Performance of MIMO system in Weibull fading channel - Channel capacity analysis
18 May 2009-pp 1735-1740
TL;DR: It is shown that the average channel capacity can be increased by increasing the fading parameter, and the proposed transmit antenna selective MIMO and the full complexity MIMo systems outperform the single-input single-output (SISO) system in terms of channel capacity.
Abstract: In this paper we investigate the performance of a transmit antenna selective multiple-input multiple-output (MIMO) (this is the proposed system), full complexity MIMO and single-input single-output (SISO) systems all operating under Weibull fading The effect of increasing the number of antennas together with applying maximal-ratio combining (MRC) on the signal-to-noise ratio is studied SNR is shown to increase with an increase in the number of antennas used, and this in turn increases the channel capacity The system performance in terms of the channel capacity is also studied We show that the average channel capacity can be increased by increasing the fading parameter Increasing the fading parameter leads to a decrease in the severity of fading, meaning that signals can be decoded with reduced probability of error We also show that the proposed transmit antenna selective MIMO and the full complexity MIMO systems outperform the single-input single-output (SISO) system in terms of channel capacity
Citations
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TL;DR: It is shown how the proposed EW distribution offers an excellent fit to simulation and experimental data under all aperture averaging conditions, under weak and moderate turbulence conditions, as well as for point-like apertures.
Abstract: Nowadays, the search for a distribution capable of modeling the probability density function (PDF) of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging still continues. Here, a family of PDFs alternative to the widely accepted Log-Normal and Gamma-Gamma distributions is proposed to model the PDF of the received optical power in free-space optical communications, namely, the Weibull and the exponentiated Weibull (EW) distribution. Particularly, it is shown how the proposed EW distribution offers an excellent fit to simulation and experimental data under all aperture averaging conditions, under weak and moderate turbulence conditions, as well as for point-like apertures. Another very attractive property of these distributions is the simple closed form expression of their respective PDF and cumulative distribution function.
152 citations
TL;DR: In this article, the exponentiated Weibull (EW) distribution has been proposed to model the probability density function of irradiance fluctuations, along with a physical justification for the appearance of the model.
Abstract: Many distributions have been proposed to model the probability density function of irradiance fluctuations. The most widespread models nowadays are the Lognormal (LN) and Gamma–Gamma (GG) distributions. Albeit these models comply with the actual PDF data most of the time, neither of them works in all scenarios and, depending on the conditions, one of the two have to be chosen. In this paper, a new model is presented resulting in the exponentiated Weibull (EW) distribution, along with a physical justification for the appearance of the model. Previously published data are used to compare the new model with the LN and GG distributions. Results suggest that the EW distribution is the better fit for data under all aperture averaging conditions and weak-to-strong turbulence regime.
102 citations
Dissertation•
17 May 2013
TL;DR: In this paper, the authors proposed a new model for the irradiance fluctuations in FSO links under atmospheric turbulence, in the presence of aperture averaging; resulting in the exponentiated Weibull (EW) distribution.
Abstract: Free-space optical (FSO) communications is drawing increasing attention as a promising technology to overcome bandwidth shortage, of an evermore crowded wireless marketplace. Currently radio-frequency (RF) technology struggles to cope with the ever increasing demand for high-bandwidth data. Moreover, as the number of users increases, the RF spectrum is getting so crowded that there is virtually no room for new wireless services, with the additional inconvenient of limited bandwidth restriction for using a RF band and the license fees that have to be paid for such bands. FSO communications offer clear advantages over other alternatives such as narrower and more secure beams, virtually limitless bandwidth and no regulatory policies for using optical frequencies and bandwidth. Moreover, in the space sector FSO technology is becoming more attractive for satellite communication systems due to the less mass and power requirements --compared to RF.
The major drawback for deploying wireless links based on FSO technology is the perturbation of the optical wave as it propagates through the turbulent atmosphere. Many effects are produced, of which the most noticeable is the random fluctuations of the signal-carrying laser beam irradiance (intensity), phenomenon known as scintillation and quantified by the scintillation index (SI). The statistical analysis of the random irradiance fluctuations in FSO links is conducted through the probability density function (PDF), from which one can obtain other statistical tools to measure link performance such as the probability of fade and the bit error-rate (BER). Nowadays, the most widespread models for the irradiance data are, by far, the Lognormal (LN) and Gamma-Gamma (GG) distributions. Although both models comply with actual data in most scenarios neither of them is capable of fitting the irradiance data under all conditions of atmospheric turbulence for finite receiving aperture sizes, i.e. in the presence of aperture averaging. Furthermore, there are several cases where neither the LN or the GG model seem to accurately fit the irradiance data, specially in the left tail of the PDF.
The work presented in this thesis is devoted to propose a new model for the irradiance fluctuations in FSO links under atmospheric turbulence, in the presence of aperture averaging; resulting in the exponentiated Weibull (EW) distribution. A physical justification for the appearance of the new model is provided along with numerous test scenarios in the weak-to-strong turbulence regime --including numerical simulations and experimental data-- to assess its suitability to model the irradiance data in terms of the PDF and probability of fade. Here, a semi-heuristic approach is used to find a set of equations relating the EW parameters directly to the SI. Such expressions were tested offering a fairly good fitting the actual PDF of irradiance data. Furthermore, for all the scenarios tested a best fit version of the EW PDF is obtained and always presents itself as an excellent fit to the PDF data. The new model has been compared to the LN and GG distributions proving to cope to the predictions made by those and, in some cases, even outperforming their predictions. Additionally, a new closed-form expression has been derived for estimating the BER performance under EW turbulence, for intensity-modulation/direct-detection (IM/DD) systems using on-off keying (OOK) modulation. Moreover, this expression has been extended to include pointing errors. Finally, the exponentiated Weibull PDF has been proved to be valid with fully and partially coherent beams.
