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• W2322048989 abstract "The minimum frequency spacing to attain orthogonality between FDMA accesses is derived for QPSK, OQPSK and MSK modulations under the assumption that the modulation symbol times of the accesses are synchronized. The frequency spacing required for QPSK is 1/(2Tb)where Tb is the bit duration. This spacing is half that required for OQPSK and onethird that required for MSK. The effects of desynchronization errors on orthogonal QPSK are then derived for a variety of situations. The use of orthogonal synchronous QPSK in situations where synchronization is practicable or innate to the communications architecture enables a significant improvement in bandwidth efficiency and negligible performance loss in comparison to conventional FDMA implementations using filtered asynchronous QPSK, OQPSK or MSK. The three popular modulation schemes: quadraphase shift keying (QPSK), offset QPSK (OQPSK), and minimum shift keying (MSK) all have the high performance and constant envelope characteristics achievable with binary antipodal PSK while having increased bandwidth efficiency due to simultaneous use of both quadrature channels. In practice, in order to maximize bandwidth efficiency and reduce cross-talk due to adjacent channel interference these waveforms are narrowband filtered at the transmitter and receiver. As a consequence of this filtering, losses are introduced due to non-ideal signal processing, intersymbol interference and residual cross-talk. If the satellite and/or terminal high power amplifiers are operated near saturation, there are additional losses due to spectral sidelobe regrowth (tail regeneration) following the non-linearity [I]. Filtered QPSK is more sensitive to spectral regrowth than either filtered OQPSK or filtered MSK and for this reason OQPSK or MSK a re frequently chosen for FDMA applications rather than QPSK[2]. These comparative advantages of OQPSK and MSK over QPSK are under the implicit assumption (though the assumption is rarely stated) that the individual FDMA accesses sharing a given band are asynchronous, i. e., that the symbol timing of individual links as seen at a given receive terminal are mutually independent random variables. This assumption is valid, for instance, if there is no common time reference and each transmitted access is generated by a different terminal whose internal clock accuracy or differential propagation delay is on the order of one or more modulation symbols. However, there are situations such as the case where many FDMA accesses of the same modulation and data rate originate at a single terminal transmitter and are combined into channel groups, where synchronous transmission (at least within channel groups) is innate to the communication archi-tecture. In this case, as will be shown below, zero-cross-talk (i. e., orthogonality) between accesses can be obtained without recourse to any filtering. For such situations the comparative bandwidth efficiency advantage of OQPSK and MSK over QPSK is reversed. Indeed, the minimum frequency separation required for orthogonality for QPSK will be only half that required for OQPSK and one-third that required for MSK. The fact that no filtering is required for orthogonal synchronous QPSK eliminates entirely the commonly cited drawback of filtered QPSK (as opposed to filtered OQPSK or MSK): that of spectral regrowth after processing by non-linear elements in the transmission chain. The advantage of orthogonal synchronous QPSK over orthogonal synchronous OQPSK is rather surprising, given that both modulations have identical power spectra. This result is an example of the inadequacy of the power spectrum as a tool for the analysis of cross-talk phenomena in situations where an underlying non-stochastic waveform structure (such as synchronization) exists. The approach used here is motivated by the treatment of crosstalk for these modulations developed in [3], but diverges from [3] in a number of key respects. First, [3] is concerned with cross-talk between asynchronous accesses whereas the treatment here emphasizes synchronous accesses. Second, [3] develops worst-case bounds for cross-talk losses whereas here, explicit combinatorial expressions are developed for these losses. Lastly, the conclusion in [3] is that MSK is the waveform of choice for the asynchronous case. In contrast, the conclusion here is that QPSK is the best choice for the synchronous case. 2. Orthogonalitv Conditions We derive the orthogonality conditions in detail for the QPSK case. The analogous formulas for OQPSK may be derived in a similar manner and are stated without proof. The formulas for MSK are derived in the Appendix. For all three modulations considered, the symbol interval T, is twice the information bit interval Tb. For QPSK the received signal from two QPSK accesses over a symbol interval T, = 2Tb is of the form [+cos (v(t z) + 8) 2 sin (v(t z) + e)] 0 2 t 5 2Tb (1) where for convenience in (1) we have assumed that the symbol begins at t = 0 The first term represents the desired signal at angular frequency w and the second term represents a single adjacent QPSK signal at frequency v which is delayed in time by z and has an arbitrary phase offset 6 . The signs of the inphase and quadrature components of both signals are independent random variables. We now determine the contribution of the interfering signal to the matched filter output of an ideal QPSK receiver. As pointed out in [4], without loss of generality we may limit the analysis to the in-phase component of the matched filter and assume that the polarity of the in-phase signal component is positive ( + m c o s wt). We may also assume that 0 2 z 5 Tb. With these assumptions we have as the in-phase contribution to the matched filter output: Copyright Q 1994 by Philip M. Fishman. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. 2Tb u = J r(t) cos mtdt 0 where ~ ~ & f ? is the desired signal contribution and QA ( t ) = sin ( ~ ( t r ) + 8) (4) We rewrite (2) in normalized form as where A I S is the adjacent signal-to-desired signal power ratio and X will be a discrete random variable depending on the polarity of IA(0) and QA(0) and on whether IA(t) and QA(t) change sign at time r . We now consider the properties of X . Note that during the interval [O,~T,] the desired signal Is(t) is constant in polarity, but IA(0) can be of the same or opposite polarity to Is(0) (two equa-probable events). Moreover, at timer, IA(t) can either change or not change its polarity (two equa-probable events). Combining, we get four equa-probable events associated with IA(t) on the interval [ o , ~ T ~ ] . Similarly, QA(0) can be of the same or opposite polarity to Is(0) and can change or not change polarity at timez. Since there are four equally likely possibilities for IA(t) and four equally likely and independent possibilities for QA(t) we obtain a total of 16 possibilities, each occumng with probability 1/16. Let I. denote the contribution of IA(t) to X when IA(0) is of the same sign as Is(0) and does not have a sign change at timez and let Il denote the contribution of IA(r) to X when IA(0) is of the same sign as Is(0) and does have a sign &ange at timero. Let Q and Ql be defined analogously for the contribution of QA(t) to X . It is obvious that if IA(0) is of opposite sign to Is(0) and does not have a sign change, that the contribution of IA (t) to X will be -I0. Similarly, if I, (0) is of opposite sign to Is(0) and does have a sign change, that the contribution of IA (t)to X will be I,. From these observations we conclude that X is a 16 valued random variable taking the following values, each with probability 1/16:" @default.
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• W2322048989 date "1994-02-28" @default.
• W2322048989 modified "2023-09-23" @default.
• W2322048989 title "Orthogonal synchronous QPSK as a bandwidth efficient modulation scheme for FDMA applications" @default.
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• W2322048989 doi "https://doi.org/10.2514/6.1994-1152" @default.
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