Performance Analysis of Frequency Domain Equalization in SC-FDMA Systems
19 May 2008-pp 4342-4347
TL;DR: The performance of linear receivers for detection of the single carrier frequency division multiple access transmission over frequency-selective fading channels is investigated and the approximate average bit error rate expressions as functions of the average receive signal to noise ratio are obtained.
Abstract: The performance of linear receivers for detection of the single carrier frequency division multiple access transmission over frequency-selective fading channels is investigated in this work. Firstly, the cumulative distribution functions (CDF) of output signal to interference plus noise ratios (SINR) with zero forcing frequency domain equalization (ZF-FDE) and minimum mean squared error frequency domain equalization (MMSE-FDE) are derived by employing the numerical inversion of Laplace transforms. Next, based on the CDFs of the output SINRs, the approximate average bit error rate expressions as functions of the average receive signal to noise ratio for Gray-coded quaternary phase shift keying constellations are obtained. Finally, analytical and Monte Carlo simulated results are compared, and they perfectly agree for both ZF-FDE and MMSE-FDE.
Citations
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30 Nov 2009
TL;DR: The performance advantage of SC-FDMA with MMSE equalizer over OFDMA can be restored by adopting multistage IC techniques, using the knowledge of CFOs and TOs of different users at the receiver.
Abstract: In this paper, we present a comparison between the sensitivity of SC-FDMA and OFDMA schemes to large carrier frequency offsets (CFO) and timing offsets (TO) of different users on the uplink. Our study shows the following observations: 1) In the ideal case of zero CFOs and TOs (i.e., perfect synchronization), the uncoded BER performance of SC-FDMA with frequency domain MMSE equalizer is better than that of OFDMA due to the inherent frequency diversity that is possible in SCFDMA. Also, because of inter-symbol interference in SC-FDMA, the performance of SC-FDMA with MMSE equalizer can be further improved by using low-complexity interference cancellation (IC) techniques. 2) In the presence of large CFOs and TOs, significant multiuser interference (MUI) gets introduced, and hence the performance of SC-FDMA with MMSE equalizer can get worse than that of OFDMA. However, the performance advantage of SC-FDMA with MMSE equalizer over OFDMA (due to the potential for frequency diversity benefit in SC-FDMA) can be restored by adopting multistage IC techniques, using the knowledge of CFOs and TOs of different users at the receiver.
58 citations
TL;DR: Simulation results show that the SC-FDMA with companding system has a lower PAPR when compared with the conventional SC- FDMA system, while the complexity of the system slightly increases.
Abstract: In this paper, a companding technique is proposed to effectively reduce the peak-to-average power ratio (PAPR) in single-carrier frequency division multiple access (SC-FDMA) systems. By companding the samples with large amplitudes, while enhancing those with small amplitudes, a significant reduction in the PAPR can be achieved. The performance of the proposed SC-FDMA with companding system is studied and compared with that of the standard SC-FDMA system. Simulation results show that the SC-FDMA with companding system has a lower PAPR when compared with the conventional SC-FDMA system, while the complexity of the system slightly increases. Results also reveal that the companding coefficient must be chosen carefully in order to limit the PAPR without introducing degradations into the bit error rate performance.
34 citations
TL;DR: Simulation results show that MSC-SA, M.SC-CRDSA,MSC- CRDSA-3, and Msc-IRSA schemes significantly outperform conventional ones, and the M SC-CRdSA scheme is superior to MSC's other schemes, in terms of throughput, stability and energy efficiency.
Abstract: Multisatellite cooperative random access (MSC-RA) scheme is proposed in low earth orbit (LEO) satellite networks. In the scheme, a packet structure based on single carrier interleaved frequency division multiple access (SC-IFDMA) is designed to overcome the effect of users’ propagation delays on the received signals at satellite nodes, which ensures the synchronization of received signals. The transmission model from multiple terminals to multiple satellite nodes in a slot can be equivalent to a virtual multi-input multioutput model, and MSC detection is employed to decode multiple collided packets. The MSC detection can be applied to slotted ALOHA (SA), contention resolution diversity slotted ALOHA (CRDSA), CRDSA-3, and irregular repetition slotted ALOHA (IRSA) protocols, which are dubbed MSC-SA, MSC-CRDSA, MSC-CRDSA-3, and MSC-IRSA, respectively. At the gateway station, the MSC detection and iterative interference cancellation processing are alternately conducted for multiple collided packets at satellite nodes. The performance of these MSC-RA schemes is evaluated via mathematical analysis and computer simulation in terms of throughput, stability and energy efficiency. Simulation results show that MSC-SA, MSC-CRDSA, MSC-CRDSA-3, and MSC-IRSA schemes significantly outperform conventional ones, and the MSC-CRDSA scheme is superior to MSC-SA, MSC-CRDSA-3 and MSC-IRSA schemes.
