Computer simulations are conducted to evaluate the performance of bit error rate (BER) and packet error rate (PER) in the IEEE 802.15.3a DS-UWB system. In the simulation, the relationship between SNR and Eb/N0 can be defined as
( )
the bit rate, B is the bandwidth of the chip sequence, and Nc is the processing gain.When the system transmit power is normalized to one, the noise power given by σ2corresponding to a specific Eb/N0 can be generated by
2 0
b
N
σ = E (3.22)
The numbers of equalizer tap for different situations (CM1 to CM4) are listed in Table 3.2. In the following simulations, we choose the mandatory BPSK modulation
mode operating in the low band and the best 90 out of 100 channel realizations. All of the system parameters are estimated by the algorithms mentioned in Sections 3.2 and 3.3. In the first simulation, we evaluate the DS-UWB system performance with 110 Mbps data rate. The BER and PER performances as a function of input SNR Eb/N0 are shown in Figures 3.15 and 3.16 respectively. It is observed that with sufficient equalizer taps, the BER and PER system performances decrease as Eb/N0 increase. Besides, under longer range environments like CM3 and CM4, the system performances are a little worse than that in shorter range environments due to the inaccuracy of system parameter estimation. Next, the BER and PER performances with 220 Mbps data rate are shown in Figures 3.17 and 3.18 respectively. Compared with the 110 Mbps mode, both BER and PER performances are worse due to the shorter spreading code length which will induce more serious ISI. Finally, BER and PER performances with 500 Mbps data rate are shown in Figures 3.19 and 3.20 respectively. The shorter spreading code length and higher code rate lead the system performances to be worse compared with the previous modes.
3.5 Summary
In this chapter, we first introduce the S-V model which is used to form indoor UWB channel environment. Compared with conventional narrowband channel models, the clustering phenomenon is observed in the channel. Furthermore, the dense and long delay spread multipaths will lead some receiver function blocks to be modified. All the receiver function block algorithms have been described in Sections 3.2 and 3.3. The channel characteristic of dense multipaths will cause the conventional EL code-tracking loop to fail and the proposed EL code-tracking loop with multipath cancellation scheme can effectively overcome this problem. Besides,
the channel length is different under different situations (CM1 to CM4), and we have defined different numbers of equalizer tap in Section 3.3. The performance of all algorithms mentioned in this chapter has been evaluated by Matlab. Computer simulations show that the proposed algorithms work as expected.
fc
Figure 3.1 Simulation of passband system in terms of equivalent complex baseband system
0 50 100 150 200 250 -1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Impulse response realizations
Time (nS)
Figure 3.2 Superposition of 100 impulse responses based on the CM3 channel model (NLOS up to 10 m with average RMS delay spread of 15 ns).
0 20 40 60 80 100 120 140 160 180 200 -60
-50 -40 -30 -20 -10 0
Average Power Decay Profile
Delay (nsec)
Average power (dB)
Figure 3.3 Average power decay profile for the channel model CM3 (NLOS up to 10 m with average RMS delay spread of 15 ns).
Figure 3.4 IEEE 802.15.3a DS-UWB receiver working flow
Figure 3.5 Proposed receiver architecture of IEEE 802.15.3a DS-UWB system
2
>
Figure 3.6 Code acquisition structure of IEEE 802.15.3a DS-UWB system
Loop
Figure 3.7 Conventional early-late code tracking loop architecture
Tc
Late Early
Figure 3.8 Comparison between early and late edges for the detecting path
Late Early
Tc
Figure 3.9 Comparison between early and late edges under dense multipaths environment
TED Loop Filter
x
mx
mMultipath Compensation
Unit Timing tracker 2 Timing tracker N
α
1α
2α
NFigure 3.10 Structure of cancellation mechanism for IEEE 802.15.3a DS-UWB system
x
mx
mFigure 3.11 Proposed code tracking loop with multipath cancellation scheme for IEEE 802.15.3a DS-UWB system
∑ 2 1
Figure 3.12 Proposed automatic frequency control loop architecture for IEEE 802.15.3a DS-UWB system
Figure 3.13 Decision feedback equalizer architecture
(a)
(b)
Figure 3.14 Average power decay profile for different situations (a) CM1 and CM2 (b) CM3 and CM4
Figure 3.15 BER performances of DS-UWB system with 110 Mbps data rate under different environments (CM1 to CM4)
Figure 3.16 PER performances of DS-UWB system with 110 Mbps data rate under different environments (CM1 to CM4)
Figure 3.17 BER performances of DS-UWB system with 220 Mbps data rate under different environments (CM1 to CM4)
Figure 3.18 PER performances of DS-UWB system with 220 Mbps data rate under different environments (CM1 to CM4)
Figure 3.19 BER performances of DS-UWB system with 500 Mbps data rate under different environments (CM1 to CM4)
Figure 3.20 PER performance of DS-UWB system with 500 Mbps data rate under different environments (CM1 to CM4)
Table 3.1 Multipath channel target characteristics and model parameters
Table 3.2 Equalizer tap numbers for different environments
CM 1 CM 2 CM 3 CM 4
FFF 18 40 80 120
FBF 9 20 40 60
Chapter 4
Pre-Rake Diversity Combining Technique for IEEE 802.15.3a DS-UWB System
Because of the long delay spread characteristic of UWB channel, the receiver needs an equalizer with large number taps to overcome the multipath ISI effect. This leads the complexity of receiver to increase. Hence, we will use the Pre-Rake diversity combining technique into IEEE 802.15.3a DS-UWB system to reduce the receiver complexity. The rest of this chapter is organized as follows. Pre-Rake diversity combining concepts will be introduced in Section 4.1. According to the UWB environment, we propose Selective-Pre-Rake diversity combining using the channel information on the L strongest paths in Section 4.2. Channel estimation algorithms will be developed in Section 4.3. Although the Pre-Rake diversity combining technique is adopted to effectively capture multipath energy, we propose a simplified equalizer at receiver to improve system performance in Section 4.4.
