- Research Article
- Open Access

# Blind CP-OFDM and ZP-OFDM Parameter Estimation in Frequency Selective Channels

- Vincent Le Nir
^{1}Email author, - Toon van Waterschoot
^{1}, - Marc Moonen
^{1}and - Jonathan Duplicy
^{2}

**2009**:315765

https://doi.org/10.1155/2009/315765

© Vincent Le Nir et al. 2009

**Received:**14 November 2008**Accepted:**1 June 2009**Published:**5 July 2009

## Abstract

A cognitive radio system needs accurate knowledge of the radio spectrum it operates in. Blind modulation recognition techniques have been proposed to discriminate between single-carrier and multicarrier modulations and to estimate their parameters. Some powerful techniques use autocorrelation- and cyclic autocorrelation-based features of the transmitted signal applying to OFDM signals using a Cyclic Prefix time guard interval (CP-OFDM). In this paper, we propose a blind parameter estimation technique based on a power autocorrelation feature applying to OFDM signals using a Zero Padding time guard interval (ZP-OFDM) which in particular excludes the use of the autocorrelation- and cyclic autocorrelation-based techniques. The proposed technique leads to an efficient estimation of the symbol duration and zero padding duration in frequency selective channels, and is insensitive to receiver phase and frequency offsets. Simulation results are given for WiMAX and WiMedia signals using realistic Stanford University Interim (SUI) and Ultra-Wideband (UWB) IEEE 802.15.4a channel models, respectively.

## Keywords

- Root Mean Square Deviation
- Channel Model
- Additive White Gaussian Noise
- Cyclic Prefix
- OFDM Symbol

## 1. Introduction

Spectral monitoring has received considerable attention in the context of opportunistic and cognitive radio systems. Blind modulation recognition (with no a priori information) consists in identifying the different signal components (air interfaces) that are present in an observed spectrum. A survey of algorithms currently available in literature can be found in [1]. While past studies have focused on single-carrier modulations, research has recently also focused on the identification of multicarrier modulations. On one hand, mixed moments [2] and fourth-order cumulants [3, 4] can be used to discriminate between single-carrier and multicarrier modulations and to estimate their parameters. For instance, the fourth-order cumulants of OFDM signals converge to 0 as the number of subcarriers increases independently of the Signal-to-Noise Ratio (SNR) and hence can be used to distinguish between single-carrier modulations and multicarrier modulations propagating through an Additive White Gaussian Noise (AWGN) channel. Unfortunately, mixed moments and fourth-order cumulants do not perform well for more realistic channels, that is, frequency selective channels with time and frequency offsets. On the other hand, cyclic autocorrelation-based features [5–7] have been proposed to discriminate between single-carrier and multicarrier modulations in time dispersive channels and affected by AWGN, carrier phase, and time and frequency offsets.

Moreover, a number of procedures [8–11] have been proposed using autocorrelation- and cyclic autocorrelation-based features to extract parameters for OFDM signals using a Cyclic Prefix time guard interval (CP-OFDM) and propagating through a frequency selective channel. In this paper, we review the existing techniques presented in [5–12] using autocorrelation- and cyclic autocorrelation-based features for CP-OFDM signals in frequency selective channels to determine the power, oversampling factor, useful time interval, cyclic prefix duration, number of subcarriers, and time and frequency offsets. The carrier frequency of the signal of interest is first estimated by an energy detector in the spectral domain followed by a downconversion to baseband for further analysis. Then, we propose a blind parameter estimation technique based on a power autocorrelation feature which can be operated in frequency selective channels and applied to OFDM signals using a Zero Padding time guard interval (ZP-OFDM). The zero padding, in particular, excludes the use of the autocorrelation- and cyclic autocorrelation-based techniques. The proposed technique leads to an efficient estimation of the symbol duration and zero padding duration, and it is insensitive to phase and frequency offsets.

In Section 2, we review the blind parameter estimation using features based on autocorrelation and cyclic autocorrelation for CP-OFDM signals. In Section 3, we present the blind parameter estimation using a new feature based on power autocorrelation for ZP-OFDM signals. Simulation results are given in Section 4 for WiMAX and WiMedia signals using realistic Stanford University Interim (SUI) and Ultra Wide-Band (UWB) IEEE 802.15.4a channel models respectively [13, 14].

## 2. Blind Parameter Estimation Using Features Based on Autocorrelation and Cyclic Autocorrelation

In this section, we review different algorithms used for the estimation of the carrier frequency, power, and oversampling factor of an observed signal component. Then the features based on autocorrelation and cyclic autocorrelation are presented for CP-OFDM signals to estimate the useful time interval, cyclic prefix duration, and the number of subcarriers in frequency selective channels.

### 2.1. Estimation of the Carrier Frequency

### 2.2. Estimation of the Oversampling Factor and Power Spectral Density

where is the vector of transmitted symbols, which have been oversampled by a factor , the 's are the multipath channel coefficients with the number of channel taps, is the vector of Additive White Gaussian Noise (AWGN), is the receiver phase offset, and is the receiver frequency offset.

