Optimum receiver design for OFDM-based broadband transmission_dba_其他

<html xmlns="http://www.w3.org/1999/xhtml"><head><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/1148472/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><title></title></head><body><div id="sidebar" style="display: none"><div id="outline"></div></div><div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/1148472/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1668 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 11, NOVEMBER 1999</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">Optimum Receiver Design for Wireless</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">Broad-Band Systems Using OFDM—Part I</div><div class="t m0 x1 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">Michael Speth, Student Member, IEEE, Stefan A. Fechtel, Member, IEEE, Gunnar Fock, and Heinrich Meyr,</div><div class="t m0 x4 h5 y5 ff2 fs3 fc0 sc0 ls0 ws0">Fellow, IEEE</div><div class="t m0 x5 h6 y6 ff3 fs4 fc0 sc0 ls0 ws0">Abstract— Orthogonal frequency-division multiplexing</div><div class="t m0 x1 h6 y7 ff4 fs4 fc0 sc0 ls0 ws0">(OFDM) is the technique of choice in digital broad-band</div><div class="t m0 x1 h6 y8 ff4 fs4 fc0 sc0 ls0 ws0">applications that must cope with highly dispersive transmission</div><div class="t m0 x1 h6 y9 ff4 fs4 fc0 sc0 ls0 ws0">media at low receiver implementation cost. In this paper, we</div><div class="t m0 x1 h6 ya ff4 fs4 fc0 sc0 ls0 ws0">focus on the inner OFDM receiver and its functions necessary to</div><div class="t m0 x1 h6 yb ff4 fs4 fc0 sc0 ls0 ws0">demodulate the received signal and deliver soft information to</div><div class="t m0 x1 h6 yc ff4 fs4 fc0 sc0 ls0 ws0">the outer receiver for decoding. In Part I of this paper, the effects</div><div class="t m0 x1 h6 yd ff4 fs4 fc0 sc0 ls0 ws0">of relevant nonideal transmission conditions are thoroughly</div><div class="t m0 x1 h6 ye ff4 fs4 fc0 sc0 ls0 ws0">analyzed: imperfect channel estimation, symbol frame offset,</div><div class="t m0 x1 h6 yf ff4 fs4 fc0 sc0 ls0 ws0">carrier and sampling clock frequency offset, time-selective</div><div class="t m0 x1 h6 y10 ff4 fs4 fc0 sc0 ls0 ws0">fading, and critical analog components. Through an appropriate</div><div class="t m0 x1 h6 y11 ff4 fs4 fc0 sc0 ls0 ws0">optimization criterion (signal-to-noise ratio loss), minimum</div><div class="t m0 x1 h6 y12 ff4 fs4 fc0 sc0 ls0 ws0">requirements on each receiver synchronization function are</div><div class="t m0 x1 h6 y13 ff4 fs4 fc0 sc0 ls0 ws0">systematically derived. An equivalent signal model encompassing</div><div class="t m0 x1 h6 y14 ff4 fs4 fc0 sc0 ls0 ws0">the effects of all relevant imperfections is then formulated in</div><div class="t m0 x1 h6 y15 ff4 fs4 fc0 sc0 ls0 ws0">a generalized framework. Part I concludes with an outline of</div><div class="t m0 x1 h6 y16 ff4 fs4 fc0 sc0 ls0 ws0">synchronization strategies to be detailed in Part II.</div><div class="t m0 x5 h6 y17 ff3 fs4 fc0 sc0 ls0 ws0">Index Terms—OFDM, receiver design, synchronization.</div><div class="t m0 x6 h7 y18 ff1 fs3 fc0 sc0 ls0 ws0">I. INTRODUCTION</div><div class="t m0 x1 h8 y19 ff4 fs6 fc0 sc0 ls0 ws0">T</div><div class="t m0 x7 h7 y1a ff1 fs3 fc0 sc0 ls0 ws0">HE MODULATION scheme orthogonal frequency-</div><div class="t m0 x7 h7 y1b ff1 fs3 fc0 sc0 ls0 ws0">division multiplexing (OFDM), chosen for the two</div><div class="t m0 x1 h7 y1c ff1 fs3 fc0 sc0 ls0 ws0">European terrestrial broadcasting standards—digital audio</div><div class="t m0 x1 h7 y1d ff1 fs3 fc0 sc0 ls0 ws0">broadcasting (DAB) and digital video broadcasting (DVB-</div><div class="t m0 x1 h7 y1e ff1 fs3 fc0 sc0 ls0 ws0">T) [2], [3], is now considered a mature and well-established</div><div class="t m0 x1 h7 y1f ff1 fs3 fc0 sc0 ls0 ws0">technology for digital broadcasting applications. Thanks to its</div><div class="t m0 x1 h7 y20 ff1 fs3 fc0 sc0 ls0 ws0">virtues, it is currently under investigation for further broad-</div><div class="t m0 x1 h7 y21 ff1 fs3 fc0 sc0 ls0 ws0">band applications such as wireless asynchronous transfer mode</div><div class="t m0 x1 h7 y22 ff1 fs3 fc0 sc0 ls0 ws0">and wireless networks [4]. For an introduction into the basics</div><div class="t m0 x1 h7 y23 ff1 fs3 fc0 sc0 ls0 ws0">of OFDM, refer to [5] and [6].