Finally, we evaluate the proposed system in Section 4.5.
4.1 Pre-Rake Diversity Combining for DSSS Communications Systems
In a wireless communication environment, the combination of the received signals from diverse independent paths or mediums can improve the system performance. For systems operating in a multipath environment, signals of any two paths with a propagation delay difference of more than the chip duration Tc are separated at the output of the matched filter as two distinct peaks. These peaks which represent the signal strength from each path can be combined to reduce the fading effects of the channel.
4.1.1 Diversity Combining Methods
The diversity combining methods directly applicable to the DS-SS communications are as follows [28]:
1. Selection combining: in this method the signal from the path with the highest power is selected and the remaining signals are discarded. For example, if path i has the highest received power, the weighing factor wi is set to one (or generally to a constant) and all the other wk are set to zero.
2. Maximum ratio combining: in this method the phase locked signals from each path are added together in a way that the more powerful signals are emphasized and the less reliable ones are suppressed. In other words the factors wk are related to the individual path strength. For a Maximum Ratio combiner the BER can be calculated from [28]
1
where is the average SNR of the ith path.
3. Equal gain combing: where the phase locked output of path diverse signals are combined equally with all weighing factors ak set to a constant. This method is inferior than the Rake method by only about 1.3 dB when the number of diversity paths is more than 3 [29].
4.1.2 Rake Combining Scheme
The Rake combining is a form of the maximum ratio combining method in DSSS communications. The only difference is that tap settings for ak factors are carried out in intervals and not continuously as it would be done in an ideal maximum ratio combiner. A Rake diversity combiner is shown in Figure 4.1. The input signal is s(t). The filter is matched to s(t) and its output would be equal to the input of the spreader if noise and multipaths did not exist. Hence, the signal at the output of the matched filter can be written as sum of the signals from L different paths
The optimum weighting factors of Figure 4.1 can be derived for the Rake combining diversity method to be proportional to the individual path strengths [29]. And the Rake combining concept is shown in Figure 4.2.
4.1.3 Pre-Rake Combining Scheme
The Pre-Rake combining is to move the diversity combiner to the transmitter [30], and the block diagram is shown in Figure 4.3. The Pre-Rake combining concept is shown in Figure 4.4. The Rake signal was seen to be a combining of the multipath signals. If the strength and the corresponding relative phase of a path can be measured for the present data burst and estimated for the near future, a number of future transmissions can be arranged so the received signal has the characteristic of a Rake diversity signal. Each one of these transmissions is delayed according to the estimated relative path delay, and amplified according to the estimated path strength and relative path phase. This is almost an identical operation to the one performed in a Rake receiver, the only difference being that this time the operation is done in the transmitter. It could be said that the Pre-Rake concept is to accentuate transmission for the more reliable paths and suppress those less reliable.
4.2 Pre-Rake Diversity Combining for IEEE 802.15.3a DS-UWB System
The structure of Pre-Rake system has been shown in Section 4.1. The transmitted signal as the form in (3.9) with data sequence d ∈ + −n { 1, 1} and
and the Pre-Rake combiner (PRC) which is defined by the time-reversal and conjugation of the channel response [31] defined in (3.7) is given by
( ) 1 *
( )
The received signal can be rewritten by ( ) ( ) ( ) ( ) ( )
1 t
r t =s t ∗h t ∗h t +n t (4.5)
hence we can split the received symbol into the part containing desired symbol and the other one for the ISI which can be given by
( ) 1 * ( ) * ( ) ( ) ( )
Assume the transmit signal power is Psignal and AWGN noise power is σ . The 2 power of received symbol can be expressed as
( )2 2
1 signal D signal ISI
E r k⎡⎢⎣ ⎤⎥⎦ =P E P⎡⎣ ⎤⎦+P E P⎡⎣ ⎤⎦+σ (4.7)
We can now define the effective SNR as
signal
However, it is impossible to combine all multipath under UWB channel due to the extreme large number of multipaths. Hence, the Selective-Pre-Rake (S-Pre-Rake) diversity combining proposed in [32] will be a suitable technique for DS-UWB system to combine multipath energy effectively.
