Partial Transmit Sequence (PTS)

The method of dividing the OFDM subcarriers into M disjoint sub-blocks critically impacts performance and complexity. Common approaches include:

• Adjacent Partitioning: Assigns contiguous subcarrier blocks. Simple but offers limited PAPR reduction due to high correlation between adjacent subcarriers.
• Interleaved Partitioning: Distributes subcarriers in a round-robin fashion. Achieves the best PAPR reduction performance but requires the highest computational complexity.
• Pseudo-Random Partitioning: Uses a pseudo-random pattern to assign subcarriers. Provides a practical trade-off between performance and complexity, and is the most commonly adopted scheme.

Each sub-block is multiplied by a complex phase rotation factor b_m selected from a finite set. The set size determines the search space:

• A typical set is {±1, ±j}, allowing four phase states (0°, 90°, 180°, 270°).
• For M sub-blocks and W phase factors, the total number of candidate sequences is W^(M-1) (one sub-block is fixed to avoid ambiguity).
• The exponential growth in candidates with M is the primary computational bottleneck, driving the need for sub-optimal search algorithms.

The receiver must know which phase combination was selected to correctly demodulate the data. This requires transmitting side information (SI) as overhead:

• The number of bits required is log₂(W^(M-1)) bits per OFDM symbol.
• SI must be heavily protected with error-correcting codes, as a single bit error corrupts the entire symbol.
• Blind PTS techniques eliminate SI by embedding the phase information in the signal structure (e.g., using pilot subcarrier power ratios), trading receiver complexity for spectral efficiency.

The primary cost of PTS lies in the repeated Inverse Fast Fourier Transforms (IFFTs) required to evaluate each candidate sequence. Key complexity factors include:

• Number of IFFTs: An exhaustive search requires W^(M-1) IFFT operations per symbol.
• Peak Power Calculation: Each candidate's PAPR must be computed from its time-domain samples.
• Complexity Reduction: Iterative flipping algorithms and gradient-based searches reduce complexity from exponential to linear in M with minimal performance loss, making real-time implementation feasible.

PTS belongs to the class of distortionless PAPR reduction techniques, offering a distinct advantage over clipping-based methods:

• No In-Band Distortion: Unlike Crest Factor Reduction (CFR), PTS does not degrade Error Vector Magnitude (EVM).
• No Out-of-Band Emissions: PTS introduces zero spectral regrowth, fully preserving the Adjacent Channel Leakage Ratio (ACLR).
• Trade-off: This fidelity comes at the cost of computational complexity and the spectral overhead of side information, making it ideal for systems where signal integrity is paramount.

To avoid the exponential complexity of exhaustive search, sub-optimal iterative algorithms are used in practice:

• Process: Starting with an initial phase vector, the algorithm iteratively flips the phase of each sub-block and keeps the change if PAPR decreases.
• Convergence: Typically converges in a few iterations, reducing the number of IFFTs from W^(M-1) to a linear function of M.
• Performance: Achieves PAPR reduction within 0.5–1.0 dB of the exhaustive search optimum, making it the standard approach for practical PTS implementations in FPGA and DSP platforms.

A probabilistic PAPR reduction scheme that generates multiple candidate transmit sequences by multiplying the original OFDM data block by different phase rotation vectors. The candidate with the lowest PAPR is selected for transmission.

• Requires transmission of side information (SI) to inform the receiver which phase vector was used
• Computational complexity scales with the number of candidate sequences
• Unlike PTS, SLM applies phase rotations to all subcarriers rather than partitioned sub-blocks
• Achieves comparable PAPR reduction gain to PTS but with different complexity trade-offs

A deterministic PAPR reduction method that reserves a subset of subcarriers exclusively for carrying a peak-canceling signal. These reserved tones do not carry user data, avoiding in-band distortion on data-bearing subcarriers.

• The peak-canceling signal is computed to subtract from amplitude peaks in the time domain
• No side information required—the receiver simply ignores reserved tones
• Performance depends on the number and placement of reserved tones
• Often combined with iterative clipping and filtering for aggressive PAPR targets

A PAPR reduction technique that dynamically extends outer constellation points outward within tolerable error vector magnitude (EVM) limits. By allowing constellation points to move away from decision boundaries, ACE creates degrees of freedom for peak reduction without increasing bit error rate.

• Operates on a per-subcarrier basis with constellation-aware constraints
• No side information overhead—the receiver treats extended points as normal symbols
• Particularly effective for QAM modulation schemes with corner points
• Can be implemented iteratively using projection onto convex sets (POCS)

An iterative CFR process that applies hard amplitude limiting followed by frequency-domain filtering to suppress out-of-band spectral regrowth. The fundamental trade-off is between PAPR reduction aggressiveness and in-band distortion measured as EVM.

• Peak regrowth occurs after filtering, necessitating multiple iterations
• Simple to implement but introduces in-band distortion that degrades modulation accuracy
• Often used as a baseline comparison for more sophisticated techniques like PTS
• Filter design critically impacts the ACLR compliance of the final signal

The statistical tool used to evaluate and compare PAPR reduction techniques. A CCDF curve shows the probability that a signal's instantaneous power exceeds a given threshold relative to its average power.

• PTS performance is typically measured as PAPR reduction gain at a specific CCDF point (e.g., 10⁻⁴)
• The steepness of the CCDF curve indicates how effectively peaks are suppressed
• Engineers use CCDF plots to determine required power amplifier back-off
• Standard reference for comparing SLM, PTS, TR, and clipping-based methods

The broader category of signal conditioning techniques that deliberately limit peak amplitude to improve power amplifier efficiency. PTS is a probabilistic CFR method operating at the symbol level, while clipping-based approaches operate on the time-domain waveform.

• CFR is mandatory in modern base stations to meet efficiency and linearity requirements
• Can be implemented as a multi-stage cascade combining different reduction strategies
• The choice between PTS, SLM, clipping, and TR depends on latency, complexity, and EVM budgets
• Often paired with digital predistortion (DPD) for complete transmitter linearization