Tone Reservation (TR)

TR exploits the orthogonality of OFDM subcarriers. A peak-canceling signal is constructed entirely on reserved tones that are disjoint from data tones. Because data and reserved tones occupy non-overlapping frequency bins, the cancellation signal causes zero in-band distortion on the data subcarriers at the receiver after FFT processing. This is the fundamental advantage over clipping-based Crest Factor Reduction (CFR).

The Tone Reservation Ratio (TRR) defines the percentage of total subcarriers allocated to peak reduction rather than data transmission.

• Typical values: 5% to 15% of total subcarriers
• Trade-off: Higher TRR enables more aggressive PAPR reduction but directly reduces spectral efficiency (throughput)
• 5G NR context: A 10% reservation on a 100 MHz carrier sacrifices 10 MHz of data bandwidth for improved Power Amplifier (PA) efficiency

The peak-canceling signal is generated by time-shifting and scaling a reference kernel. This kernel is a pre-computed waveform with a dominant time-domain peak, constructed by assigning specific magnitudes and phases to the reserved tones. The kernel is designed to approximate a Dirac delta function within the constraints of the reserved tone set, enabling precise peak cancellation at detected locations.

TR typically employs an iterative clipping and filtering process on the reserved tones only:

1. Detect the time-domain sample with the largest magnitude exceeding the target threshold
2. Shift the reference kernel to align with the peak location
3. Scale and subtract the kernel to cancel the peak
4. Repeat until all peaks fall below the threshold or a maximum iteration count is reached This iterative approach handles peak regrowth that occurs when canceling one peak affects neighboring samples.

TR is classified as a distortionless PAPR reduction technique, distinguishing it from methods like clipping and filtering.

• TR: Cancellation energy is confined to reserved tones, leaving data tones pristine. EVM on data subcarriers is theoretically zero.
• Clipping/CFR: Applies nonlinearity directly to the composite signal, causing in-band distortion (EVM degradation) and out-of-band spectral regrowth (ACLR degradation).
• Hybrid approaches: Combine TR with soft clipping on data tones for extreme PAPR targets.

The iterative peak detection and cancellation loop imposes significant computational overhead compared to simpler methods like hard clipping.

• Peak search: Requires scanning all time-domain samples per iteration
• Kernel convolution: Each cancellation step involves adding a shifted kernel, equivalent to a filtering operation
• Optimization: Fast Fourier Transform (FFT)-based implementations can accelerate the process by operating in the frequency domain
• Hardware: Typically implemented on FPGA or ASIC in baseband processors to meet microsecond-level latency budgets

The fundamental problem that Tone Reservation solves. PAPR quantifies the ratio of peak instantaneous power to average power in a signal envelope. High PAPR forces power amplifier back-off into inefficient operating regions.

• Definition: ( \text{PAPR}{\text{dB}} = 10 \log{10} \frac{\max|x(t)|^2}{E[|x(t)|^2]} )
• Impact: A 3 dB PAPR reduction can improve PA efficiency by 10-15%
• Measurement: Characterized via Complementary Cumulative Distribution Function (CCDF) curves
• TR Advantage: Unlike clipping methods, TR achieves PAPR reduction without in-band distortion

A CFR technique closely related to Tone Reservation that subtracts shaped cancellation pulses at detected peak locations. While TR operates in the frequency domain by allocating reserved tones, peak cancellation works in the time domain.

• Pulse Design: Cancellation pulses are pre-computed to match the spectral mask of the reserved tones
• Computational Trade-off: Peak cancellation requires peak detection and pulse subtraction per peak; TR solves a convex optimization problem
• Spectral Control: Both methods confine cancellation energy to reserved or out-of-band frequencies
• Implementation: Peak cancellation is often preferred in FPGA-based DPD systems for lower latency

A probabilistic alternative to Tone Reservation that generates multiple candidate OFDM symbols from the same data and transmits the one with lowest PAPR. Unlike TR, SLM requires side information transmission.

• Mechanism: Multiply data subcarriers by ( U ) different phase rotation sequences
• Overhead: Must transmit ( \log_2 U ) bits of side information per symbol for recovery
• Comparison to TR: SLM achieves 2-4 dB PAPR reduction without reserved tone overhead, but at the cost of increased computational complexity and side channel vulnerability
• Hybrid Use: SLM can be combined with TR for additive PAPR reduction gains

The critical metric that Tone Reservation preserves by design. EVM measures the deviation of received constellation points from ideal positions, representing in-band distortion.

• TR Advantage: Since reserved tones carry no data, the peak-canceling signal is orthogonal to data subcarriers — zero EVM contribution
• Clipping Penalty: Hard clipping at CR = 4 dB typically introduces 2-5% EVM
• Regulatory Limits: 3GPP specifies maximum EVM of 3.5% for 256-QAM in 5G NR
• Trade-off: TR avoids EVM degradation but consumes 5-20% of subcarriers as reserved tones

The out-of-band emission metric that Tone Reservation must carefully control. While TR avoids in-band distortion, the peak-canceling signal on reserved tones can leak into adjacent channels if not properly designed.

• Constraint: TR optimization must include spectral mask constraints on reserved tone power
• Regulatory Requirement: 3GPP mandates ACLR > 45 dB for base stations
• Design Challenge: Aggressive PAPR reduction increases reserved tone power, potentially violating ACLR limits
• Joint Optimization: Modern TR algorithms solve a constrained optimization balancing PAPR reduction against ACLR compliance