3 Intercarrier Interference (ICI) Compensation in IEEE 802.15.a
3.3 Zero Padded Prefix (ZPP) OFDM System
where the channel estimation data power have been selected to be equal to one. The noise samples N1,k and N2,k are statistically independent, thus the variance of their sum divide by two is a half of the variance of the individual noise samples.
3.3 Zero Padded Prefix (ZPP) OFDM System
Due to the IFFT precoding and the insertion of CP at the transmitter, OFDM entails redundant block transmissions and employs simple equalization of
frequency-selective finite impulse response (FIR) channels. At the receiver, intersymbol interference (ISI) and intercarrier interference (ICI) can be eliminated by discarding the CP. Unless zero, flat fades can be removed by dividing each subchannel’s output with the channel transfer function at the corresponding subcarrier. Therefore, most current wireless OFDM-based systems use a CP to eliminate the effect of multipath.
However, the same multipath robustness can be obtained by using a zero padded prefix (ZPP) instead of the CP [21]-[23]. At transmitter, zero symbols are appended after the IFFT-precoded information symbols in each block of the ZPP OFDM transmission. When the number of zero symbols equals the CP length, the ZPP OFDM system can provide the same multipath robustness as the CP OFDM system.
What we have to modify at the receiver is to collect additional samples corresponding to the length of the prefix and to use the overlap-and-add method to obtain the circular convolution structure.
Due to ZPP, the “time domain” received signal of OFDM symbol can be expressed as the length of the ZPP and use an overlap-and-add method, the received signal of
OFDM symbol can be expressed as
From Equation 3.23, we see that the ZPP OFDM system with overlap-and-add method is equivalent to the CP OFDM system, because they have the same overall transceiver transfer function. It is, thus, not surprising that they has identical property:
complexity, spectral efficiency, and multipath robustness.
Though, there are many the same characterizes between two systems. They still have some differences. The most important advantage of using a ZPP is that power backoff at the transmitter can be avoided. When a CP is used, the transmitted signal will have the structure resulting from CP. This correlation in the transmitted signal induces ripples in the average PSD. Because the FCC limits the PSD of UWB, any ripples in the PSD will lead to power back off at the transmitter. In fact, the amount of power backoff to conform to the restriction of FCC is equal to the peak-to-average ratio of the PSD. For a MB OFDM system, this power backoff will arrive at 1.5 dB, which would result in a lower overall range for the system. When the ZPP instead of the CP, the ripples in the PSD can be reduced to zero with enough averaging. The transmitted signal does not have any structure; because it is completely random.
Figures 3.8 and 3.9 indicate the ripples in the PSD for a MB OFDM system that uses a CP and ZPP. From two figures, they show that the ZPP will result in a PSD with zero ripples and a zero power backoff at the transmitter. This implies that the system will achieve the maximum range possible. In addition to the ripples in the PSD, the CP OFDM system has to spend the energy for CP, but the ZPP OFDM system does
not. However, the receiver will pick up larger noise because the ZPP OFDM system uses an overlap-and-add method to obtain the circular convolution property. This will lead to the noise enhancement as shown in Figure 3.10.
3.3.1 ZPP OFDM System Model for Long Delay
Spread Channel
Although, the channel impairment can be overcome by introducing ZPP and completely eliminated by the simple one-tap equalizer in case the length of ZPP is longer than that of the channel impulse response. However, the large bandwidth of the MB OFDM waveform (528 MHz) significantly increases the ability of the receiver to resolve the different reflections in the channel and shortens the OFDM symbol duration. These results make the length of the channel impulse response may be longer than the length of ZPP, especially for CM4 channel. Consequently, the ISI and ICI will be induced and result in performance degradation [24]-[30].
Analysis of ISI and ICI
Figure 3.11 describes the ISI and ICI are introduced in the multipath channels.
The ISI results from the portion of the previous symbol included in the current FFT window. The ICI is caused by the current symbol loss due to the long delayed paths exceed the prefix interval. The influence of ISI and ICI can be analyzed based on the above observation. The received signal can be written in the frequency domain as follows
n = * n − ICI * n + ISI * n−1+ n
Y FHF X FH F X FH F X N (3.24)
where F is a FFT matrix, then H, HICI and HISI are given as
0 2 1
where Nzp is the length of ZPP, and L is the length of the channel impulse response.
The shapes of HICI and HISI are shown in Figure 3.12. ISI is caused by the non-zero components of HISI, and the ICI results from an element loss that distorts a cyclic shift formation in HICI. According to the two relationships, the performance degradation due to ISI and ICI can be evaluated.
At first, signal-to-interference ratio (SIR) is calculated as a function of the amount of ISI and ICI. Assuming without loss of generality the ideal signal power is that of the received symbol when the length of the ZPP is longer than the channel
impulse response. Besides, according to the Specification of MB OFDM system, there are 128 subcarriers in one OFDM symbol. The ideal OFDM symbol power is defined as
where E{.} is an expectation function and x(MOD(j-i,N)) is the transmitted signal of MOD(j-i,N)th subcarrier. Then, the E{x(n)} is zero-mean with unit variance and uncorrelated because the data and channel are independent. From Figure 3.12, power of ISI and ICI are given as
However, the MB OFDM system uses the modulation technique and the multibanding approach dividing the spectrum into several sub-bands. The transmitted OFDM symbols are conveyed across all sub-bands. So the received OFDM symbols suffer only the impact of ICI.