selective fading channels has drawn attention to modulation schemes with high spectral efficiency such as QAM. With the aim of increasing the “diversity order” of the signal set we consider multidimensional rotated QAM constellations. Very high diversity orders can be achieved and this results in an almost Gaussian performance over the fading channel, This multidimensional modulation scheme is essentially uncoded and enables one to trade diversity for system complexity, at no power or bandwidth expense