</div><div class="t m0 x8 h7 y24 ff1 fs3 fc0 sc0 ls0 ws0">The main advantage of OFDM is that it allows transmission</div><div class="t m0 x1 h7 y25 ff1 fs3 fc0 sc0 ls0 ws0">over highly frequency-selective channels at a low receiver</div><div class="t m0 x1 h7 y26 ff1 fs3 fc0 sc0 ls0 ws0">implementation cost. In particular, costly equalizers needed</div><div class="t m0 x1 h7 y27 ff1 fs3 fc0 sc0 ls0 ws0">in single-carrier systems are dramatically simpliﬁed or even</div><div class="t m0 x1 h7 y28 ff1 fs3 fc0 sc0 ls0 ws0">obsolete in the case that differential modulation schemes are</div><div class="t m0 x1 h7 y29 ff1 fs3 fc0 sc0 ls0 ws0">used [7].</div><div class="t m0 x8 h7 y2a ff1 fs3 fc0 sc0 ls0 ws0">A well-known problem of OFDM is its vulnerability to</div><div class="t m0 x1 h7 y2b ff1 fs3 fc0 sc0 ls0 ws0">synchronization errors. Many publications have therefore been</div><div class="t m0 x1 h7 y2c ff1 fs3 fc0 sc0 ls0 ws0">concerned with this topic. Nevertheless, two questions remain.</div><div class="t m0 x9 h9 y2d ff1 fs5 fc0 sc0 ls0 ws0">Paper approved by Y. Li, the Editor for Wireless Communication Theory</div><div class="t m0 x1 h9 y2e ff1 fs5 fc0 sc0 ls0 ws0">of the IEEE Communications Society. Manuscript received August 3, 1998;</div><div class="t m0 x1 h9 y2f ff1 fs5 fc0 sc0 ls0 ws0">revised February 3, 1999.</div><div class="t m0 x9 h9 y30 ff1 fs5 fc0 sc0 ls0 ws0">M. Speth, G. Fock, and H. Meyr are with the Institute for Integrated</div><div class="t m0 x1 h9 y31 ff1 fs5 fc0 sc0 ls0 ws0">Systems in Signal Processing (ISS), Aachen University of Technology, D-</div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls0 ws0">52056 Aachen, Germany (e-mail: speth@ert.rwth-aachen.de; fock@ert.rwth-</div><div class="t m0 x1 h9 y33 ff1 fs5 fc0 sc0 ls0 ws0">aachen.de; meyr@ert.rwth-aachen.de).</div><div class="t m0 x9 h9 y34 ff1 fs5 fc0 sc0 ls0 ws0">S. A. Fechtel is with Inﬁneon Technologies AG i.Gr., D81541 M</div><div class="t m0 xa h9 y35 ff1 fs5 fc0 sc0 ls0 ws0">¨</div><div class="t m0 xb h9 y34 ff1 fs5 fc0 sc0 ls0 ws0">unchen,</div><div class="t m0 x1 h9 y36 ff1 fs5 fc0 sc0 ls0 ws0">Germany (e-mail: fechtel@hl.siemens.de).</div><div class="t m0 x9 h9 y37 ff1 fs5 fc0 sc0 ls0 ws0">Publisher Item Identiﬁer S 0090-6778(99)08924-2.</div><div class="t m0 xc h7 y6 ff1 fs3 fc0 sc0 ls0 ws0">1) How much of the theoretical performance of OFDM</div><div class="t m0 xd h7 y38 ff1 fs3 fc0 sc0 ls0 ws0">can be actually realized, taking into account all receiver</div><div class="t m0 xd h7 y39 ff1 fs3 fc0 sc0 ls0 ws0">components?</div><div class="t m0 xc h7 y3a ff1 fs3 fc0 sc0 ls0 ws0">2) How much of the implementation beneﬁts remain when</div><div class="t m0 xd h7 y3b ff1 fs3 fc0 sc0 ls0 ws0">taking into account the complexity of algorithms needed</div><div class="t m0 xd h7 y3c ff1 fs3 fc0 sc0 ls0 ws0">for synchronization?</div><div class="t m0 xc h7 y3d ff1 fs3 fc0 sc0 ls0 ws0">This paper is divided into two parts. In the ﬁrst part, we</div><div class="t m0 xe h7 y3e ff1 fs3 fc0 sc0 ls0 ws0">thoroughly analyze the impact of receiver imperfections on the</div><div class="t m0 xe h7 y3f ff1 fs3 fc0 sc0 ls0 ws0">system performance and show how receiver components can</div><div class="t m0 xe h7 y40 ff1 fs3 fc0 sc0 ls0 ws0">be optimized in a systematic manner. In the second part, we</div><div class="t m0 xe h7 y41 ff1 fs3 fc0 sc0 ls0 ws0">demonstrate the optimization methodology for the example of</div><div class="t m0 xe h7 y42 ff1 fs3 fc0 sc0 ls0 ws0">a receiver based on the European digital terrestrial TV standard</div><div class="t m0 xe h7 y43 ff1 fs3 fc0 sc0 ls0 ws0">DVB-T and analyze the achievable performance as well as the</div><div class="t m0 xe h7 y44 ff1 fs3 fc0 sc0 ls0 ws0">resulting complexity.