27 citations
Cites methods from "Performance Analysis of Frequency D..."
...To obtain the vector Sk that is constructed by kth SC-IFDMA symbol of q packets in the received signals, the ML detection [23], [24] is employed, which is expressed as follows:...
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TL;DR: An analytical study of the bit error rate (BER) for single-carrier frequency-division multiple access (SC-FDMA) transmission over frequency-selective fading channels when zero-forcing frequency-domain equalization is applied.
Abstract: In this paper, we present an analytical study of the bit error rate (BER) for single-carrier frequency-division multiple access (SC-FDMA) transmission over frequency-selective fading channels when zero-forcing frequency-domain equalization is applied. SC-FDMA, which can be described as a precoded version of orthogonal frequency-division multiple access (OFDMA), is regarded as a promising candidate for next mobile communication systems due its favorable envelope characteristics and low peak-to-average-power ratio (PAPR), compared with that of OFDMA. We focus on Nakagami-m fading channels and provide a method to calculate BER values with a single numerical computation. We provide a closed-form expression for the BER with binary phase-shift keying (BPSK) and square M-ary quadrature amplitude modulation (M-QAM) under the assumption of independence among channel frequency responses for allocated subcarriers.
24 citations
Cites background from "Performance Analysis of Frequency D..."
...In [8], this drawback is overcome by computing numerically the cumulative distribution function (CDF) of the instantaneous signal-to-noise ratio (SNR) under the assumption of independence among allocated subcarriers....
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...In SC-FDMA, that SNR is related to the harmonic mean of random variables [8], which also appears in the study of relays [10]....
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TL;DR: This paper presents an analytical study of the average bit error probability (ABEP) for interleaved single-carrier frequency-division multiple-access systems over independent but not necessarily identically distributed Nakagami-m fading channels with fading parameters {m} being integers when either zero-forcing (ZF) or minimum-mean-square-error (MMSE) frequency-domain equalization (FDE) is applied.
Abstract: In this paper, we present an analytical study of the average bit error probability (ABEP) for interleaved single-carrier frequency-division multiple-access (SC-FDMA) systems over independent but not necessarily identically distributed Nakagami-m fading channels with fading parameters {m} being integers when either zero-forcing (ZF) or minimum-mean-square-error (MMSE) frequency-domain equalization (FDE) is applied. Under the assumption of independence among channel frequency responses (CFRs) at the allocated subcarriers for a specific user, accurate and closed-form numerical ABEP computations of the generalized hierarchical M -ary pulse amplitude and square/rectangular M-ary quadrature amplitude modulations for both ZF-FDE and MMSE-FDE are developed by exploiting the derived statistics of the equalized noise, including the probability density function and cumulative distribution function. More importantly, the ABEP derivation is based on the real distribution of the CFRs without applying the widely used Nakagami-m approximation of the CFRs in previous literature, resulting in a more accurate ABEP analysis.
22 citations
Cites background or methods from "Performance Analysis of Frequency D..."
...Another attempt to examine the ABEPs for both ZF-FDE and MMSE-FDE is given in [8] under the assumption of independence among the channel frequency responses (CFRs) at the allocated subcarriers for a specific user....
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...Specifically, in [8], the approximate ABEPs are derived in such a manner that the cumulative distribution function (cdf) of the instantaneous signal-to-noise ratio (SNR) is first calculated based on the numerical Laplace transforms and then fed into another numerical computation....
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References
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01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
"Performance Analysis of Frequency D..." refers background or methods in this paper
...equation (3.471.9) in [ 13 ], we can obtain the MGF of Θ .I t will be detailed in the future work....
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...Subsequently, using the Laplace transform differentiation property [ 13 ], the CDF of Θ is obtained by...
