| Sažetak | U fokusu istraživanja je vršna performansa prijenosa OFDM signala višestaznim kanalom, odnosno intenzitet neuklonjivih pogrešaka bita - rezidualni BER, u uvjetima visokog odnosa snaga signala i šuma i manje vremenske disperzije (npr. u zatvorenom prostoru). Na temelju postavljenoga analitičkog modela mehanizma generiranja pogrešaka - inherentne slabosti OFDM s aspekta zadržavanja ortogonalnosti u uvjetima višestazne propagacije, izvedena je originalna formula za procjenu rezidualnog BER-a. Dobiveni izraz uključuje kako odgovarajuće modificirani standardni parametar vremenske disperzije kanala – srednje kvadratno raspršenje kašnjenja profila, tako i parametre OFDM signala. Valjanost modela najprije je verificirana rezultatima problemski specifičnih Monte Carlo simulacija, a zatim odgovarajućim ispitivanjem za LTE silaznu vezu, provedenom na industrijski standardnom LTE programskom simulatoru. Analitički i programskim simulacijama, pokazana je zavisnost performanse ne samo od vrijednosti standardnih parametara disperzije, nego i od oblika profila. Nadalje, iako primjena cikličnog prefiksa nije nužno predviđena razvijenim modelom predviđanja učestalosti neuklonjivih pogrešaka, njegovom jednostavnom modifikacijom, lako se simulira djelovanje cikličnog prefiksa, proizvoljno izabrane duljine. Adekvatnost ovoga izbora može se ocijeniti temeljem postignutog kompromisa između ciljne kvalitete (BER) i prihvatljivog smanjenja efektivne brzine prijenosa. Tako je, za konkretni primjer eksponencijalnog profila, nedvojbeno pokazano da je, za dane uvjete i postavljeni prag kvalitete, standardna tzv. normalna duljina cikličnog prefiksa neopravdano predimenzionirana u odnosu na identificiranu optimalnu vrijednost. Konačno, razvijeni model predviđanja omogućuje i jednostavno modeliranje utjecaja netočnosti frekvencije podnositelja na rezidualni BER, dodavanjem ekvivalentne vremenske disperzije, jednakog efekta na performansu. Ovo je verificirano simulacijama za slučaj maksimalnih Dopplerovih pomaka frekvencija podnositelja, definiranih za standardne modele profila kašnjenja. |
| Sažetak (engleski) | The so-called residual channel is determined by the intensity of errored symbols that could not be corrected by physical layer. In this sense, it is especially important to provide higher protocol layers with a robust real-time prediction of channel state, especially the BER over the residual channel. So, e.g. in LTE systems, OFDM signal is not considerably distorted by multipath channel unless time dispersion surpasses a certain predefined level. However, when this occurs, the remaining symbol errors cannot be eliminated by usual measures at the physical layer such as e.g. increasing transmitter power. Such residual errors determine the irreducible (residual) probability of OFDM symbol error (error floor), whose estimation is very important in system design. With this respect, irreducible errors generating mechanism of OFDM symbol transmission over multipath radio channel, under condition of high signal-to-noise ratio and small time dispersion (indoor), is investigated here. Then, according to the standard multipath channel model, the received signal can be modeled as consisting of scaled, delayed and phase-shifted replicas (echoes) of the transmitted signal. In this case, symbol errors occur due to time-dispersion-induced mutual time non-alignment of echoes that are advanced or delayed with respect to the chosen sampling instant (e.g. mean delay of the power profile). This implies that time dispersion disables ideal overlapping of correlative receiver integration period with entire periods of echoes of the actual OFDM symbol. Consequently, a part of each echoed symbol is left to be incorrectly correlatively integrated by a neighboring (orthogonal) subcarrier, which creates the intersymbol interference and seriously disrupts the detection process. By means of stochastic signal modelling and analysis for given conditions, original explicit expressions for residual BER prediction were derived, as a function of accordingly modified channel time dispersion parameters and OFDM signal characteristics. Specifically, it was shown that the residual symbol error rate can be estimated by means of relevant channel and signal statistical parameters: rms delay spreads, normalized to the original symbol interval and distinguished for the advanced and delayed multipath echoes with respect to the chosen sampling instant, as well as by their corresponding composite powers, relative to the total mean power of all echoes, and finally, by variances of differences between the observed neighboring OFDM symbols, normalized to the amplitude of original symbols. In order to check the derived analytical formulas, the residual BER was estimated two way: first by means prediction and then by using Monte Carlo simulations, both implemented in MATLAB simulation environment. Two-delay, rectangle and exponential average power delay profiles were simulated, generating up to one million instantaneous profiles. High consistency was found for all profiles under test, so confirming the accuracy of the developped BER prediction expressions. Moreover, in addition to conducting extensive problem-specific MC simulations, wider experimental verification of the developped OFDM transmission peak performance model was done on the physical layer of the LTE downlink, by using industry-standard program simulator. I addition to the exponential delay profile, the EPA model was used, too. The achieved test results were in very good accordance with the ones coming out of prediction formulas and MC tests. Furthermore, analyzing the developped BER expression, its sensitivity to delay profile shape was shown, meaning that various profiles having the same rms delay spread, do not necessarily have equal residual BER values. These expectations were experimentally verified by comparison of the peak performance values obtained for the three selected profiles, as the two-delay profile showed the best performance, followed by the rectangle and the exponential profile. This also confirms analytically backed expectation that symmetrical delay profiles produce lesser residual BER than the asymmetrical ones, having the same delay spread. In addition, as the developped BER prediction model does not necessarily require application of cyclic prefix, it is shown that by simple modification – eliminating a number of “inner“ echoes of the dispersive channel (that is effectively done by cyclic prefix), it is possible to emulate the action of cyclic prefix (of arbitrary length). This “cutting“ of echoes enables modeling of BER as a function of cyclic prefix length, which in turn provides the possibility for testing adequacy of applied standard cyclic prefix lenghts, as well as estimating optimal value as compromise between quality (BER) and reduction of data rate. With this respect, only exponential profile was simulated (as the only one capable of generating long delayed individual echoes). For preselected maximal delay of the profile, it was shown that the so called normal cyclic prefix length of 4.69 s is unjustifiably overdimensioned. This is valid for indoor, as well as for EPA channel model, where almost always the presassumed model limitations apply (high SNR and neglectable Dopplerov shift). Finally, though not initially set up as a goal and expected contribution of the thesis, the impact of subcarrier frequency inacurracy, or Doppler shift on the performance of transmission of OFDM signal via multipath channel was investigated by adding equivalent time dispersion, producing equal effect on the residual BER. With this regard, the impact of standard maximal Doppler shift values for EPA, EVA and ETU profile models was preliminary investigated, too, so verifying the potential of the developped residual BER model to include this very important distortion that could seriously disturb orthogonality of OFDM signal transmitted via time dispersive channel. |