</div><div class="t m0 xc h7 y45 ff1 fs3 fc0 sc0 ls0 ws0">One of the major features of OFDM is the possibility to</div><div class="t m0 xe h7 y46 ff1 fs3 fc0 sc0 ls0 ws0">sacriﬁce some bandwidth (thus optimality) for the beneﬁt of</div><div class="t m0 xe h7 y47 ff1 fs3 fc0 sc0 ls0 ws0">a simple receiver implementation. However, in order to apply</div><div class="t m0 xe h7 y48 ff1 fs3 fc0 sc0 ls0 ws0">the OFDM principle, the following requirements must hold.</div><div class="t m0 xc h7 y49 ff1 fs3 fc0 sc0 ls0 ws0">• The channel must be quasi-static within one symbol</div><div class="t m0 xf h7 y4a ff1 fs3 fc0 sc0 ls0 ws0">duration.</div><div class="t m0 xc h7 y4b ff1 fs3 fc0 sc0 ls0 ws0">• The channel dispersion must be limited in time.</div><div class="t m0 xc h7 y4c ff1 fs3 fc0 sc0 ls0 ws0">• The analog components must have near-ideal character-</div><div class="t m0 xf h7 y4d ff1 fs3 fc0 sc0 ls0 ws0">istics (e.g., linearity).</div><div class="t m0 xe h7 y4e ff1 fs3 fc0 sc0 ls0 ws0">While it is possible to relax these requirements somewhat</div><div class="t m0 xe h7 y4f ff1 fs3 fc0 sc0 ls0 ws0">and compensate the detrimental effects by appropriate algo-</div><div class="t m0 xe h7 y50 ff1 fs3 fc0 sc0 ls0 ws0">rithms (see e.g., [8], [9]), such schemes are not considered</div><div class="t m0 xe h7 y51 ff1 fs3 fc0 sc0 ls0 ws0">here since—at least for the relevant case of a large number</div><div class="t m0 xe h7 y52 ff1 fs3 fc0 sc0 ls0 ws0">of subcarriers—they counteract the notion of OFDM being</div><div class="t m0 xe h7 y53 ff1 fs3 fc0 sc0 ls0 ws0">the technique of choice when it comes to implement low-</div><div class="t m0 xe h7 y54 ff1 fs3 fc0 sc0 ls0 ws0">complexity broad-band receivers.</div><div class="t m0 xc h7 y55 ff1 fs3 fc0 sc0 ls0 ws0">In the receiver design, we follow the principle of synchro-</div><div class="t m0 xe h7 y56 ff1 fs3 fc0 sc0 ls0 ws0">nized detection [10]. The receiver is divided in an inner and</div><div class="t m0 xe h7 y57 ff1 fs3 fc0 sc0 ls0 ws0">outer part. The transmission parameters—carrier frequency</div><div class="t m0 xe h7 y58 ff1 fs3 fc0 sc0 ls0 ws0">offset, sampling clock offset, timing offset—and the channel</div><div class="t m0 xe h7 y59 ff1 fs3 fc0 sc0 ls0 ws0">are estimated in the inner receiver and then compensated for</div><div class="t m0 xe h7 y5a ff1 fs3 fc0 sc0 ls0 ws0">as if the estimates were the true parameters. The compensated</div><div class="t m0 xe h7 y5b ff1 fs3 fc0 sc0 ls0 ws0">signal is then used to decode the transmitted data in the</div><div class="t m0 xe h7 y5c ff1 fs3 fc0 sc0 ls0 ws0">outer receiver. Of course, the parameter estimates bear some</div><div class="t m0 xe h7 y5d ff1 fs3 fc0 sc0 ls0 ws0">estimation errors, resulting in a performance loss. In order to</div><div class="t m0 xe h7 y5e ff1 fs3 fc0 sc0 ls0 ws0">arrive at the best compromise between the conﬂicting objec-</div><div class="t m0 xe h7 y5f ff1 fs3 fc0 sc0 ls0 ws0">tives of minimizing this performance loss and simultaneously</div><div class="t m0 xe h7 y60 ff1 fs3 fc0 sc0 ls0 ws0">minimizing receiver complexity, the following approach is</div><div class="t m0 xe h7 y61 ff1 fs3 fc0 sc0 ls0 ws0">taken.</div><div class="t m0 xc h7 y62 ff1 fs3 fc0 sc0 ls0 ws0">• A system model comprising all relevant effects of the</div><div class="t m0 xf h7 y63 ff1 fs3 fc0 sc0 ls0 ws0">inner and outer receiver is developed.</div><div class="t m0 xc h7 y64 ff1 fs3 fc0 sc0 ls0 ws0">• An optimization criterion is formulated that allows to</div><div class="t m0 xf h7 y65 ff1 fs3 fc0 sc0 ls0 ws0">evaluate the quality of each relevant receiver component.</div><div class="t m0 x10 h9 y66 ff1 fs5 fc0 sc0 ls0 ws0">0090–6778/99$10.00</div><div class="t m0 x11 ha y67 ff5 fs5 fc0 sc0 ls0 ws0"> 1999 IEEE</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div></body></html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/1148472/bg2.jpg"><div class="t m0 x1 h2 y68 ff1 fs0 fc0 sc0 ls0 ws0">SPETH et al.: WIRELESS BROAD-BAND SYSTEMS USING OFDM—I 1669</div><div class="t m0 x8 h7 y69 ff1 fs3 fc0 sc0 ls0 ws0">• Next, the impact of imperfect transmission parameters on</div><div class="t m0 x12 h7 y6a ff1 fs3 fc0 sc0 ls0 ws0">the receiver performance is analyzed.