Although the FIRP OFDM signal can reduce PAPR significantly, it suffers from the BER degra-dation incurred by its high frequency selectivity. As a result, in order to limit the frequency selec-tivity, an all-pass filter pre-filtering(APFP) method, with unit magnitude response, is exploited.
Since all-pass filter does not change the magnitude of a channel, the frequency selectivity in-creasing problem faced by FIRP can be totaly prevented.
It is notable that the APFP method is analogous to the SLM method, for they both change only the phases of input symbol vectors in frequency domain. However, as presented in the
chapter 3, additional bandwidth is sacrificed for the transmission of the phase sequence index in the SLM method, whereas the APFP method, which uses the pilot to estimate the effective channel, needs not the transmission of the phase sequence index. Besides, the complexity of the APFP method is lower than IFFT. Therefore, using the APFP method may be a good solution in both complexity reduction and frequency selective mitigation in the FIRP method.
In the following, we review the transfer function and the corresponding impulse response of a first-order all-pass filter. The transfer function of a firs-order all-pass filter is written as
H(z) = z−1− z∗0 where u[n] is an unit step function.
In the previous section, the information of effective channel length is needed at receiver.
However, when using all-pass filter, the effective channel is an infinite impulse response(IIR) filter and its effective channel length is, strictly speaking, unlimited. Fortunately, from (4.7), it is observed that most energy is concentrated in the most few preceding taps, and the effect of other taps can be neglected. However, as different z0s will produce different effective channel length, the effective channel length might have a wide range. Hence, it is difficult to apply time-domain channel estimation described in section 4.4. This problem can be easily solved by using frequency-domain channel estimation to replace time-domain channel estimation. In other words, the channel frequency response can be interpolated from pilot subcarriers.
On the other hands, in order to use time domain channel estimation and use the same number of pilot subcarriers as the FIRP method, we constrain the amplitude of z0 between 0.01 and 0.5.
1The constraint is made so that the system is causal and stable.
By this way, the most energy of all pass filter will concentrate on the forward taps, so using the time domain cahnnel estimation will not cause serious mistake.
4.6 Simulation results
The simulation parameters are listed in Table 4.1.
Table 4.1: Simulation parameters
In Fig.4.5, the PAPR reduction performance of different taps FIRP OFDM signals and APFP OFDM signals is presented. In addition, it is also compared to the tone reservation(TR) method [6]. The TR method is formulated as convex optimization problem in Appendix A ac-cording to reference [6]. We just use matlab software to solve the complex optimization problem.
Although the APFP method can suppress frequency selectivity, the PAPR reduction performance is inferior to the FIRP method. There is a tradeoff between the PAPR reduction performance
and the BER degradation. Moreover, the PAPR reduction performance of the FIRP method and the APFP method are both superior to the TR method.
In Fig.4.6-Fig.4.7, we compare the BER performance of Lf = 3 taps FIRP OFDM signal with and without channel coding. Without channel coding, the BER degradation of the FIRP OFDM signal approximates to 8dB. Remarkably, with channel coding, the BER degradation of the FIRP OFDM signal shrinks from 8dB to 2.7dB. The BER penalty is severe in the FIRP OFDM signals. It is apparent that the BER distortion of the FIRP OFDM signal can be lightened with channel coding.
In Fig.4.8, the BER performance of the APFP method, which uses different pilot num-ber to estimate the effective channel in frequency domain, is presented. It is intuitive that the channel estimation becomes more precise when more pilot subcarriers are used to interpolate the effective channel. Therefore, the BER performance of the APFP method will be improved when more pilot subcarriers are used.
In Fig.4.9, we compare the BER performance of the AFPF and FIRP method. In the APFP method, the amplitude of z0is constrained between 0.01 and 0.5. In the FIRP method, the filter number is 3. The pilot subcarriers in both methods are the same. It is obvious that the APFP method has better BER performance compared to the FIRP method due to the usage of all pass filters.
Figure 4.4: 802.11n Physical model B:Power delay profile.
Figure 4.5: The PAPR reduction behavior of the FIRP and the APFP method as compared with the TR method.
Figure 4.6: BER performance of the FIRP method without channel coding.
Figure 4.7: BER performance of the FIRP method with channel coding.
Figure 4.8: BER performance of the APFP method.
Figure 4.9: BER performance of the APFP method compared with the FIRP(taps=3) method.
CHAPTER
5
The clipped OFDM with CDMA side information
5.1 Motivation
Clipping is a simple method to reduced the PAPR of OFDM signal. However, because clipping is a nonlinear process, it has two main drawbacks. First, clipping generates self interference by distorting signal amplitude which increases the BER. Second, it also gives rise to re-growth of the high frequency components.
The basic idea of this method is that we use the CDMA signals to transmit the clipped signals. However, because the clipped signals are directly transmitted by CDMA without any modulation scheme used, the demodulation of the clipped signals will be interfered. With the increase of the clipped signals, the interference to each demodulated clipped signal will be con-siderable. As another point of view, the BER performance of the proposed method may be
infe-rior to the clipping method if the number of clipped signals is not small enough or the clipping level is not low enough. Thus, in order to highlight the performance of the proposed method, we deal with the special case that few peaks of OFDM signals with high PAPR are clipped. Then, CDMA signals are utilized to transmit the lost information caused by clipping. At receiver, af-ter detecting the clipped peaks, the clipped OFDM signal can be restored within an acceptable distortion range.
Because a portion power of OFDM is used to transmit the clipped signals by CDMA, we expect that the OFDM signal will have some BER distortion. Even though the clipped signals can be reconstructed perfectly, the BER degradation is still unavoidable. Thus, we have to find a “suitable” power ratio that the clipped signals can be reconstructed as perfect as possible and the power loss of OFDM can be minimized.
5.2 System model
We assume that an OFDM signal has M peaks clipped. A PN code with a choosen phase is used to transmit the M clipped signals. The code length is equal to FFT size. Then, the different sampling time of an OFDM signal can be represented by different phase code. In Fig.5.1, the transmitted signal can be expressed as
x = GFHd− Gϵ + αG
∑M i=1
˜cis˜i (5.1)
where G is the operation of adding CP, ˜s1· · · ˜sM are the clipped signals, ˜c1· · · ˜cM are different phase PN codes to carry the clipped time index, α is a coefficient to adjust the power ratio between OFDM and CDMA signal, ϵ is the clipped signal vector of OFDM, ˜s1· · · ˜sM are the nonzero elements in ϵ.
Figure 5.1: Block diagram of clipped OFDM and CDMA transmitter.
The clipping ratio [8] is defined as
CR = A
σ (5.2)
where A is a clipping level and σ is the rms of an OFDM signal.
The received signal y can be represented as y = Hx + n
= HGFHd + αHG
∑M i=1
˜cis˜i− HGϵ + n