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Abstract
Abstract: In this paper, an approximate analytical expressionfor the peak-to-average power ratio (PAPR) of a MultiCarrier CodeDivision Multiple Access (MC-CDMA) signal isderived. Then, it is demonstrated that the PAPR of a MC-CDMA system employingWalsh-Hadamard (WH) codes can be suitably reduced by resorting to a judicious strategy for the allocation of the spreading signaturecodes. Eventually, a lowcomplexity implementation of the proposed strategy is presented and the relevant benefits, in terms of peaksignal occurrence and robustness against nonlinear distortions, is numerically assessed over conventional random allocation strategy.1. INTRODUCTIONMULTI-CARRIER (MC) code-division multiple access (CDMA) is a transmission techniqueoffering many appealing properties, such as robustness against multipath fading channels and flexiblemultiple access capability 1. However, any MC signal (including MC-CDMA) experiences a high peakto-average power ratio (PAPR), i.e., the peaks of the instantaneous power are much higher than the averagepower level. Cosequently, the signal reveals vulnerable to nonlinear distortions induced by the highpower amplifier (HPA) of the transmitter which entail both signal-to-noise ratio (SNR) degradation and outof-band emission (OBE) 2. Such a limiting feature spurred a massive research effort aimed at devisingefficient techniques for PAPR reduction in MC signals. A comprehensive survey of PAPR reductiontechniques for orthogonal frequency-division multiplexing (OFDM) is presented in 3, while the OBEissue is addressed in 4. Some techniques originally devised for OFDM have been successfullydemonstrated to be applicable to MC-CDMA, too, such as the partial transmit sequences (PTS) 5 and theselective mapping (SLM) 6 methods. Both the techniques reveal effective, but require also sideinformation at the receiver and additional processing at the transmitter. In the particular case of MC-CDMAsystems, the code-spreading stage, which enables multi-user access, has a twofold importance. i) it makes theanalytical characterization of the PAPR more involved; ii) it provides an extra degree of freedom incontrolling the PAPR, for instance by carefully selecting the code set among those available from theliterature, or by suitably modifying an already existing set, or by designing a completely new code set.Concerning the former issue, several works focusing on the analytical characterization of thePAPR for MC-CDMA signals in a multi-user context and on its dependence on the spreadingsignature properties (mainly, code auto- and cross-correlations) have appeared in the literature.However, most of them had to face critical difficulties in the analytical evaluation of signal peak power Pmaxdistribution. To this respect, Choi and Hanzo 7 derived an analytical upper- bound of the crest factor(CF) for a MC-CDMA system using complementary (CP) codes, to be employed as a criterion for theselection of the lowest-PAPR code set. However, such a method is applicable to MC-CDMA systemswith binary phase shift keying (BPSK) modulation and 2 or 4 codes, only. Furthermore, in 8 it isdemonstrated that an accurate estimate of the PAPR for a MC-CDMA signal cannot be achieved by resortingto simplistic upper-bound approaches. So, a more accurate characterization of the PAPR distributionshall be obtained by means of a statistical approach. For instance, a closed-form approximation forthe PAPR distribution, based on the level-crossing rate analysis, is derived in 9 for OFDM, but, up todate and to the best of authors knowledge, no simple and reliable analytical tool for the evaluationof the PAPR of a MC-CDMA signal is available in the literature.
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Copyright © 2023 MORE S C. This is an open access article distributed under the Creative Commons Attribution License.