</div><div class="t m0 x8 h7 y6b ff1 fs3 fc0 sc0 ls0 ws0">• From this analysis, an equivalent system model at subcar-</div><div class="t m0 x12 h7 y6c ff1 fs3 fc0 sc0 ls0 ws0">rier level is derived that allows a simpliﬁed description</div><div class="t m0 x12 h7 y6d ff1 fs3 fc0 sc0 ls0 ws0">of all relevant receiver impairments.</div><div class="t m0 x1 h7 y6e ff1 fs3 fc0 sc0 ls0 ws0">After a short discussion of possible training data formats and</div><div class="t m0 x1 h7 y6f ff1 fs3 fc0 sc0 ls0 ws0">their impact on synchronization, we introduce a generalized</div><div class="t m0 x1 h7 y70 ff1 fs3 fc0 sc0 ls0 ws0">structure for OFDM receivers. This structure will be the basis</div><div class="t m0 x1 h7 y71 ff1 fs3 fc0 sc0 ls0 ws0">for the receiver developed in the second part of this paper.</div><div class="t m0 x13 h7 y72 ff1 fs3 fc0 sc0 ls0 ws0">II. OFDM S</div><div class="t m0 x14 h7 y73 ff1 fs5 fc0 sc0 ls0 ws0">IGNAL MODEL</div><div class="t m0 x8 h7 y74 ff1 fs3 fc0 sc0 ls0 ws0">We consider an OFDM system using an inverse fast Fourier</div><div class="t m0 x1 h7 y75 ff1 fs3 fc0 sc0 ls0 ws0">transform (IFFT) of size</div><div class="t m0 x15 h7 y76 ff1 fs3 fc0 sc0 ls0 ws0">for modulation. Each OFDM</div><div class="t m0 x1 h7 y77 ff1 fs3 fc0 sc0 ls0 ws0">symbol is composed of</div><div class="t m0 x16 h7 y78 ff1 fs3 fc0 sc0 ls0 ws0">data symbols , where</div><div class="t m0 x9 h7 y79 ff1 fs3 fc0 sc0 ls0 ws0">denotes the OFDM symbol time index and denotes the</div><div class="t m0 x1 h7 y7a ff1 fs3 fc0 sc0 ls0 ws0">subcarrier frequency index. The output of the IFFT is discrete</div><div class="t m0 x1 h7 y7b ff1 fs3 fc0 sc0 ls0 ws0">time with sampling time</div><div class="t m0 x17 h7 y7c ff1 fs3 fc0 sc0 ls0 ws0">. In order to limit the</div><div class="t m0 x1 h7 y7d ff1 fs3 fc0 sc0 ls0 ws0">transmit signal to a bandwidth smaller than</div><div class="t m0 x18 h7 y7e ff1 fs3 fc0 sc0 ls0 ws0">(thus allowing</div><div class="t m0 x1 h7 y7f ff1 fs3 fc0 sc0 ls0 ws0">a simple “T-spaced” OFDM receiver), the number</div><div class="t m0 x19 h7 y80 ff1 fs3 fc0 sc0 ls0 ws0">is chosen</div><div class="t m0 x1 h7 y81 ff1 fs3 fc0 sc0 ls0 ws0">small enough to provide that so-called “guard bands” at the</div><div class="t m0 x1 h7 y82 ff1 fs3 fc0 sc0 ls0 ws0">edges of the transmission spectrum are left free. Using these</div><div class="t m0 x1 h7 y83 ff1 fs3 fc0 sc0 ls0 ws0">guard bands, the (periodic) spectrum is limited by using an</div><div class="t m0 x1 h7 y84 ff1 fs3 fc0 sc0 ls0 ws0">appropriate analog transmission ﬁlter</div><div class="t m0 x1a h7 y85 ff1 fs3 fc0 sc0 ls0 ws0">. The transmitted</div><div class="t m0 x1 h7 y86 ff1 fs3 fc0 sc0 ls0 ws0">complex baseband signal can then be described by</div><div class="t m0 x1b h7 y87 ff1 fs3 fc0 sc0 ls0 ws0">(1)</div><div class="t m0 x1 h7 y88 ff1 fs3 fc0 sc0 ls0 ws0">where</div><div class="t m0 x1c h7 y89 ff1 fs3 fc0 sc0 ls0 ws0">denotes convolution. Each data symbol is shaped</div><div class="t m0 x1 h7 y8a ff1 fs3 fc0 sc0 ls0 ws0">by a rectangular pulse of length</div><div class="t m0 x1d h7 y8b ff1 fs3 fc0 sc0 ls0 ws0">and modulated onto a</div><div class="t m0 x1 h7 y8c ff1 fs3 fc0 sc0 ls0 ws0">subcarrier with (baseband) frequency</div><div class="t m0 x1e h7 y8d ff1 fs3 fc0 sc0 ls0 ws0">. In order</div><div class="t m0 x1 h7 y8e ff1 fs3 fc0 sc0 ls0 ws0">to avoid intersymbol interference (ISI), the OFDM symbol is</div><div class="t m0 x1 h7 y8f ff1 fs3 fc0 sc0 ls0 ws0">preceded by a guard interval of length</div><div class="t m0 x1f h7 y90 ff1 fs3 fc0 sc0 ls0 ws0">. Taking this into</div><div class="t m0 x1 h7 y91 ff1 fs3 fc0 sc0 ls0 ws0">account, the resulting subcarrier pulses are</div><div class="t m0 x20 h7 y92 ff1 fs3 fc0 sc0 ls0 ws0">else.