text: This section is intended to introduce the reader to various aspects of art, which may be related to the present embodiments that are described below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light.
  Many modern communication systems utilize multicarrier modulation techniques, such as Orthogonal Frequency Division Multiplexing (OFDM). OFDM is a technique of encoding digital data on multiple carrier frequencies. In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard bands are not required. This greatly simplifies the design of both the transmitter and the receiver; unlike conventional frequency division multiplexing (FDM), a separate filter for each sub-channel is not required. The orthogonality allows for efficient modulator and demodulator implementation using the Fast Fourier Transform (FFT) algorithm on the receiver side, and inverse FFT on the transmitter side. In particular, the size of the FFT identifies the number of carriers in the OFDM modulation system. Frequency selective channels are characterized either by their delay spread or coherence bandwidth. In a single carrier system, such as the eight level vestigial sideband (8-VSB) signal transmission system, a single fade or interference can cause the whole link to fail, but in multi-carrier systems, like OFDM, only a few of the total sub carriers will be affected. This way, multipath fading can be easily eliminated in OFDM, with simpler equalization techniques than in single carrier systems. OFDM is used in systems for terrestrial television signal transmission (e.g., digital video broadcast standards DVB-T and DVB-T2) as well as cellular telephone and wireless data signal transmission, among others.
  For the DVB-T2 system, there are several different FFT sizes to choose from, specifically, 1K, 2K, 4K, 8K, 16K, and 32K, where the number of carriers is equal to two to the N power that most closely equals the value indicated above in thousands. As the size of the FFT increases, the roll-off of the spectrum gets increasingly sharper. Normally, for each FFT size, only a fixed number of the OFDM carriers are used and at the edges of the spectrum, some of the carriers are not used to allow the spectrum to roll-off enough to not interfere into the adjacent channel. For the large FFT sizes (16K, 32K, etc.), the roll-off is very sharp allowing for some additional OFDM carriers to be utilized. At these higher FFT values, the DVB-T2 specification allows for either the normal number of carriers or an extended number of carriers to be used. This is signaled to the receiver using the L1 pre-signaling data.
  Further, each of the carriers may be modulated based on a modulation code word set. The modulation depth or constellation pattern may vary from quadrature phase shift keying (QPSK) using two bit code words to 256 level quadrature amplitude modulation (256-QAM) using 8 bit code words.
  OFDM modulation has been adopted for use in digital terrestrial television standards, e.g., the DVB-T/DVB-T2 standards in Europe, and the integrate services digital broadcast standard ISDB-T standard in Japan. DVB-T, the 1st generation of European Digital Terrestrial Television (DTT), is the most widely adopted and deployed standard. Since its publication in 1997, over 70 countries have deployed DVB-T services and 45 more have adopted (but not yet deployed) DVB-T. This well-established standard benefits from massive economies of scale and very low receiver prices. Like its predecessor, DVB-T2 uses OFDM (orthogonal frequency division multiplex) modulation with a large number of sub-carriers delivering a robust signal, and offers a range of different modes, making it a very flexible standard. DVB-T2 uses the same error correction coding as used in the DVB-S2 standard for satellite signals and the DVB-C2 standard for cable signals: Low Density Parity Check (LDPC) coding combined with Bose-Chaudhuri-Hocquengham (BCH) coding, offering a very robust signal. The number of carriers, guard interval sizes and pilot signals can be adjusted, so that the overheads can be optimized for any target transmission channel. DVB-T2 offers more robustness, flexibility and at least 50% more efficiency than any other DTT system. It supports standard definition (SD), high definition (HD), ultra high definition (UHD), mobile TV, or any combination thereof.
  OFDM has also been adopted in other wireless communication networks such as, but not limited to, the Institute of Electrical and Electronics Engineers Standard IEEE 802.11 wireless standard, the cellular 3G partnership project long term evolution (3GPP LTE) standard, and the digital audio broadcast (DAB) standard. OFDM has also been used in other wired protocols including, but not limited to, multimedia over cable alliance (MoCA) system for coaxial cable, and the asymmetrical digital subscriber line (ADSL) and very high bit rate DSL (VDSL) system for telephone lines. The attributes and parameters described above also apply equally to these OFDM implementations.
