Keywords

1 Introduction

As we all know, the RF channel is the time-varying and disperse channel, and it has the selective fading of time frequency and space. The occupied bandwidth in the communication of shortwave is mainly limited to the 3 kHz till now. It is difficult to raise the bandwidth and data rate because of the high complexity of time-domain equalizer. The technology of frequency domain equalization is proposed to resolve this problem owing to its low calculation of the SC system in a large degree [1]. SC-FDE has a advantage of reduced peak-to-average ratio requirements (PARR) and low sensitive to the freq offset compared to OFDM. The paper does a research on the SC-FDE based on the MATLAB simulator [2].

2 Sc-Fde

2.1 The Principle and Structure

SC-FDE and OFDM are closed in the system structure, and both have the similar means of signal processing that in each of these frequency domain systems. Figure 19.1 gives the system flow of SC-FDE, and the concrete digital signal processing is described as follows: the sending part first adopts technology of bit-to-symbol mapping of QPSK, then adding unique words (UW) to data framing, at last data frames are sent through the channel to transmit after shaped filtering. At the receiving part, the UW in each data block is used to estimate the characteristics of the channel and get the equalizing coefficients. To the data received, processing of FFT is used to get the frequency characteristics. The equalizing coefficients are multiplied by the corresponding data in the sub channels, then the data is converted to time domain by the IFFT module and UW is removed. At last the demapping and decision module realize the function of demapping and decision.

Fig. 19.1
figure 1

The flow of the SC-FDE

Full size image

At last the output symbols of the demapping and decision module in time domain become:

$$ z_{n} = \frac{1}{N}\sum\limits_{k = 0}^{N - 1} {W_{k} Y_{k} H} e^{{j\frac{2\pi }{N}kn}} + \frac{1}{N}\sum\limits_{k = 0}^{N} {W_{k} V_{k} } e^{{j\frac{2\pi }{N}kn}} $$
(19.1)

2.2 Frequency Domain

The precondition of adopting the FDE is the data block transmission by adding UW to realize the conversion from linear convolution to cycle convolution. Meanwhile the Channel characteristic is known. The process is that the equalizer produces the inverse characteristics to offset the function of the channel, so it can resist the ISI caused by RF channel. Also we can consider it that the equalizer is used to convergent the extended energy of symbol transmitting to its own time slot. It is equal to invert a filter to make it with the sub-channel to have characteristics of banner and liner phase [3]. Figure 19.2 shows the flow of FDE, in which y(k) are symbols received and Y(k) are the in the frequency domain. Z(k) are the multiplication of Y(k) and W(k), and Z(k) are z(k) by FFT.

Fig. 19.2
figure 2

The flow of FDE

Full size image

The technology of FDE contains liner equalization and nonlinear equalization, and it is divided by the structure of equalizer, that is whether the output is used for feedback. Liner equalization includes zero forcing ZF and MMSE, while nonlinear equalization is mainly the decision feedback equalization with the shortcoming of error propagation. This paper simulates the SC-FDE adopting the liner equalization including ZF and MMSE. The equalizing coefficients with ZF are:

$$ W(z) = \frac{1}{H(z)},(k = 0,1 \ldots n - 1) $$
(19.2)

And using MMSE is:

$$ W(k) = \frac{{H^{*} (k)\sigma_{S}^{2} }}{{|H(k)|^{2} \sigma_{S}^{2} + \sigma_{N}^{2} }} = \frac{{H^{*} (k)}}{{|H(k)|^{2} + \frac{{\sigma_{N}^{2} }}{{\sigma_{S}^{2} }}}} $$
(19.3)

We can conclude that from the formula, MMSE method considers the influence of noise and channel at the same time has better performance than ZF method especially in the condition of low SNR, while the ZF method has a less calculation [4].

3 Simulation of SC-FDE

3.1 Design of the Data Frame Structure

In this simulation, adopts the 2UW frame structure, shown as in the Fig. 19.3. UW at the head of data block is used as guard interval similar to the CP inverted in OFDM data blocks [5], while UW has its own feature that UW is fixed and known to the receiver so it can be conveniently used to channel estimation as the training sequences [6]. So in the 2 UW in the continuous data blocks the first one is used as guard interval and the second is used to channel estimation, so it has a better property of channel estimation. Now this frame structure is widely used in the SC-FDE and has good performance.

Fig. 19.3
figure 3

The data frame structures of SC-FDE

Full size image

On the ideal condition UW should have the feature of constant-amplitude in the frequency domain because of its function of channel estimation, so that it can produce relative stable frequency response to test the channel characteristics at frequency points. This paper adopts the Zadoff-Chu sequences [7–9] which have a outstanding of the const amplitude in time and frequency domain. This simulation uses the Zadoff-Chu sequences which are defined as follow:

$$ C(k) = \exp \left[j2\pi \frac{M}{N}\left(\frac{k(k + 1)}{2} + qk\right)\right],k = 0,1, \ldots N - 1\;\left( {\text{N is odd}} \right) $$
(19.4)
$$ C(k) = \exp \left[j2\pi \frac{M}{N}\left(\frac{{k^{2} }}{2} + qk\right)\right],k = 0,1, \ldots N - 1\;\left( {\text{N is even}} \right) $$
(19.5)

3.2 Simulation Results

This simulation adopts the data frame of 2UW under the third channel model of DRM standard. Table 19.1 gives the parameters of simulation system and Table 19.2 shows the parameters of DRM channel 2. Figure 19.4 shows the simulation results under the parameters in Table 19.1. We can see the system displays a better performance after equalization, and adopting MMSE method is also better than ZF method with the SNR increasing.

Table 19.1 The simulation parameters of SC-FDE
Full size table
Table 19.2 The parameters of DRM channel 2
Full size table
Fig. 19.4
figure 4

The simulation result of SC-FDE

Full size image

Table 19.3 shows three series of parameters of SC system, in which length of UW is fixed, while length of data block is different. Figures 19.5 and 19.6 show the error rate curves under different parameters adopting ZF method (Fig. 19.5) and MMSE method (Fig. 19.6). We can see that whether MMSE or ZF is used the performance under the first parameters is best, under parameters 3 is better and the parameters 2 the last. So it can be concluded that the shorter the data block is, the performance of system is better, and the ability to resist the time-varying feature is stronger, however the effective data rate is reduced.

Table 19.3 Three kinds of simulation parameters
Full size table
Fig. 19.5
figure 5

Simulation results with ZF method

Full size image
Fig. 19.6
figure 6

Simulation results with MMSE method

Full size image

4 Summaries

This paper describes the principle of SC-FDE and gives the methods of channel estimation and equalization. Also this paper has a study on the frame structure and displays the performance of SC system based on the 2UW frame structure under the DRM channel by MATLAB simulation tool. We can see that in the broadband RF communication, SC-FDE has a good performance to resist multiple-path effect and is paid more and more attention to by the people owing to its advantage compared to the TDE and OFDM. It can be said that SC-FDE has a broad application prospect in the broadband RF communication.