^{1}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

A novel peak-to-average power ratio (PAPR) reduction technique for orthogonal frequency division multiplexing (OFDM) systems is addressed. Instead of using dedicated pilots for PAPR reduction as with tone reservation (TR) method selected by the DVB-T2 standard, we propose to use existing pilots used for channel estimation. In this way, we avoid the use of reserved tone pilots and then improve the spectral efficiency of the system. In order to allow their recovery at the receiver, these pilots have to follow particular laws which permit their blind detection and avoid sending side information. In this work, we propose and investigate a multiplicative law operating in discrete frequency domain. The operation in discrete domain aims at reducing degradation due to detection and estimation error in continuous domain. Simulation results are performed using the new DVB-T2 standard parameters. Its performance is compared to the DVB-T2 PAPR gradient algorithm and to the second-order cone programming (SOCP) competitive technique proposed in the literature. We show that the proposed technique is efficient in terms of PAPR reduction value and of spectral efficiency while the channel estimation performance is maintained.

orthogonal frequency division multiplexing (OFDM) technology has been the subject of numerous dissertations in recent years, mainly due to its several advantages for mobile wireless communications. It has been adopted in several systems mainly in digital video broadcasting (DVB) standards [

However, a main drawback of OFDM technique is the high peak-to-average power ratio (PAPR) of the transmitted signal. High PAPR value implies sophisticated and, thus, expensive radio transmitters with high-power amplifiers (HPAs) operating on a very large linear range at the transmitter side. Moreover, the nonlinearity of the HPA leads to in-band distortion, which increases the bit error rate (BER) of the system, and to out-of-band (OOB) distortion, which introduces high adjacent channel interference.

Various approaches have been proposed as summarized in [

Some methods recently proposed do not need this SI transmission [

With the limitations of ACE technique for rotated constellation schemes and those of TR by spectral efficiency loss, an innovative technique which could be implemented for rotated constellation and without efficiency loss is clearly needed. In this paper, we adopt, as in [

The proposition of this work is multifold. First, instead of using dedicated pilots for PAPR reduction, we expend the idea of [

The remainder of this paper is organized as follows. Section

Let

In this study, the PAPR performance is evaluated using the complementary cumulative distribution function (CCDF). It is defined by the probability that the PAPR value exceeds a given threshold

In an OFDM0-based system (like DVB standards), the main idea of the TR technique is to use reserved pilots in order to reduce the PAPR value at the input of the power amplifier of the time domain transmitted signal.

Let us consider

Pilots insertion scheme.

The OFDM baseband signal in time domain, after pilot insertion, becomes

The added that signal

The PAPR reduction problem can be formulated as follows: reducing PAPR value leads to the minimization of the maximum peak value of the combined signal

Equation (

Since the set

This method, adopted in DVB-T2 standard, is a suboptimal solution of the SOCP method. It is based on the gradient iterative method using the clipping process. In order to apply this technique, the technical specifications of DVB-T2 allowed 1% of active subcarriers for PAPR reduction issues. The pilots signal used for PAPR, defined as a reference kernel signal, is given by

For each iteration, the peak position

Principle of peak suppression by reference kernel signal.

The procedure of the PAPR reduction algorithm is given as follows.

the initial values for peak reduction signal in time domain are set to zero:

find the maximum magnitude of

if

if

terminate the iteration. The transmitted signal is obtained by:

The overall process of the gradient iterative-based method is summarized in Figure

Principle of gradient iterative algorithm proposed in DVB-T2.

The conventional TR method uses dedicated pilots for PAPR reduction issue leading to a spectral efficiency loss. In this proposition, we use some of the scattered pilots dedicated to channel estimation for both PAPR reduction and channel estimation purposes. The main problem turns out then to find the pilot symbols at the transmitter which minimizes the PAPR value but also to find these pilot symbols at the receiver in order to achieve channel estimation.

That is, in order to achieve both operations, that is, PAPR reduction and channel estimation, the set

General principle of the proposed method.

The choice of

Multiplicative law scheme.

In order to describe the channel estimation scheme and pilots recovery, frequency nonselective fading per subcarrier and time invariance during one OFDM symbol are assumed. Furthermore, the absence of intersymbol interference and intercarrier interference is guaranteed by the use of a guard interval longer than the maximum excess delay of the impulse response of the channel. In conventional OFDM schemes and under these assumptions, the received signal at the output of the FFT operation could be written as

In conventional OFDM systems, the channel estimation is done by estimating the pilot channel coefficients

Conventional channel estimation scheme in OFDM systems.

Modified channel estimation scheme.

In order to accomplish the first step, we assume that the channel is almost constant between two successive OFDM symbols, that is, we assume that

estimation and decision of

estimation and decision of

In the appendix, these probabilities are calculated in the case of AWGN channel. We obtain

The estimation and detection of

Simulation results are performed using DVB-T2 parameters. Some of the main parameters are summarized in Table

Simulation parameters, extracted from DVB-T2 standard.

