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Fast-Than-Nyquist (FTN) transmission is a promising method to improve the spectrum efficiency for future wireless communication systems. However, this benefit of FTN is at the price of inducing the inter-symbol interference (ISI), which increases the complexity of the receiver. In this paper, a circulated block transmission scheme for FTN signaling, i.e. CB-FTN system is proposed. The detail implementation structure of CB-FTN transceiver is presented, in which the ISI caused by FTN transmission is canceled by the frequency-domain equalization (FDE), and the inter-block interference (IBI) caused by the multi-path channel is overcome by the cyclic-prefix. The postprocessing signal to noise ratio (pSNR) is analyzed for the CB-FTN receiver with zero-forcing FDE in AWGN channel, which is verified by the simulation results. Moreover, the BER performances and computational complexity of CB-FTN system are compared with the existed scheme.

How to further improve the spectrum efficiency of transmission scheme is one of major issues for future wireless communication systems. Non-orthogonal transmission technologies have opened a door for the breakthrough in the above challenge. One of potential solutions is faster-than-Nyquist (FTN) signaling, which was first studied by Mazo in 1975. It was shown that by intentionally introducing inter-symbol inference (ISI), FTN signaling with sinc pulse can achieve 25% higher symbol rate than Nyquist signaling in additive white Gaussian noise (AWGN) channels [

Although the FTN signaling can improve the spectrum efficiency, the inevitable inter-symbol interference (ISI) has to be properly addressed to guarantee the error performance. Therefore, the major concern in FTN signaling is the detection algorithms [

Except the equalizer designed for the FTN receiver, some efforts are also put into designing the FTN transmission schemes [

In [

In this paper, we proposed a circulated block transmission scheme for FTN signaling, i.e. CB-FTN system. By circulated sample blocking and CP padding, the CB-FTN system can achieve higher transmission rate than that of Nyquist system and meanwhile eliminate the IBI by FDE with the estimated channel frequency response. In addition, by exploiting the circulation property of the sample block, the ISI can be canceled by FDE with the circular self-correlation function of pulse-shaping filter as well.

The continuous-time FTN signaling can be expressed as

where

Assume

By properly system parameters designing,

where L is the length of

The structure of the CBT-FTN transmitter is illustrated in

After the FTN filtering, the output signal could be expressed as

Then, by circulated blocking processing, the output signal could be given by

, (5)

where

Finally, the data block is padded with CP to form the circularly sample- blocked FTN signaling

The structure of the CB-FTN receiver is illustrated as in

circularly blocked FTN signaling

After the CP removing from the received signal

where

Assume the perfect channel estimation is achieved and zero-forcing (ZF) equalization is applied, the output of channel equalization could be expressed as

where

If ignoring the effects of AWGN, the output of circulated match-filtering becomes

Let

then

, (10)

Hence,

where

The vector form of the transmitted CB-FTN signal without the CP can be described as

where

At the receiver, after CP removing and Q-tone channel FDE, the output signal can be given as

where

After circulated match-filtering, the output signal becomes

According to (9),

Therefore, the first term of (15) can be viewed as the output of vector

If the FDE utilized to cancel the ISI, the detect metric vector of demodulated symbols can be expressed as

where

For ZF FDE, the ISI equalization matrix is

Assume

The noise components, i.e. the second term in (17) can be written as

The covariance matrix of noise vector can be expressed as

Let

and

Since

where

Therefore, we have

Then by (26), the variance of the noise can be given by

As a result, by (20) and (25), the post-processing SNR can be described as

In fact, for Nyquist transmission,

The performances of the proposed scheme are evaluated in this section. The system parameters for simulations are presented in

In order to achieve higher spectrum efficiency, the CB-FTN system stuffs more data symbols in one data block than Nyquist system, which will cause the ISI within one block inevitably. Due to the cyclic property of CB-FTN signaling, according to (9), the equivalent impulse response of the ISI caused by FTN time

Parameters | Simulation Systems | |
---|---|---|

Nyquist rate transmission | FTN rate transmission | |

Modulation scheme | QPSK | |

Type of pulse-shaping filter | RRC | |

Roll-off factor | 0.3 | |

Length of filter ( | 241 | |

Up-sampling rate ( | 20 | |

# of shift samples of shaping filtering ( | 20 | 16, 18 |

# of symbols carried by one circulated block (D) | 16 | 20 |

Length of circulated block (Q) | 320 | 320, 360 |

Time squeezing ratio ( | 1 | 0.8, 0.9 |

Spectrum efficiency (bps/Hz) | 2 | 2.5, 2.22 |

squeezing is symmetric, as shown in

In order to implement FDE with fast Fourier transform, the length of circulated block

The BER performances of CB-FTN system with turbo coding and ZF-FDE are illustrated in

of transmitters of both schemes are similar, but with different implementation structure.

As mentioned in above section, the scheme in [

512, the length of symbol-based CP/CS should be

operations are unnecessary for the CB-FTN transmitter utilizing circulated blocking operation to form the circulated sample block, which is equivalent to only 32 data symbols passed through the pulse-shaping filter.

In this paper, a circulated block transmission scheme is proposed for FTN signaling, i.e. CB-FTN system. By circulated sample blocking and CP padding, the FDE can be utilized to cancel the IBI induced by wireless multipath channel. Moreover, by exploiting the circulation property of the sample block, the ISI caused by FTN filtering, can be eliminated by FDE with the circular self-corre- lation function of pulse-shaping filter as well. The equivalent impulse response and effects of the ISI are illustrated and analyzed by simulation. The theoretical post-processing SNR are analyzed for the CB-FTN receiver with ZF FDE in AWGN channel, which is verified by the simulation results. Moreover, the BER performances of the CB-FTN system are illustrated and compared with the existed scheme. It can be found that both schemes have very close BER performances, but the former has much lower computational complexity of transmitter than the latter.

This work is supported by the International cooperation project of National Natural Science Foundation of China (No. 6146136001), and the capability improvement project of Zhangjiang Administrative Committee of Shanghai Municipality (No. 2016-14).

Li, M.Q., Lai, S.H. and Peng, Y.Q. (2017) A Circulated Block Transmission Scheme for FTN Signaling. Int. J. Communications, Network and System Sciences, 10, 269-279. https://doi.org/10.4236/ijcns.2017.108B029