01.12.2019 | Research | Ausgabe 1/2019 Open Access

# Frequency-domain subcarrier diversity receiver for discrete Hartley transform OFDM systems

## Authors’ information

## 1 Introduction

## 2 Method

^{∗}, (.)

^{T}, and (.)

^{H}denote conjugation, transposition, and conjugate transpositions, respectively. N is the number of OFDM subcarriers, which is chosen to be a power of two, while n and k are the time index and the subcarrier index, respectively. The operator E[.] denotes expectation.

## 3 System model

_{b}is the energy per bit. The data symbols are first converted into a parallel stream and then fed to the IDFT to modulate N orthogonal subcarriers. For convenience, analogously to the conventional DFT-OFDM, we will denote the input to the DHT as the time domain and the output as the frequency-domain. The output of the IDHT is the time-domain OFDM symbol \(\{x(n)\}_{n=0}^{N-1}\), where x(n) is given by

## 4 Detection

### 4.1 Observations

### 4.2 Detection scheme

^{H}H)

^{−1}H

^{H}we get

## 5 Statistical analysis

_{o}. It can be shown that the variance of \(\tilde {W}(N-k)\) is equal to the variance of \(\tilde {W}(k)\).

_{o}(·) is the 0th order Bessel function of the first kind, f

_{d}is the maximum Doppler frequency, T is the data symbol period, and \(\sigma ^{2}_{h(l)}\) is the variance of h(l). If the channel is assumed to be constant during an entire OFDM symbol then f

_{d}=0 and (29) reduces to

## 6 Performance analysis

### 6.1 Group 1

_{1}which can be shown to be equal to [27]

### 6.2 Group 2

^{2}+|β(k)|

^{2}) in (41) is chi-square distributed with 4 degrees of freedom. Define the variable λ

_{2}as

_{2}is obtained by [28]

### 6.3 Group 3

_{3}=|α(k)|

^{2}+|β(k)|

^{2}. The density function of λ

_{3}is [28, 29]

_{3}becomes

## 7 Numerical results

Parameter | Value |
---|---|

Number of subcarriers (N) | 64, 256 |

Number of OFDM symbols simulated | 4×10 ^{6} |

Modulation scheme | BPSK |

OFDM symbol duration | 20 μs |

Guard type and length | Cyclic prefix (16–64 subcarriers) |

Channel delay | [0 1500 4000] μs |

Channel gain | [0−4−8] dB |

^{−5}, and outperforms the generalized DHT-OFDM by 12 dB at an average BER of 10

^{−5}. The superior performance of the proposed system is due to the fact that rather than diagonalizing the channel matrix, the proposed system uses the coupling between subcarriers to increase the diversity gain and hence achieve better BER performance.

_{o}level [30]. It can be seen in Fig. 6 that the proposed DHT-OFDM system suffers from an approximately 5.5, 2, and 1 dB increase in PAPR when compared to the DHT-precoded OFDM, the conventional DFT-OFDM, and the generalized DHT-OFDM systems, respectively. This is a minor trade-off when considering the large gains obtained in average BER as shown in Fig. 4.

## 8 Conclusions

^{−5}. In terms of PAPR, the proposed system suffers from an approximately 5.5, 2, and 1 dB increase in PAPR when compared to the DHT-precoded OFDM, the conventional DFT-OFDM, and the generalized DHT-OFDM system, respectively. This is a minor trade-off when considering the large gains obtained in average BER.