# Peak-to-average power-ratio reduction for OFDM systems based on method of conditional probability and coordinate descent optimization

## Summary (2 min read)

### Introduction

- Orthogonal frequency-division multiplexing (OFDM) has recently been used for data transmission in a number of communication systems [1][2].
- A major problem associated with OFDM is its large peak-to-average power-ratio (PAPR) which renders system performance sensitive to distortion introduced by nonlinear devices, e.g., power amplifiers (PAs).
- Recently, a number of algorithms [3]-[5] have been proposed to reduce the PAPR of the transmit signal before it enters the PAs.
- A new constellation is proposed whereby the data are represented either by points in the original constellation or by extended points.
- The performance of the proposed algorithms can be further improved by combining them with the selective mapping (SLM) algorithm [3].

### II. PAPR REDUCTION VIA CONSTELLATION EXTENSION

- Consider an N -subcarrier OFDM transmitter as illustrated in Fig. 1, where S/P, P/S, and D/A represent serialto-parallel, parallel-to-serial, and digital-to-analog converter, respectively, and the block labeled as “Amp.” represents a power amplifier.
- A 16-QAM modulation is adopted for each subcarrier and its constellation is shown in Fig. 2a.
- The proposed constellation extension scheme is illustrated in Fig. 2b where any data point with a value greater than or equal to 4 and less than 12 can be represented by a pair of two possible constellation points.
- The authors objective is to obtain an optimal representation of the data points by either the exterior or the extended points such that the PAPR of the OFDM symbol X is minimized.
- For this reason, a reasonable suboptimal solution to the PAPRreduction problem in (3) can be obtained by solving the problem in (6).

### B. Algorithm Based on Coordinate Descent Optimization

- The idea of CDO [8] can be applied to reduce the value of f(s) iteratively where only one element of the sign vector s is allowed to switch in each iteration.
- Since the value of f(s) is monotonically reduced in each iteration, the CDO technique can be applied to enhance the performance of the MCP algorithms proposed in Secs. III.A and B.

### C. Combination of the Proposed and the SLM Algorithms

- In the proposed algorithms only one data set has been utilized for PAPR reduction.
- The performance can be improved by combining the proposed algorithms with the SLM algorithm, as illustrated in Fig.
- First, multiple candidate data sets are generated at the transmitter.
- Second, for each of the data sets the proposed MCP algorithm is applied and the one with the least PAPR is selected.
- Third, the selective rotation (SR) [5] and CDO algorithms are applied to the data set selected in the second stage for further PAPR reduction.

### D. Computational Complexity Analysis

- Note that compared with the scheme in Fig. 2c, the scheme in Fig. 2b requires fewer extended points for PAPR reduction.
- Statistically, the number of variables in (6) associated with the scheme in Fig. 2b is two thirds that associated with the scheme in Fig. 2c.
- Since the computation complexity of the MCP and CDO algorithms is propotional to the number of variables in problem (6), the computation required by the algorithms using the scheme in Fig. 2b is only about two thirds that required by the algorithms using the scheme in Fig. 2c.

### IV. SIMULATIONS

- The proposed algorithms were applied to an OFDM system with 64 subcarriers and the performance was evaluated and compared with that of the algorithms proposed in [4][5].
- In order to approximate the analog signal accurately, oversampling was applied as in [5].
- Applying the proposed algorithms to the extended constellations in Fig. 2b and 2c, the clipping probabilities versus various power threshold values are plotted as the solid and dash curves in Fig. 4, respectively, also known as Example.
- Second, it can be observed from Fig. 5 that the performance can be further improved by combining the proposed algorithms with the SLM algorithm.
- The CPU time required by the former scheme is only about two thirds that required by the latter one.

### V. CONCLUSIONS

- Two new algorithms for PAPR reduction based on a new constellation extension scheme have been proposed.
- Simulations have demonstrated that the proposed algorithms outperform the SLM algorithm in [4] in terms of PAPR reduction and the algorithm in [5] in terms of computational complexity.

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##### References

8,781 citations

### "Peak-to-average power-ratio reducti..." refers methods in this paper

...The minimax optimization problem in (6) is an integer programming problem which can be solved by using the MCP along with the pessimistic estimator reported in [6][7] or by using the CDO reported in [8]....

[...]

485 citations

### "Peak-to-average power-ratio reducti..." refers methods in this paper

...PAPR-REDUCTION ALGORITHMS The minimax optimization problem in (6) is an integer programming problem which can be solved by using the MCP along with the pessimistic estimator reported in [6][7] or by using the CDO reported in [8]....

[...]

...Two new algorithms are then developed by applying the so-called method of conditional probablity (MCP) [6]-[7] and coordinate descent optimization (CDO) [8], which can be used to find the optimal representation of the OFDM signal....

[...]

301 citations

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289 citations