Mode (OFDM size) | 2 K |
---|---|

Number of subcarriers | |

Guard interval length | |

Modulation | 16-QAM, 64-QAM |

Coding rate | |

Oversampling factor | |

Number of subcarriers used for PAPR reduction |

Let us consider SOCP solution with a number of pilot tones

CCDF performance of multiplicative law using SOCP solution, continuous

Figure

We consider now the multiplicative law with

CCDF performance of multiplicative law in discrete domain, 16-QAM,

In Figure ^{-3}. It is also compared with the SOCP solution for multiplicative law (

PAPR gain at a CCDF = 10^{-3} as a function of

Now, considering a discrete ^{-3} and when ^{-3}, the performance in terms of PAPR when

CCDF comparison in two cases:

In terms of complexity, the discrete solution is less complex than the SOCP solution (optimal solution). Indeed, our proposed PAPR reduction technique aims at searching the optimal solution in terms of

In [

Finally, the performance in terms of PAPR gain is presented in Figure

CCDF performance as a function of

First of all, one of the main advantages of this technique is that it could be used with rotated constellation schemes of DVB-T2 standard. This is not the case for ACE technique adopted in DVB-T2, where there is a restriction on rotated constellations. On the other hand, when the pilots are boosted by a factor

PAPR effective gain.

We evaluate in Figure

PAPR effective gain: comparison between proposed and DVB-T2 TR techniques, 16-QAM.

We also note that the optimal boost factor decreases when the number

PAPR effective gain: comparison between proposed and DVB-T2 TR techniques, 64-QAM.

The goal of this section is to show how the system performance is affected by the use of dedicated channel estimation for both PAPR reduction and channel estimation issues.

In order to give more insights about the proposed technique, the error detection probability (EDP) of a sequence used for PAPR and channel estimation is first evaluated. Then, the mean square error (MSE) of channel estimation is performed with respect to the signal to noise ratio (SNR) of the system. The simulation results obtained hereafter are achieved at the output of the Wiener filter. The latter is a 1D filter applied in the frequency domain only. An improvement of the results could be obtained by filtering in 2D, that is, frequency and time domain.

First, we verify the analytical performance evaluated in expressions (

Analytical and simulated error detection probability.

Figure

Error detection probability as a function of elementary steps.

Figure ^{-7} at the output of the channel decoder is equal to 6.2 dB at a coding rate

MSE of channel coefficients estimation, 2 K mode, 16-QAM modulation, and F1 channel [

We also evaluate the bit error rate (BER) of the overall DVB-T2 system. The F1 channel coefficients are estimated through dedicated pilots and then by applying a 2D Wiener filtering. Figure

BER performance, 2 K mode, 16-QAM modulation, and F1 channel.

Now, we consider a time-varying TU6 channel model given in [

BER performance, 2 K mode, 16-QAM modulation, and TU6 channel.

Based on the conclusions given in previous sections, this section summarizes optimal parameters and the corresponding PAPR effective gains using the proposed technique. The different results previously presented have been obtained in the 2 k mode. The same analysis has been done in the 8 k mode. Tables

Optimal parameters using the proposed technique, 2 K mode.

Modulation | Number of pilots: PP2 | Elementary steps of | PAPR effective gain | ||
---|---|---|---|---|---|

16-QAM | 143 | 32 | 5 dB | 1.49 dB | |

143 | DVB-T2 ( | 1.19 dB | |||

64-QAM | 143 | 32 | 7 dB | 1.80 dB | |

143 | DVB-T2 ( | 1.16 dB |

Optimal parameters using the proposed technique, 8 K mode.

Modulation | Number of pilots: PP2 | Elementary steps of | PAPR effective gain | ||
---|---|---|---|---|---|

16-QAM | 569 | 128 | 5 dB | 1.47 dB | |

569 | DVB-T2 ( | 1.39 dB | |||

64-QAM | 569 | 128 | 5 dB | 1.48 dB | |

569 | DVB-T2 ( | 1.38 dB |

A novel PAPR reduction method based on channel estimation pilots is addressed in this paper. By using channel estimation pilots to reduce PAPR value, dedicated pilots for PAPR reduction purpose are avoided improving the spectral efficiency of the system. These pilots have to be related by a particular law in order to allow their detection at the receiver side. Multiplicative law in discrete frequency domain is then investigated. Simulations, using the new DVB-T2 standard chain, showed that with appropriate parameters, the proposed method can achieve up to 1.80 dB in terms of PAPR effective gain. In comparison with the gradient-based method initially proposed in DVB-T2, the proposed method presents better performance in terms of PAPR reduction while avoiding the use of dedicated pilots. As a consequence, it allows achieving 1% of spectral efficiency gain. At the receiver side, only a slight modification is required. Simulations have shown that no degradation is caused by this additional function. The obtained results demonstrate the relevance of this method for future broadcasting of OFDM-based systems.

This section aims to compute the error detection probability of the pilot sequence. It involves the computation of the error detection probability of Δ and

From (

Equation (

Let

According to Property

Let

According to Property

Assuming

Let

To compute the error detection probability of

The authors would like to thank the CELTIC ENGINES project for its support of this work.