  Recently, the Advanced Television Systems Committee (ATSC), which proposes terrestrial broadcasting digital television standards in the U.S., announced a call for proposals for the next generation (named ATSC 3.0) physical layer. ATSC 3.0 will provide even more services to the viewer and increased bandwidth efficiency and compression performance, which requires breaking backwards compatibility with the currently deployed version, ATSC A/53, which comprises an 8-VSB (8 level, Vestigial Sideband) modulation system. ATSC 3.0 is expected to emerge within the next decade and it intends to support delivery to fixed devices of content with video resolutions up to Ultra High Definition having 3840 pixels by 2160 pixels at 60 frames per second (fps). ATSC 3.0 may utilize many of the principles outlined above related to OFDM and may further include a plurality of signal modulation constellation patterns. The intention of the system is to support delivery to portable, handheld and vehicular devices of content with video resolution up to High Definition having 1920 pixels by 1080 pixels at 60 fps. The system is also expected to support lower video resolutions and frame rates.
  Despite its competitive attributes, however, OFDM signals have a major disadvantage compared to single carrier signals: a high Peak-to-Average Power Ratio (PAPR). When the OFDM signal is transformed to the time domain, the resulting signal is the sum of all the sub-carriers, which may add up in phase, resulting in a signal peak up to N times higher than the average signal power, where N is the number of sub-carriers. This characteristic leads the OFDM signals to be very sensitive to nonlinearities of analog components of the transceiver, in particular those of the High Power Amplifier (HPA) at the emission.
  An HPA is conceived to operate in its saturation zone, which corresponds to its high efficiency region. However, in this zone, the HPA has a severe nonlinear behavior. These nonlinearities are sources of In-Band (IB) distortions which can both degrade the link performance in terms of Bit Error Rate (BER) and also cause significant Out-Of-Band (OOB) interference products that make it harder for the operator to comply with stringent spectral masks. The simplest solution to this problem is to operate the HPA in the linear region by allowing a large enough amplifier back-off. However, this approach degrades the power efficiency of the system and often leads to unacceptable cost-efficiency conditions in the overall system. For all these reasons, reducing the PAPR of OFDM signals is increasingly being considered to be very important in maintaining the cost-effectiveness advantages of OFDM in practical systems, especially as new systems like DVB-T2 are being specified with large numbers of carriers (up to 32K and 256-QAM modulation).
  Many techniques have been proposed to reduce PAPR values in OFDM systems, but most of them either reduce the efficiency of the transmission or deliberately degrade the quality of the transmitted signal. For example, an Active Constellation Extension (ACE) mechanism has been proposed as an efficient method to reduce the PAPR values in both single input single output (SISO) and multiple input multiple output (MIMO) communication systems and have also been adopted for use with DVB-T2 broadcast systems. However, these systems are not optimal for all signal modulation constellation patterns. For example, ATSC 3.0 is considering using two dimensional (2D) non-square constellation patterns containing 16, 64, or 256 constellation symbols or points. The ACE mechanism works well with QAM modulated sub-carriers using square constellation because the boundary points of the square QAM constellation are extended following the real or imaginary axis direction. However, the ACE techniques as used with DVB-T2, as well as similar PAPR reduction techniques, have very low efficiency for non-square constellations proposed for ATSC 3.0.
  When a new broadcast system is deployed, as it will eventually be the case for ATSC 3.0, the new broadcast system may co-exist with the existing system for some time. In addition, there is usually some channel re-alignment involved where channels are moved around the available spectrum to accommodate both new and existing channels. This planning process can be quite difficult as it must take into account the interference between the various channels when planning where the channels can be located. The co-existence condition highlights the importance of considering PAPR reduction techniques one of the priorities of the new system, particularly because of potential adjacent and co-channel interferences with the pre-existing single carrier system. Therefore, there is a need for an improvement to the PAPR reduction techniques used in conjunction with OFDM systems based on new and different signal modulation constellation patterns, including the OFDM system for ATSC 3.0.