3.1 Channel Estimation
3.1.1 Proposed Scheme #1
Guard interval of OFDM system is a cyclic extension of the symbol, repetition of tail part of the symbol so equalization can be achieved easily in frequency domain.
Well, where is the circular prefix during DSSS preamble?
If we do not considering the length of FFT window, two successive identical spreading sequences can meet our requirements; that is, the former is regarded as the circular prefix of the latter. Notice that the length of spreading code in this case is equivalent to the length of circular prefix, the maximum delay this format can suffer.
Figure 3.1 illustrates that though spreading sequences are linear convolved with multipath, we can conduct the latter sequence as circular convolved with multipath under condition of two successive identical spreading sequences,
FFT Window 1
Sk− Sk Sk
( )
h t
Figure 3.1 2 successive identical symbol lead to circular property
, where Si is some spreading sequence, Sk is the same with the previous Sk−1, and the curved arrow represents multipath effect h t
( )
. Hence, if the maximum delay of does not exceed the length of spreading code, the multipath channel frequency response, where Yi
( )
ω is received signals that is the results of transmitted signal convolved with multipath effect, and Si( )
ω is the frequency response of spreading sequence . Generally, in order to ensure detecting of packet and estimation of unideal factors, the modulation during preamble is usually simpler than that in data frame and, in other words, is with longer distance between code sets than modulation of data. As a result, this situation can occur frequently and easily during preamble of common DSSS system, and an estimation scheme can thus be developed based on such a simple concept.Si
There are still two improvements in algorithm itself: noise suppression of noise and enhancement of tolerance of multipath maximum delay. According to equation (3.2)
( ) ( ) ( )
PN( ) ( ) ( )
PN(
y t =x t ⊗h t ⊗S − =t h t ⊗⎡⎣x t ⊗S −t
)
⎤⎦ (3.2), we can employ the technique on transmitted signal as well as on correlation output with PN code, x t
( )
⊗SPN(
−t)
, to obtain channel frequency response. This concept is similar to the use of spreading sequence to raise SNR; that is, to reduce noise relatively. For limitation of multipath length, unlike initial consideration of one symbol as circular prefix, two or more symbols are taken into account, and the criterion depends on the specifications of platforms, standard requirements, or environments.Finally, a general process chart is carried out as following Figure 3.2.
2/more symbol of
Figure 3.2 consideration of multiple symbols
For example of IEEE 802.15.4 [12], the preamble field is composed of 32 binary zeroes, and each 4 zeroes of them will be spread by only one 32-chips long PN sequence. If the length of FFT window is 32, merely one spreading sequence will be included and if it is 64, two is consider. And with increase of FFT window, the tolerance of multipath maximum delay and the precision of estimation are stronger and sharper also.
This concept is actually simple, but it is restricted by defined preamble format, and it seems to have some difficulty in our choice, IEEE 802.11g ERP-DSSS mode.
The resources in proposed receiver for channel estimation are 64-point FFT that is equipped for OFDM system and 11-chips Barker sequence as the PN code for DSSS system. The number of FFT points decides the FFT window; the length of PN code, that of circular prefix. Under these constraints, the only problem is that the length of FFT is not multiple of the length of Barker sequence, and one (11 ) or two ( ) chips of the last symbol in FFT window must be cut off so the condition of circular prefix can no longer be achieved easily. However, because the characteristics of Barker codes are almost mutual irrelevant except totally matching between received signals and prepared barker correlator, the correlation output will be stable excluding the occurrence of correlation peak, seeing Figure 3.3.
3 32 1
× − =
11 6 64× − =2
stable parts
Figure 3.3 features of correlation over 11M Hz
Even though some correlation chips has to be cut, the remaining of stable parts resemble the stable parts in front of referenced FFT window, and those chips can still result in “pseudo” circular property. As a result, channel estimation has no need to adopt additional IFFT because of adaptive algorithms and can be accomplished by equation (3.1) again even if the preamble of 802.11g ERP-DSSS/CCK mode has no prepared format for frequency domain operation. The numbers of cut-off chips are one for 32-point FFT window and two for 64-point FFT window, so the length of pseudo circular prefix is consequently nine for 32-point FFT and eight for 64-point FFT (only stable parts, 10 chips, are able to produce circular condition).
Estimation condition mentioned above is illustrated in Figure 3.4, and Figure 3.5 is data flow of scheme #1 combined with OFDM equalization, which the intersection of yellow block and green block stands for sharing parts. Figure 3.6 is the estimation result under a randomly generated IEEE multipath model with RMS delay 100 ns and SNR 7 dB by means of 64-point FFT. Note that the sampling rate is 11M Hz per second, i.e. sample time, T , is 90.9 ns and so multipath model does. Proposed s scheme #1 endures at most nine chips long multipath fading. Clearly, the first eight estimated multipath impulse responses almost reach the ideal ones to some extent in Figure 3.6. Though maximum delay of multipath model we used exceeds what scheme #1 can bear, the excess multipath tails influence so slightly that estimation errors of excess parts are still small enough. The estimation result will also be supported by simulation result in chapter 4 with proposed equalization and demapper.
Buffer
Pre-stored Pattern FFT M U X
peak trigger CMP
Timing & Operation Mode Control Frequency Response of Buffer Multiplier Point-by-point Frequency Response of Pre-stored Pattern
Match filter OFDM signal Frequency Response of Pre-stored Long Preamble
Pattern Recognition CFR
sequential samples at 11 MHz/sec ERP-DSSS/CCK ERP-OFDM
Figure 3.5 data flow of proposed scheme #1 channel estimation combined with OFDM channel estimation
Figure 3.6 estimation result of scheme #1 and ideal CIR over 11M Hz
However, regarding the large excess delays of the JTC channels and multipath spacings shorter than sample time, such method operating at symbol rate is not feasible since the resolution is too low to react the channel impulse response. In contrast to the symbol rate estimator, a fractionally-spaced process is based on sampling the incoming signal at least as fast as the Nyquist rate. In facts, most equalizers that have outstanding performance are with at least s2
T -spacing or even smaller spacing, and it means 22 MHz or higher sampling rate is needed in our design. New problem appears. Figure 3.7 is correlation cases with 22 MHz sampling.
Unlike Figure 3.3, it has a sub-peak at last and it explains why the same technique no longer works at 22 MHz. After cutting off in FFT window, the sub-peak will be taken away, but the correlation chips originally regarded as pseudo cyclic prefix still keep the sub-peak. When operating rate of estimator is increased to 22 MHz, the correlation property originally used to produce pseudo circular condition over Barker code sampled at 11 MHz is destroyed over Barker code sampled at 22 MHz. How large the estimation error would consequently be is shown in Figure 3.8, and the influence will also be proven by simulation results. For higher sampling rate, it seems that we need a more robust, accurate estimation scheme.
Figure 3.7 features of correlation over 22M Hz
Figure 3.8 estimation result of scheme #1 and ideal CIR over 22M Hz