</div><div class="t m0 x1b h7 y93 ff1 fs3 fc0 sc0 ls0 ws0">(2)</div><div class="t m0 x1 h7 y94 ff1 fs3 fc0 sc0 ls0 ws0">The resulting symbols are of length</div><div class="t m0 x1e h7 y95 ff1 fs3 fc0 sc0 ls0 ws0">, which is</div><div class="t m0 x1 h7 y96 ff1 fs3 fc0 sc0 ls0 ws0">equivalent to</div><div class="t m0 x14 h7 y97 ff1 fs3 fc0 sc0 ls0 ws0">samples.</div><div class="t m0 x1 h5 y98 ff2 fs3 fc0 sc0 ls0 ws0">A. Transmission over Frequency-Selective Fading Channels</div><div class="t m0 x8 h7 y99 ff1 fs3 fc0 sc0 ls0 ws0">The signal is transmitted over a frequency selective fading</div><div class="t m0 x1 h7 y9a ff1 fs3 fc0 sc0 ls0 ws0">channel</div><div class="t m0 x1b h7 y9b ff1 fs3 fc0 sc0 ls0 ws0">(3)</div><div class="t m0 x1 h7 y9c ff1 fs3 fc0 sc0 ls0 ws0">which is comprised of the actual channel impulse response</div><div class="t m0 x1 h7 y9d ff1 fs3 fc0 sc0 ls0 ws0">(CIR) and the transmission ﬁlter</div><div class="t m0 x21 h7 y9e ff1 fs3 fc0 sc0 ls0 ws0">. We will further assume</div><div class="t m0 x1 h7 y9f ff1 fs3 fc0 sc0 ls0 ws0">that the channel taps are uncorrelated with respect to each other</div><div class="t m0 x1 h7 ya0 ff1 fs3 fc0 sc0 ls0 ws0">and can be modeled as a wide-sense stationary process where</div><div class="t m0 x1 h7 ya1 ff1 fs3 fc0 sc0 ls0 ws0">the average energy of the total channel energy is normalized</div><div class="t m0 x1 h7 ya2 ff1 fs3 fc0 sc0 ls0 ws0">to one, and the delays</div><div class="t m0 x22 h7 ya3 ff1 fs3 fc0 sc0 ls0 ws0">are taken to be constant for the</div><div class="t m0 x1 h7 ya4 ff1 fs3 fc0 sc0 ls0 ws0">time of interest. Assuming the receiver ﬁlter is ﬂat within the</div><div class="t m0 x1 h7 ya5 ff1 fs3 fc0 sc0 ls0 ws0">transmitter bandwidth, the receiver input signal is</div><div class="t m0 x1b h7 ya6 ff1 fs3 fc0 sc0 ls0 ws0">(4)</div><div class="t m0 xe h7 ya7 ff1 fs3 fc0 sc0 ls0 ws0">Sampling the signal at time instants</div><div class="t m0 x23 h7 y69 ff1 fs3 fc0 sc0 ls0 ws0">yields</div><div class="t m0 x24 h7 ya8 ff1 fs3 fc0 sc0 ls0 ws0">(5)</div><div class="t m0 xe h7 ya9 ff1 fs3 fc0 sc0 ls0 ws0">After removing the guard interval for further receiver pro-</div><div class="t m0 xe h7 yaa ff1 fs3 fc0 sc0 ls0 ws0">cessing, the</div><div class="t m0 x25 h7 yab ff1 fs3 fc0 sc0 ls0 ws0">th received OFDM symbol is represented by</div><div class="t m0 xe h7 yac ff1 fs3 fc0 sc0 ls0 ws0">samples</div><div class="t m0 x24 h7 yad ff1 fs3 fc0 sc0 ls0 ws0">(6)</div><div class="t m0 xe h7 yae ff1 fs3 fc0 sc0 ls0 ws0">Demodulation of the subcarriers via a fast Fourier transform</div><div class="t m0 xe h7 yaf ff1 fs3 fc0 sc0 ls0 ws0">(FFT) yields the received data symbols</div><div class="t m0 x24 h7 yb0 ff1 fs3 fc0 sc0 ls0 ws0">(7)</div><div class="t m0 xc h7 yb1 ff1 fs3 fc0 sc0 ls0 ws0">For the moment, we assume the channel to be constant</div><div class="t m0 xe h7 yb2 ff1 fs3 fc0 sc0 ls0 ws0">during the transmission of one OFDM symbol denoted by</div><div class="t m0 xf h7 yb3 ff1 fs3 fc0 sc0 ls0 ws0">. The demodulated data symbols ( th OFDM symbol,</div><div class="t m0 xe h7 yb4 ff1 fs3 fc0 sc0 ls0 ws0">subcarrier</div><div class="t m0 x26 h7 yb5 ff1 fs3 fc0 sc0 ls0 ws0">) can be shown to be given by [11]</div><div class="t m0 x24 h7 yb6 ff1 fs3 fc0 sc0 ls0 ws0">(8)</div><div class="t m0 xe h7 yb7 ff1 fs3 fc0 sc0 ls0 ws0">where</div><div class="t m0 x26 h7 yb8 ff1 fs3 fc0 sc0 ls0 ws0">is complex-valued additive white Gaussian noise</div><div class="t m0 xe h7 yb9 ff1 fs3 fc0 sc0 ls0 ws0">(AWGN) and</div><div class="t m0 x24 h7 yba ff1 fs3 fc0 sc0 ls0 ws0">(9)</div><div class="t m0 xe h7 ybb ff1 fs3 fc0 sc0 ls0 ws0">is the channel transfer function (CTF) at subcarrier frequency</div><div class="t m0 x27 h7 ybc ff1 fs3 fc0 sc0 ls0 ws0">. Normalizing the average power of data symbols</div><div class="t m0 xf h7 ybd ff1 fs3 fc0 sc0 ls0 ws0">and the CTF to one, the average signal-to-noise ratio</div><div class="t m0 xe h7 ybe ff1 fs3 fc0 sc0 ls0 ws0">(SNR) per symbol</div><div class="t m0 x28 h7 ybf ff1 fs3 fc0 sc0 ls0 ws0">at data subchannel level is given by</div><div class="t m0 x29 h7 yc0 ff1 fs3 fc0 sc0 ls0 ws0">(10)</div><div class="t m0 xe h7 yc1 ff1 fs3 fc0 sc0 ls0 ws0">where</div><div class="t m0 x2a h7 yc2 ff1 fs3 fc0 sc0 ls0 ws0">denotes the expected value.