On the EVM computation of arbitrary clipped multi-carrier signals
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RESEARCH
Open Access
On the EVM computation of arbitrary clipped multi-carrier signals Igal Kotzer* and Simon Litsyn
Abstract A common figure of merit in multi-carrier systems is the error vector magnitude (EVM). A method for EVM computation of a multi-carrier signal without any underlying model (e.g., the Gaussianity assumption) was proposed in a previous work of the authors. However, it addressed only the case of identical constellations and power loadings in all tones. In practice, however, the constellation and power loading may vary among the tones (e.g., boosted pilots, waterfilling and zero guard bands). Here the earlier approach is generalized in such a way that it is able to accommodate for an accurate analytical EVM computation in the cases of power loading and different constellations for different tones. Moreover, the derivation is valid for a general magnitude clipping function, so that any realistic clipper can be plugged in. 1 Introduction The use of multi-carrier (MC) communication schemes (e.g., OFDM, DMT, etc.) is very common nowadays due to its ability to cope well with channel interference while keeping the receiver complexity low, the ease of spectral mask shaping and high spectral efficiency. However, one of MC scheme’s greatest drawbacks is the high peak-toaverage power ratio (PAPR) caused by various degrees of coherent summation in the signal generation using IFFT [1]. Thus, systems utilizing MC communications must work with a large back-off in the high-power amplifier (HPA), which reduces both the efficiency of the HPA and the average power transmitted, or risk clipping. Based on the understanding that clipping is a nonlinear operation causing both in-band and out-of-band spectral noise and thus is an undesirable operation, methods for reducing the PAPR were devised. For a survey see [1-4]. Most of the power reduction methods are either statistical in nature– that is they do not guarantee PAPR limits, or iterative–in which required PAPR limits are easier to meet at the expense of computational complexity. Hence, while it is understood that the amount of clipping should be minimized, due to practical system limitations clipping cannot be entirely eliminated, but rather be set on a compromise level. Therefore, evaluating the performance of MC systems with clipping becomes relevant. * Correspondence: [email protected] School of Electrical Engineering - Systems, Tel Aviv University, Israel
Two prominent criteria for evaluating the performance of a MC system are its capacity [5-7], and the system’s error probability [8,9]. However, in engineering practice, the most popular measure is the error vector magnitude (EVM). The EVM is a figure of merit for inband distortion, which does not only quantifies the distortion but in some cases can attribute impairments to various system components [10]. Due to its popularity and troubleshooting capabilities, the EVM has become a mandatory part of a few communication standards, e.g. [[11], Tables 165, 172]. In [12] the authors express the EVM of an OFDM
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