PAPR Reduction via Constellation Extension in OFDM Systems Using Generalized Benders Decomposition and Branch-and-Bound Techniques

Abstract

In this paper, a novel Constellation Extension (CE) based approach is presented to address the high Peak-to-Average Power Ratio (PAPR) problem at the transmitter side, which is an important drawback of Orthogonal Frequency Division Multiplexing (OFDM) systems. This new proposal is formulated as a Mixed Integer Non-Linear Programming (MINLP) optimization problem, which employs Generalized Benders Decomposition (GBD) and Branch-and-Bound (BB) methods to determine the most adequate extension factor and the optimum set of input symbols to be extended within a proper quarter-plane of the constellation. The optimum technique based on GBD, denoted as Generalized Benders Decomposition for Constellation Extension (GBDCE), provides a bound with relevant improvement in terms of PAPR reduction compared with other CE techniques, although it may exhibit slow convergence. To avoid excessive processing time in practical systems, the sub-optimum Branch-and-Bound for Constellation Extension (BBCE) scheme is proposed. Simulation results show that BBCE achieves a significant PAPR reduction, providing a good trade-off between complexity and performance. We also show that the BBCE scheme performs satisfactorily in terms of Power Spectral Density (PSD) and Bit Error Rate (BER) in the presence of a non-linear High Power Amplifier (HPA).

Performance of OPS-SAP technique for PAPR reduction in IEEE 802.11p scenarios

“…Regarding the comparison of OPS-SAP scheme with CE techniques based on optimization algorithms, they have not been taken into account in the simulation scenario since these schemes are too complex. However, in [9] some results show a performance comparison between different CE techniques based on convex and non-linear optimization processes.…”

“…The key of the CE-based methods is that a set of outer constellation points of the frequency-domain transmitted signal are moved toward the outside with an extension factor in such way that the PAPR is decreased. Techniques of this type are Active Constellation Extension (ACE) [6]; CE-based on convex optimization [7,8]; CE-based on mixed-integer nonlinear programming optmimization, namely GBDCE (Generalized Benders Decomposition for Constellation Extension) [9]; and CE-based on integer-programming, called BBCE (Branch-and-Bound for Constellation Extension) [9]; metric-based CE, named Simple Amplitude Predistortion (SAP) [10]; metric-based Symbol Predistortion [11]; and metric-based schemes embedded with pilot signaling [12,13].…”

“…Most of these schemes, such as ACE [6], CE-based on convex optimization [7,8], GBDCE and BBCE [9] are formulated as optimization problems, where the computational complexity is very high. To alleviate this load, [10] and [11] propose the calculation of a metric, which defines the set of constellation points that will be expanded, and then, the frequency-domain symbols with the highest metric value are selected to be extended with a predefined scaling factor.…”

Analysis of the PAPR Behavior of the OFDM Passband Signal

“…The PAPR reduction technique called OPS-SAP was applied on these OFDM frames which consists of the creation of a finite number of orthogonal pilot sequences [1]. For each OFDM symbol a pilot sequence is selected to get the lowest PAPR when combined with the data in the modulation process.…”

“…For some years, many wireless communication systems have based the transmission of information on the Orthogonal Frequency Division Multiplexing (OFDM) scheme, which is used in standards such as Long-Term Evolution (LTE), Wireless Local Area Networks (WLAN), Digital Video Broadcasting (DVB-T), among others. The use of OFDM is due to the multiple advantages it offers against the effects of the wireless environment, however, one of the problems of OFDM is the well-known high Peak-to-Average Power Ratio (PAPR) that degrades the signal at the time of passing through a non-linear High Power Amplifier (HPA) [1].…”