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...transform. To the authors’ best knowledge, for L ≥ 2, there is no closed-form expression of the inverse Laplace transform for (19) [ 13 ]....
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TL;DR: This article develops a systematic discrete-time framework and designs novel systems for single- and multiuser wireless multicarrier communications-a field rich in signal processing challenges that holds great potential in various applications including audio/video broadcasting, cable television, modem design, multimedia services, mobile local area networks, and future-generation wideband cellular systems.
Abstract: Relying on basic tools such as eigensignals of linear time-invariant systems, linear and circular block convolution, and fast Fourier transforms (FFTs), this article develops a systematic discrete-time framework and designs novel systems for single- and multiuser wireless multicarrier communications-a field rich in signal processing challenges that holds great potential in various applications including audio/video broadcasting, cable television, modem design, multimedia services, mobile local area networks, and future-generation wideband cellular systems. Wireless multicarrier (MC) communication systems utilize multiple complex exponentials as information-bearing carriers. MC transmissions thus retain their shape and orthogonality when propagating through linear time-dispersive media, precisely as eigensignals do when they pass through linear time-invariant (LTI) systems.
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01 Jan 1986TL;DR: The text has tried to strike a balance between simplicity in exposition and sophistication in analytical reasoning, and ensure that the mathematically oriented reader will find here a smooth development without major gaps.
Abstract: The course is attended by a large number of undergraduate and graduate students with diverse backgrounds. Acccordingly, we have tried to strike a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just sketched or intuitively explained in the text, so that complex proofs do not stand in the way of an otherwise simple exposition. At the same time, some of this analysis and the necessary mathematical results are developed (at the level of advanced calculus) in theoretical problems, which are included at the end of the corresponding chapter. The theoretical problems (marked by *) constitute an important component of the text, and ensure that the mathematically oriented reader will find here a smooth development without major gaps.
1,326 citations
"Performance Analysis of Frequency D..." refers background in this paper
...,K are independent RVs, the distribution of their sum W = ∑K k=1 Xk can be obtained by computing and then inverting the transform MW (s) = ∏K k=1 MXk(s) [16]....
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TL;DR: A simple algorithm for numerically inverting Laplace transforms is presented, designed especially for probability cumulative distribution functions, but it applies to other functions as well.
Abstract: We present a simple algorithm for numerically inverting Laplace transforms. The algorithm is designed especially for probability cumulative distribution functions, but it applies to other functions as well. Since it does not seem possible to provide effective methods with simple general error bounds, we simultaneously use two different methods to confirm the accuracy. Both methods are variants of the Fourier-series method. The first, building on Dubner and Abate (Dubner, H., J. Abate. 1968. Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. JACM 15 115–123.) and Simon, Stroot, and Weiss (Simon, R. M., M. T. Stroot, G. H. Weiss. 1972. Numerical inversion of Laplace transforms with application to percentage labeled experiments. Comput. Biomed. Res. 6 596–607.), uses the Bromwich integral, the Poisson summation formula and Euler summation; the second, building on Jagerman (Jagerman, D. L. 1978. An inversion technique for the Laplace transform with applications....
750 citations
"Performance Analysis of Frequency D..." refers methods in this paper
...To visualize and verify our theoretical findings in the previous sections, simulated and analytical results for CDFs of SINRs and average BERs in multipath Rayleigh channels are presented in this section....
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...(28) Heuristically, by a glimpse at CDFs of output SINR of the equalizers at different γ̄, for example, the CDFs of the output SINRs at γ̄ = 15dB in Fig....
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...denotes binomial, A, B and C are parameters in Euler summation [9]....
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...Hence, applying the numerical inversion of Laplace transforms designed especially for CDFs [9], an approximation to PΘ(θ) can be given by P̃Θ (θ) = B∑ b=0 2−B ( B b )( exp (A/2) θ C+b∑ c=0 (−1)c δc · Re {( 2 exp ( N0 KPk )√ 1 KPk )L( A + j2πc 2θ )L 2 −1 · ( K1 ( 2 √ A + j2πc 2KPkθ ))L , (20) with δc = { 2 c = 0, 1 c = 1, 2, . . . , C, where Re{·} is the real part of the complex number, ( B b ) denotes binomial, A, B and C are parameters in Euler summation [9]....
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...This Fourier-series method is used to approximate the CDFs of output SINRs....
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