</div><div class="t m0 x2b h7 yc3 ff1 fs3 fc0 sc0 ls0 ws0">III. T</div><div class="t m0 x2c h7 yc4 ff1 fs5 fc0 sc0 ls0 ws0">RANSMISSION OF OFDM SIGNALS</div><div class="t m0 xe h5 yc5 ff2 fs3 fc0 sc0 ls0 ws0">A. Transmission Model</div><div class="t m0 xc h7 yc6 ff1 fs3 fc0 sc0 ls0 ws0">In a real-world passband transmission system, the following</div><div class="t m0 xe h7 yc7 ff1 fs3 fc0 sc0 ls0 ws0">parameters cause disturbances in the receiver.</div><div class="t m0 xc h7 yc8 ff1 fs3 fc0 sc0 ls0 ws0">• The sampling time at the receiver</div><div class="t m0 x2d h7 yc9 ff1 fs3 fc0 sc0 ls0 ws0">can no longer be</div><div class="t m0 xf h7 yca ff1 fs3 fc0 sc0 ls0 ws0">assumed to be identical with the transmitter time</div><div class="t m0 x2e h7 ycb ff1 fs3 fc0 sc0 ls0 ws0">.</div><div class="t m0 xc h7 ycc ff1 fs3 fc0 sc0 ls0 ws0">• The same holds for the carrier frequency oscillators used</div><div class="t m0 xf h7 ycd ff1 fs3 fc0 sc0 ls0 ws0">for modulating and demodulating the signal. Assuming</div><div class="t m0 xf h7 yce ff1 fs3 fc0 sc0 ls0 ws0">a small frequency offset relative to the transmission</div><div class="t m0 xf h7 ycf ff1 fs3 fc0 sc0 ls0 ws0">bandwidth, the frequency difference between transmitter</div><div class="t m0 xf h7 yd0 ff1 fs3 fc0 sc0 ls0 ws0">and receiver oscillators can be modeled as a time-variant</div><div class="t m0 xf h7 yd1 ff1 fs3 fc0 sc0 ls0 ws0">phase offset</div><div class="t m0 x2f h7 yd2 ff1 fs3 fc0 sc0 ls0 ws0">at the receiver [10].</div><div class="t m0 xc h7 yd3 ff1 fs3 fc0 sc0 ls0 ws0">• The transmitter time scale is unknown to the receiver.</div><div class="t m0 xf h7 yd4 ff1 fs3 fc0 sc0 ls0 ws0">Therefore, the receiver OFDM symbol window control-</div><div class="t m0 xf h7 yd5 ff1 fs3 fc0 sc0 ls0 ws0">ling the removal of the guard interval will usually be</div><div class="t m0 xf h7 yd6 ff1 fs3 fc0 sc0 ls0 ws0">offset from its ideal setting by a time</div><div class="t m0 x30 h7 yd7 ff1 fs3 fc0 sc0 ls0 ws0">. This timing</div><div class="t m0 xf h7 yd8 ff1 fs3 fc0 sc0 ls0 ws0">delay can equivalently be incorporated into the channel</div><div class="t m0 xf h7 yd9 ff1 fs3 fc0 sc0 ls0 ws0">model, resulting in the effective channel</div><div class="t m0 x31 h7 yda ff1 fs3 fc0 sc0 ls0 ws0">relevant to</div><div class="t m0 xf h7 ydb ff1 fs3 fc0 sc0 ls0 ws0">the receiver time scale</div><div class="t m0 x32 h2 ydc ff1 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x29 h7 ydd ff1 fs3 fc0 sc0 ls0 ws0">(11)</div><div class="t m0 x33 hb yde ff1 fs7 fc0 sc0 ls0 ws0">1</div><div class="t m0 x34 h9 ydf ff1 fs5 fc0 sc0 ls0 ws0">In the strict sense,</div><div class="t m0 x35 hc ydf ff6 fs8 fc0 sc0 ls0 ws0">h</div><div class="t m0 x36 hd ye0 ff7 fs9 fc0 sc0 ls0 ws0">"</div><div class="t m0 x37 hc ydf ff8 fs8 fc0 sc0 ls0 ws0">(</div><div class="t m0 x28 hc ydf ff6 fs8 fc0 sc0 ls1 ws0">; t</div><div class="t m0 x2f hc ydf ff8 fs8 fc0 sc0 ls2 ws0">)=</div><div class="t m0 x38 hc ydf ff6 fs8 fc0 sc0 ls0 ws0">h</div><div class="t m0 x39 hc ydf ff8 fs8 fc0 sc0 ls0 ws0">(</div><div class="t m0 x3a hc ydf ff6 fs8 fc0 sc0 ls0 ws0"></div><div class="t m0 x3b hc ydf ff9 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m0 x3c hc ydf ff6 fs8 fc0 sc0 ls3 ws0">"T; t</div><div class="t m0 x3d hc ydf ff9 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m0 x3e hc ydf ff6 fs8 fc0 sc0 ls0 ws0">"T</div><div class="t m0 x3f hc ydf ff8 fs8 fc0 sc0 ls0 ws0">)</div><div class="t m0 x2d h9 ydf ff1 fs5 fc0 sc0 ls0 ws0">, which for small</div><div class="t m0 x24 hc ydf ff6 fs8 fc0 sc0 ls0 ws0">"</div><div class="t m0 x40 h9 ydf ff1 fs5 fc0 sc0 ls0 ws0">is</div><div class="t m0 xe h9 ye1 ff1 fs5 fc0 sc0 ls0 ws0">well approximated by (11).