What Are Partial Transmit Sequences?

Partial transmit sequences (PTS) are a signal processing technique used to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. High PAPR is a fundamental problem in OFDM because the superposition of many independently modulated subcarriers can produce occasional amplitude peaks that are many times the average signal level. These peaks force power amplifiers to operate in their nonlinear region unless the amplifier is backed off substantially, wasting energy. The PTS method addresses this by partitioning the OFDM subcarriers into smaller subblocks and combining them with phase rotation factors chosen to minimize the peak amplitude of the resulting time-domain signal.

The technique was developed in the late 1990s alongside other PAPR reduction methods such as selective mapping (SLM) and clipping and filtering. PTS is notable among these alternatives because it achieves meaningful PAPR reduction without distorting the transmitted signal or requiring signal clipping. It draws on combinatorial optimization and digital signal processing, and it has become one of the most studied PAPR reduction methods in the wireless communications literature.

The PTS Method

In the PTS scheme, the input data block of N subcarriers is divided into V disjoint subblocks, each containing N/V subcarriers. Each subblock is independently transformed to the time domain using an inverse fast Fourier transform (IFFT). The resulting time-domain sequences are then rotated by phase factors drawn from a finite alphabet, typically roots of unity such as {1, -1} or {1, -1, j, -j}. The combination of phase factors that produces the lowest peak amplitude in the summed time-domain signal is selected for transmission. A review of partial transmit sequence methods published in IEEE Access surveys the primary variants and their tradeoffs in PAPR reduction gain, computational complexity, and side information overhead.

The receiver must know which phase factors were applied to reconstruct the original data. This side information is either transmitted explicitly as overhead bits or, in blind detection schemes, inferred by testing all candidate phase combinations at the receiver. Explicit side information introduces a small spectral efficiency loss, while blind detection increases receiver complexity.

Complexity Reduction and Optimization

The main practical limitation of conventional PTS is computational cost. With V subblocks and a phase alphabet of size W, an exhaustive search over all W^(V-1) combinations grows exponentially with V. Research has produced many alternatives, including iterative algorithms, genetic algorithms, and parallel tabu search methods for PTS in OFDM that achieve performance close to exhaustive search at a fraction of the computation. Stochastic optimization approaches have also been applied to the phase selection problem, treating it as a discrete optimization task over a high-dimensional search space.

Subblock partitioning strategy also affects performance. Adjacent, interleaved, and pseudo-random partitioning schemes each produce different PAPR distributions, and interleaved or pseudo-random assignments generally outperform adjacent partitioning for a given number of subblocks. Combining PTS with other techniques, such as precoding matrices or scrambling codes, can yield further gains without proportionally increasing complexity.

PAPR Performance and Signal Integrity

PTS is a distortionless technique: it does not alter the frequency-domain data symbols, only the phase rotation applied to subblocks. As a result, the error rate performance in an AWGN channel is unchanged from a system without PAPR reduction. Analysis of PAPR reduction using PTS with low computational complexity demonstrates that systems with four or eight subblocks can achieve reductions of 3 to 4 dB in PAPR with manageable search overhead.

Applications

Partial transmit sequences have applications in a range of fields, including:

• LTE and 5G NR uplink and downlink OFDM systems
• IEEE 802.11 Wi-Fi physical layer power amplifier efficiency
• Digital audio broadcasting (DAB) transmitters
• Cognitive radio systems with dynamic spectrum access
• Satellite communications using OFDM waveforms