### 2.3. Estimation of the Useful Time Interval and the CP-Length for CP-OFDM Signals

The autocorrelation function can be derived by replacing the received sequence model (3) into (9), leading to

corresponding to the search for the optimal index for which the difference between a peak (when a +− occurs) and its lowest previous point (its previous −+) is maximized. The choice of the modulus leads to an insensitivity of the autocorrelation feature to phase and frequency offsets (as the exponentials factors in (10) disappear).

Finally, time and frequency offsets can be determined using cyclostationarity properties of CP-OFDM signals with prior information on the pulse shaping filter [8] or conventional autocorrelation methods without prior knowledge on the pulse shaping filter [15].

## 3. Blind Parameter Estimation Using a Feature Based on Power Autocorrelation

## 4. Results

SUI channel models.

SUI 1 channel | |||
---|---|---|---|

Tap 1 | Tap 2 | Tap 3 | |

Delay ( s) | 0 | 0.4 | 0.9 |

Power (dB) | 0 | −15 | −20 |

factor | 4 | 0 | 0 |

Doppler (Hz) | 0.4 | 0.3 | 0.5 |

SUI 4 channel | |||

Tap 1 | Tap 2 | Tap 3 | |

Delay ( s) | 0 | 1.5 | 4 |

Power (dB) | 0 | −4 | −8 |

factor | 0 | 0 | 0 |

Doppler (Hz) | 0.2 | 0.15 | 0.25 |

OFDM signal parameters.

Parameters | WiMAX | WiMedia |
---|---|---|

Bandwidth | 10 MHz | 528 MHz |

| 256 | 128 |

Number of samples in | 64 | 37 |

| 25.6 s | 242.42 ns |

| 6.4 s | 70.07 ns |

Channels | SUI-1 4 | CM1 4 |

Nb symbols | 10 | 10 |

When using these channel models to evaluate existing modulation recognition procedures discriminating between single-carrier and multicarrier modulations based on mixed moments and fourth order cumulants [2–4], it is observed that the threshold values for the different features can vary greatly with the different channel models. Therefore, these algorithms are not suitable for the detection of an OFDM signal without a priori knowledge of the channel conditions. The detection algorithms presented in this paper, however, are not based on the search for a threshold in a particular scenario, but rather on jointly detecting/estimating OFDM parameters blindly as in [5–7, 9–11].

This characteristic can also be used for the detection of CP-OFDM signals. As the noise and the transmitted sequence are random variables which are independent and identically distributed (i.i.d), the autocorrelation function of the received sequence is 0 for . Moreover, the probability of false alarm for noise and single carrier modulations is related to the length of the window used for estimation . In our simulations, we use a received sequence (which is referred as a "block") of 3200 samples (equivalent to the number of samples for 10 CP-OFDM WiMAX symbols) and a maximum number of channel taps , giving a probability of false alarm . Consecutive blocks for noise and single carrier modulations will have a very high probability to give different estimates, while CP-OFDM signals will provide the same estimate with a very high probability. Therefore, if two consecutive blocks provide the same estimate of the useful time interval or the CP duration , we declare that a CP-OFDM signal is detected. If the consecutive blocks provide different estimates of the useful time interval or the CP duration , then the signal is declared either noise or single carrier modulation.

Estimated parameters for CP-OFDM signals using real data measurements.

Data sets | GW26 | GW24 | GW22 | GW20 | GW18 | GW16 |
---|---|---|---|---|---|---|

| 5.1 | 5.6 | 6.2 | 6.5 | 7.3 | 8.2 |

| 0.12 | 0.15 | 0.17 | 0.19 | 0.22 | 0.27 |

| 127 | 127 | 127 | 127 | 127 | 126 |

| 145.5 | 145.5 | 145.5 | 145.5 | 142.9 | 145.5 |

| 24.9 | 22.7 | 20.5 | 19.5 | 17.4 | 15.5 |

## 5. Conclusion

In this paper, we have proposed a blind parameter estimation technique based on a power autocorrelation feature applying to OFDM signals using a Zero Padding time guard interval (ZP-OFDM) which in particular excludes the use of the autocorrelation- and cyclic autocorrelation-based techniques. The proposed technique has led to an efficient estimation of the symbol duration and zero padding duration in frequency selective channels and was insensitive to receiver phase and frequency offsets. Simulation results were given for WiMAX and WiMedia signals using realistic Stanford University Interim (SUI) and Ultra-Wideband (UWB) IEEE 802.15.4a channel models, respectively. Simulation results have shown that OFDM signals without a CP (as used in WiMedia) could be detected based on their zero padding without any loss in performance compared to similar CP-OFDM parameter estimation algorithms. These techniques could be used in several applications to monitor ZP-OFDM signals and to estimate their parameters (Bluetooth 3.0, WiMedia, etc.).

## Declarations

### Acknowledgment

This research work was carried out in the frame of the European FP7 UCELLS project. The scientific responsibility is assumed by its authors.

## Authors’ Affiliations

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.