</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/1148472/bg3.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1670 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 11, NOVEMBER 1999</div><div class="t m0 x1 h9 ye2 ff1 fs5 fc0 sc0 ls0 ws0">Fig. 1. Complete baseband transmission model.</div><div class="t m0 x8 h7 ye3 ff1 fs3 fc0 sc0 ls0 ws0">All of the effects mentioned are incorporated in the equiv-</div><div class="t m0 x1 h7 ye4 ff1 fs3 fc0 sc0 ls0 ws0">alent system model depicted in Fig. 1 [10]. Equation (5) must</div><div class="t m0 x1 h7 ye5 ff1 fs3 fc0 sc0 ls0 ws0">be modiﬁed to yield</div><div class="t m0 x41 h7 ye6 ff1 fs3 fc0 sc0 ls0 ws0">(12)</div><div class="t m0 x1 h7 ye7 ff1 fs3 fc0 sc0 ls0 ws0">and (6) changes to</div><div class="t m0 x41 h7 ye8 ff1 fs3 fc0 sc0 ls0 ws0">(13)</div><div class="t m0 x1 h7 ye9 ff1 fs3 fc0 sc0 ls0 ws0">This transmission model, comprising all effects caused by the</div><div class="t m0 x1 h7 yea ff1 fs3 fc0 sc0 ls0 ws0">channel and by the inner receiver, is the basis for optimizing</div><div class="t m0 x1 h7 yeb ff1 fs3 fc0 sc0 ls0 ws0">the receiver components.</div><div class="t m0 x1 h5 yec ff2 fs3 fc0 sc0 ls0 ws0">B. Optimization Criterion</div><div class="t m0 x8 h7 yed ff1 fs3 fc0 sc0 ls0 ws0">In an analogy to [10], the OFDM receiver is divided into</div><div class="t m0 x1 h7 yee ff1 fs3 fc0 sc0 ls0 ws0">an inner receiver and an outer receiver (see Fig. 1). The task</div><div class="t m0 x1 h7 yef ff1 fs3 fc0 sc0 ls0 ws0">of the inner receiver is to provide estimates</div><div class="t m0 x42 h7 yf0 ff1 fs3 fc0 sc0 ls0 ws0">and</div><div class="t m0 x1 h7 yf1 ff1 fs3 fc0 sc0 ls0 ws0">such that the performance of the outer receiver shows no or</div><div class="t m0 x1 h7 yf2 ff1 fs3 fc0 sc0 ls0 ws0">minimal degradation compared to a “genius” receiver, which</div><div class="t m0 x1 h7 yf3 ff1 fs3 fc0 sc0 ls0 ws0">uses the true values</div><div class="t m0 x43 h7 yf4 ff1 fs3 fc0 sc0 ls0 ws0">and . An appropriate measure</div><div class="t m0 x1 h7 yf5 ff1 fs3 fc0 sc0 ls0 ws0">of inner receiver quality is therefore the additional</div><div class="t m0 x44 h7 yf6 ff1 fs3 fc0 sc0 ls0 ws0">(“SNR</div><div class="t m0 x1 h7 yf7 ff1 fs3 fc0 sc0 ls0 ws0">loss”) needed to close the gap between using the estimated</div><div class="t m0 x1 h7 yf8 ff1 fs3 fc0 sc0 ls0 ws0">(“real”) parameters in lieu of the true (“ideal”) parameters.</div><div class="t m0 x1 h7 yf9 ff1 fs3 fc0 sc0 ls0 ws0">We deﬁne the SNR loss of the system as</div><div class="t m0 x41 h7 yfa ff1 fs3 fc0 sc0 ls0 ws0">(14)</div><div class="t m0 x45 h7 yfb ff1 fs3 fc0 sc0 ls0 ws0">denotes the required for a certain performance of</div><div class="t m0 x1 h7 yfc ff1 fs3 fc0 sc0 ls0 ws0">the outer receiver assuming ideal synchronization, and</div><div class="t m0 x1 h7 yfd ff1 fs3 fc0 sc0 ls0 ws0">is the required to achieve the same performance with a real</div><div class="t m0 x1 h7 yfe ff1 fs3 fc0 sc0 ls0 ws0">receiver. Correspondingly,</div><div class="t m0 x46 h7 yff ff1 fs3 fc0 sc0 ls0 ws0">and denote the noise</div><div class="t m0 x1 h7 y100 ff1 fs3 fc0 sc0 ls0 ws0">variances at the inner receiver input that must not be exceeded</div><div class="t m0 x1 h7 y101 ff1 fs3 fc0 sc0 ls0 ws0">to achieve a certain outer receiver performance.</div><div class="t m0 x8 h7 y102 ff1 fs3 fc0 sc0 ls0 ws0">In the following section, we discuss the impact of imper-</div><div class="t m0 x1 h7 y103 ff1 fs3 fc0 sc0 ls0 ws0">fectly estimated parameters on the received signal and on</div><div class="t m0 x47 h7 y104 ff1 fs3 fc0 sc0 ls0 ws0">.