The results presented here suggest that the EW distribution presents the better fit for data under different scenarios, thus, the exponentiated Weibull distribution becomes an excellent alternative to model the PDF of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging.
34 citations
01 Aug 2015
TL;DR: The effects of the in-phase (I) and quadrature (Q) imbalance (I/Q imbalance) on a GFDM system under Weibull fading channels are studied and the average symbol error probability (SEP) performance of a system without and with I-Q imbalance compensation is presented.
Abstract: Fifth generation (5G) wireless communications promise low cost, reliable and high speed communication. To achieve this and to help overcome the drawbacks associated with orthogonal frequency division multiplexing (OFDM), waveforms such as generalized frequency division multiplexing (GFDM) and filter bank multiple carrier (FBMC) have been proposed. But just like OFDM, these waveforms suffer from the effects of radio frequency (RF) impairments thus compromising the system performance. In this paper, we study the effects of the in-phase (I) and quadrature (Q) imbalance (I/Q imbalance) on a GFDM system under Weibull fading channels. The average symbol error probability (SEP) performance of a system without and with I/Q imbalance compensation is presented. For completeness, the performance of the GFDM system is compared with that of an OFDM system. We also present results on the effects of the order of modulation and image leakage ratio on system performance.
13 citations
TL;DR: In this article, an approximate channel model is achieved by fitting the Weibull distribution, which includes the effects of atmospheric attenuation, M distributed atmospheric turbulence and nonzero boresight pointing errors.
Abstract: An aggregated channel model is achieved by fitting the Weibull distribution, which includes the effects of atmospheric attenuation, M distributed atmospheric turbulence and nonzero boresight pointing errors. With this approximate channel model, the bit error rate (BER) and the ergodic capacity of free-space optical (FSO) communication systems utilizing subcarrier binary phase-shift keying (BPSK) modulation are analyzed, respectively. A closed-form expression of BER is derived by using the generalized Gauss-Lagueree quadrature rule, and the bounds of ergodic capacity are discussed. Monte Carlo simulation is provided to confirm the validity of the BER expressions and the bounds of ergodic capacity.
5 citations
References
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TL;DR: In this article, the authors examined the performance of using multi-element array (MEA) technology to improve the bit-rate of digital wireless communications and showed that with high probability extraordinary capacity is available.
Abstract: This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.
We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
10,526 citations
11 Jun 2001
TL;DR: An upper bound on the capacity that can be expressed as the sum of the logarithms of ordered chi-square-distributed variables is derived and evaluated analytically and compared to the results obtained by Monte Carlo simulations.
Abstract: We consider the capacity of multiple-input-multiple-output (MIMO) systems with reduced complexity. One link end uses all available antennas, while the other chooses the "best" L out of N antennas. As "best", we use those antennas that maximize capacity. We derive an upper bound on the capacity that can be expressed as the sum of the logarithms of ordered chi-squared variables. This bound is then evaluated analytically, and compared to results from Monte Carlo simulations. As long as L is at least as large as the number of antennas at the other link end, the achieved capacity is close to the capacity of a full-complexity system. We demonstrate, for example, that for L=3, N=8 at the receiver, and 3 antennas at the transmitter, the capacity of the reduced-complexity scheme is 20 bits/s/Hz compared to 23 bits/s/Hz of a full-complexity scheme.
557 citations
"Performance of MIMO system in Weibu..." refers background in this paper
...Reference [4] studied the effect of antenna selection in terms of the channel capacity....
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...The advantage with MRC is that it has been observed to outperform all the other combining techniques, namely selective combining (SC) and equal gain combining (EGC) [4] and [9]....
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TL;DR: It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency and channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.
Abstract: In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.
415 citations
"Performance of MIMO system in Weibu..." refers background in this paper
...Whereas [6] investigates the performance of a wireless system with antenna selection applied at both the transmitter and the receiver ends....
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TL;DR: A theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed, and novel analytical expressions for the joint probability density function, moment-generating function, and cumulative distribution function are derived for this class of distributions.
Abstract: Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance.
240 citations
"Performance of MIMO system in Weibu..." refers background or methods in this paper
...For the Weibull fading model, the complex envelope ij h can be written as a function of the Gaussian in-phase ij X and quadrature ij Y elements of the multipath components [9]...
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...| | ij ij Z h = , the Weibull fading model, ij Z can be expressed as a power transformation of a Rayleigh distributed random variable (RV), | | ij ij ij R X jY = + as [8], [9], [10] and [11]...
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...In Weibull fading the instantaneous signal-to-noise ratio at the input of the receiver is given by [9], [10], [11] and [12]...
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...The advantage with MRC is that it has been observed to outperform all the other combining techniques, namely selective combining (SC) and equal gain combining (EGC) [4] and [9]....
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TL;DR: Analysis of multiple-input-multiple-output (MIMO) systems with antenna selection over quasi-static fading channels shows that the diversity order of the underlying space-time code is maintained, whereas the coding gain deteriorates by a value upper bounded by 10log/sub 10/(M/L) dB.
Abstract: We analyze the performance of multiple-input-multiple-output (MIMO) systems with antenna selection over quasi-static fading channels. The basic idea is that, for a given number of receive antennas, M, the receiver uses the best L out of the available M antennas where, typically, L
175 citations
"Performance of MIMO system in Weibu..." refers background in this paper
...There is a general view between in [1], [2] and [3] that antenna selection can be introduced to the system to help solve the complexity problem....
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...Antenna selection considered in [1] is applied only at the receiver end where the receive antenna with the best signal-to-noise ratio is selected....
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...The problem with antenna diversity is that it increases the system’s complexity and cost [1] and [2]....
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