The receiver working flow is described in Figure 3.4. Synchronization should be done before the rest work like channel estimation and data demodulation. Here, we consider three steps to complete the initialization of the receiver: (i) code acquisition is used to find packet start time and search all delayed path caused by multipath effect; (ii) code tracking can combat the asynchronous between transmitter and receiver due to the sampling clock error; (iii) automatic frequency control (AFC)
loop is the solution to estimate frequency offset caused by the mismatch of radio frequency (RF) component. The overall proposed receiver architecture is shown in Figure 3.5.
3.2.1 Code Acquisition
Code acquisition is usually achieved a coarse alignment within some fraction of one code-chip interval between two PN codes. Because it is the first synchronization algorithm, the rest of the synchronization process is dependent on good packet detection performed. Fortunately, the preamble of the DS-UWB system has been designed to help the detection of the start edge of the packet. The cross-correlation method takes advantage of the periodicity of the synchronization at the start of the preamble. As shown in Figure 3.6, the matched filter with the coefficient of the preamble sequence is proposed to correlate the received symbols. The preamble sequence is pre-assigned by the piconet channel of MAC layer. When some threshold of correlation is exceeded by the output power of the post-matched filter, the receiver will declare a packet detection.
3.2.2 Code Tracking Loop
Due to the sampling clock error as shown in Figure 3.7, the sampling clock error will cause slow packet shift during the transmission. In conventional DS system, Early-late (EL) code tracking loop is usually used to maintain this asynchronous [25].
Assume the IEEE 802.15.3a DS-UWB transmitter sends known preamble sequence { }a . These data symbols are spread by the spreading factor Nn c (Nc =24) using the effective spreading sequence { }c which is called PAC. The transmitted signal is v
given by
( ) 1 ( )
where g(t) is the pulse shaping defined in [9], Tc is the chip duration. After the transmitted signal travels through the multipath channel defined in (3.8), the received signal can be described by
( ) 1 i 1
( )
( )where n(t) represents the additive white Gaussian noise (AWGN) filtered by the receiver pulse matched filter, Rg(t) is the combined transmit and receive filter pulse form at the output of the matched filter which is given by
( ) *( ) ( )
R tg ∞g τ g t τ τd
=
∫
−∞ + (3.11)The conventional EL code tracking loop is shown in Figure 3.7. Output of EL timing error detector is given by
i
The timing error detector (TED) operates on two classes of samples of the matched filter output: one taken early and one taken late with respect to the detection path as shown in Figure 3.8. For a good compromise between implementation complexity and performance, the early and late branches are usually spaced half a chip apart (Tc/2) from the detection branch. In the case of no timing error, everything is apparently balanced, hence resulting on average in no signal at the output of the timing error detector at all. In the case where the signal is delayed by Tc/2, the late branch is perfectly aligned and therefore delivers a large positive output. The output of the overall timing error detector is calculated as the difference between late and early branch outputs. In the aforementioned case, this causes a
positive value at the TED output while the input signal with positive delays. In the case of negative delays with respect to the receiver time base, the output becomes negative.
If we assume a flat fading channel (L=1) case with normalized channel coefficient (α =i2 1), the mean output of the timing error detector is
[ ] Re
{
[ 2]i2 g(
c 2)
g(
c 2) }
E x = E a α ⎡⎢⎣R T + −τ τ −R −T + −τ τ ⎤⎥⎦ (3.13)
If the environment is multipath fading channel, the mean output of the timing error detector will become
[ ] i i
( ) ( )
The multipath interference terms will cause error to the output of timing error detector. Especially when the multipath is closely to the desired path as illustrated in Figure 3.9, the accuracy of the TED will be affected deeply. Unfortunately, one important characteristic of indoor UWB channel is dense multipaths due to the extreme high bandwidth which can resolve several multipath components. Therefore a new code tracking scheme should be provided to cancel the multipath interference.
According to [26], it is achievable to calculate the fading coefficients and relative delays of the multipath interference, hence the interference terms are possible to be canceled. The new code tracking loop with multipath cancellation scheme is shown in Figure 3.10, after the multipath interference being canceled, the timing error signal will be given by
l* 1 l ( ) lth path. The scheme is not limited by any assumptions made on the minimum spacing of paths. Therefore, it is able to track closely spaced paths well to and below one chip apart. The paths are tracked individually and the tracker will follow each of them correctly if they eventually diverge again. This technique proposed in [26] is not limited by the fact that it has to focus to the stronger paths, as often supposed in heuristic solutions for dealing with this type of scenarios. But under indoor UWB environment, the closed multipaths are rich; this will cause the cancellation mechanism to be too complex. Hence we propose a new multipath interference cancellation scheme computes neighboring interference only. As shown in Figure 3.9, the interference can be calculated by the peak value of the neighboring with a scale. The scale value can be obtained due to the known transmitted pulse waveform. Hence the proposed code tracking loop with multipath cancellation scheme shown in Figure 3.11 is less complex compared with the technique proposed in [26].
3.2.3 Automatic Frequency Control Loop
Because of the mismatch of the RF component between transmitter and receiver, the received signal will suffer phase rotation caused by the frequency offset. The received signal at baseband after sampling which is given by
2 s
j fnT
n n
r =s e− π∆ (3.16)
where sn is the transmitted signal, ∆f is the difference between the transmitter and
receiver carrier frequencies, Ts is the sampling period. In DS-UWB system, the proposed preamble can help receiver to use efficient maximum likelihood algorithm to estimate and correct for the frequency offset, before the actual information portion of the packet starts.
The proposed automatic frequency control loop [27] which operates on the received is shown in Figure 3.12. The complex conjugate of the received data delayed by NTs will become
This gives an angle proportional to the frequency offset, and the frequency offset estimator is formed as
ˆ 1
2 s
f z
πNT
∆ = ( (3.19)