</div><div class="t m0 x1 h7 y105 ff1 fs3 fc0 sc0 ls0 ws0">As we are primarily interested in the receiver operating under</div><div class="t m0 x1 h7 y106 ff1 fs3 fc0 sc0 ls0 ws0">close-to-ideal conditions (steady-state tracking), the analysis is</div><div class="t m0 x1 h7 y107 ff1 fs3 fc0 sc0 ls0 ws0">based on a small signal model where a particular parameter</div><div class="t m0 x1 h7 y108 ff1 fs3 fc0 sc0 ls0 ws0">of interest is assumed to be the only receiver disturbance,</div><div class="t m0 x1 h7 y109 ff1 fs3 fc0 sc0 ls0 ws0">implying that all other parameters are ideal and the channel</div><div class="t m0 x48 h7 y10a ff1 fs3 fc0 sc0 ls0 ws0">is static, except where stated otherwise.</div><div class="t m0 xc h7 y10b ff1 fs3 fc0 sc0 ls0 ws0">IV. E</div><div class="t m0 x49 h7 ye3 ff1 fs5 fc0 sc0 ls0 ws0">FFECTS OF NONIDEAL TRANSMISSION CONDITIONS</div><div class="t m0 xe h5 y10c ff2 fs3 fc0 sc0 ls0 ws0">A. Effects of an Imperfect Channel Estimate</div><div class="t m0 xc h7 y10d ff1 fs3 fc0 sc0 ls0 ws0">Channel estimation is mandatory if coherent modulation is</div><div class="t m0 xe h7 y10e ff1 fs3 fc0 sc0 ls0 ws0">used. Given a minimum mean square-error channel estimator</div><div class="t m0 xe h7 y10f ff1 fs3 fc0 sc0 ls0 ws0">designed to cope with worst-case channel conditions, the</div><div class="t m0 xe h7 y110 ff1 fs3 fc0 sc0 ls0 ws0">(sub)channel estimate (CTF sample</div><div class="t m0 x4a h7 y111 ff1 fs3 fc0 sc0 ls0 ws0">) is well modeled as</div><div class="t m0 xe h7 y112 ff1 fs3 fc0 sc0 ls0 ws0">the true CTF sample</div><div class="t m0 x4b h7 y113 ff1 fs3 fc0 sc0 ls0 ws0">disturbed by AWGN</div><div class="t m0 x29 h7 y114 ff1 fs3 fc0 sc0 ls0 ws0">(15)</div><div class="t m0 xe h7 y115 ff1 fs3 fc0 sc0 ls0 ws0">where the power</div><div class="t m0 x4c h7 y116 ff1 fs3 fc0 sc0 ls0 ws0">of the estimation noise is a</div><div class="t m0 xe h7 y117 ff1 fs3 fc0 sc0 ls0 ws0">function of the channel noise variance. The optimum outer re-</div><div class="t m0 xe h7 y118 ff1 fs3 fc0 sc0 ls0 ws0">ceiver features maximum-likelihood (ML) sequence estimation</div><div class="t m0 xe h7 y119 ff1 fs3 fc0 sc0 ls0 ws0">using the signal pair</div><div class="t m0 x4d h7 y11a ff1 fs3 fc0 sc0 ls0 ws0">delivered by the inner receiver.</div><div class="t m0 xe h7 y11b ff1 fs3 fc0 sc0 ls0 ws0">The resulting performance, given a certain</div><div class="t m0 x4e h7 y11c ff1 fs3 fc0 sc0 ls0 ws0">and , is well</div><div class="t m0 xe h7 y11d ff1 fs3 fc0 sc0 ls0 ws0">approximated by a receiver facing a perfectly known channel</div><div class="t m0 xe h7 y11e ff1 fs3 fc0 sc0 ls0 ws0">and Gaussian noise</div><div class="t m0 x4f h7 y11f ff1 fs3 fc0 sc0 ls0 ws0">of increased power</div><div class="t m0 x29 h7 y120 ff1 fs3 fc0 sc0 ls0 ws0">(16)</div><div class="t m0 xe h7 y121 ff1 fs3 fc0 sc0 ls0 ws0">In order to attain the original receiver performance</div><div class="t m0 x29 h7 y92 ff1 fs3 fc0 sc0 ls0 ws0">(17)</div><div class="t m0 xe h7 y122 ff1 fs3 fc0 sc0 ls0 ws0">must hold. From (14) and (17), we can directly derive the loss</div><div class="t m0 xe h7 y123 ff1 fs3 fc0 sc0 ls0 ws0">in performance</div><div class="t m0 x29 h7 y124 ff1 fs3 fc0 sc0 ls0 ws0">(18)</div><div class="t m0 xe h7 y125 ff1 fs3 fc0 sc0 ls0 ws0">For the two-dimensional Wiener channel estimator of [12], the</div><div class="t m0 xe h7 y126 ff1 fs3 fc0 sc0 ls0 ws0">estimation noise power is given by</div><div class="t m0 x29 h7 y127 ff1 fs3 fc0 sc0 ls0 ws0">(19)</div><div class="t m0 xe h7 y128 ff1 fs3 fc0 sc0 ls0 ws0">where</div><div class="t m0 x50 h7 y129 ff1 fs3 fc0 sc0 ls0 ws0">is the estimator gain factor, so that the performance</div><div class="t m0 xe h7 y12a ff1 fs3 fc0 sc0 ls0 ws0">loss becomes</div><div class="t m0 x29 h7 y12b ff1 fs3 fc0 sc0 ls0 ws0">(20)</div><div class="t m0 xe h7 y12c ff1 fs3 fc0 sc0 ls0 ws0">The factor</div><div class="t m0 x51 h7 y12d ff1 fs3 fc0 sc0 ls0 ws0">results from optimization of the estimator. Its</div><div class="t m0 xe h7 y12e ff1 fs3 fc0 sc0 ls0 ws0">value depends on the number of training data available, the</div><div class="t m0 xe h7 y12f ff1 fs3 fc0 sc0 ls0 ws0">assumed worst-case channel characteristics and the allowable</div><div class="t m0 xe h7 y130 ff1 fs3 fc0 sc0 ls0 ws0">complexity [13].</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>