The concept of S-Pre-Rake is shown in Figure 4.5. The system selects only the strongest P paths to combine energy. The equivalent channel h'p =h't *h at receiver is still similar to a single path channel. Next, we need to define the Rake finger number for different situation by the equivalent channel h . The system 'p parameters are selected by the ratio of desired path power to ISI path power D
ISI
P P , the result is shown in Figure 4.6. Hence the S-Pre-Rake finger number can be defined in Table 4.1.
4.3 Channel Estimation for IEEE 802.15.3a DS-UWB System
In order to achieve S-Pre-Rake technique, the channel impulse response must be estimated first. Though blind methods have received a great deal of research attention their initial data detection errors will inhibit adoption, especially in burst-mode systems. Therefore, block-oriented approaches that use preamble sequence estimation are more reliable.
4.3.1 Channel Estimation via Correlation
The transmitted and received signal as mentioned in (3.9) and (3.10), here we use the matrix form h=[α α0, , ,1 αL−1]T to represent proposed S-V model channel. And the transmitted preamble spread by the PAC is denoted by s=[s0,s1,…,sNc-1]T, so that the received signal r=[r0,r1,…,rL+Nc-2]T is given by
= +
r Sh w (4.11)
where S is the Toeplitz (L+Nc-1)×L matrix which is represented by
0
The correlation is performed between the received signal and a copy of the transmitted sequence to obtain the estimated channel h=[α α0, , ,1 αL−1]T given
and (4.13) can be rewritten as
= + autocorrelations which is given by
0 1 1
and each element is given by
1
The optimum correlation-based estimate using this technique would be achieved using a sequence with an ideal thumbtack autocorrelation so that 1 T
N S S= W= I is a diagonal matrix. Hence [33] defined V=W-I is the sidelobe interference matrix.
The jth row (or column) of V means the interference that corrupts the jth path estimated α . j
4.3.2 Channel Estimation with Sidelobe Cancellation
The estimated interference can be cancelled from all path estimates simultaneously to obtain an improved impulse response estimate h via
( )
The estimate can be improved by increasing the accuracy of the correlation result h . A sequential computation (SC) presented in [33] can be devised wherein the sidelobe interference contributions are computed for each tentative estimate h j with the following formula
( )
where
{ }
ej Lj 1= is the usual standard orthonormal basis for RL.
4.4 Simplified Receiver Architecture
In section 4.2, the ability of S-Pre-Rake diversity combining has been proved.
Although the S-Pre-Rake diversity combining scheme can form a strong single main path, the rest paths which will induce multipath ISI still can not be eliminated completely. As shown in Figure 4.6, the ratio of desired path power to ISI path power will be saturated between 0 dB and 2 dB. In order to achieve better performance, a simple equalizer at receiver is required can effectively improve system performance.
On the other words, the MMSE DFE taps numbers can be decreased significantly.
4.4.1 Post-Cursor Multipath Cancellation
Besides the MMSE DFE mentioned in section 3.3.2. A more simplified post-cursor multipath cancellation (PCMC) scheme proposed in [34] is a less complexity DFE that cancels post-cursor ISI only. As shown in Figure 4.7. Compared to the MMSE DFE, PCMC DFE has only the FBF part. And the tap weights are calculated by the estimated channel h =[α α0, , ,1 … αL−1] to cancel all the post secondary paths signal to preserve the main path signal; the output will be given by
( ) ( ) 1 ( )
Since the PCMC DFE cancels post-cursor ISI only. Compared with the MMSE DFE, the system performance is a little worse but the complexity is largely decreased
because the inverse matrix computation is unnecessary.
4.5 Computer Simulations
In this section, computer simulations are conducted to evaluate the channel estimation and BER performance of IEEE 802.15.3a DS-UWB systems. In the first simulation, the channel estimation performance of different methods can be measured by comparing the mean square error (MSE)
( ) (
T)
MSE =E ⎡⎢⎣ h−h h−h (4.20) ⎤⎥⎦
whose comparison results for each channel (CM1 to CM4) are shown in Figure 4.8.
The techniques with sidelobe cancellation scheme outperform the correlation method as mentioned in Section 4.3.
In the second simulation, we evaluate the BER performances of the DS-UWB system with a joint design of S-Pre-Rake scheme at the transmitter and a simple equalizer at the receiver. In the following simulations, we choose the mandatory BPSK modulation mode operating in the low band the best 90 out of 100 channel realizations. The S-Pre-Rake finger numbers are listed in Table 4.1 and the equalizer tap numbers are listed in Table 4.2. The BER performances of the DS-UWB system of 110 Mbps data rate in CM3 and CM4 by using S-Pre-Rake diversity combining and different equalizer types compared with a high complexity equalizer are shown in Figures 4.9 and 4.10 respectively. It is observed that the performance of using a high complexity equalizer gains 1 to 2 dB for a BER of 10-3 compared with the proposed joint design systems. The performances of the simplified MMSE DFE are superior to the PCMC DFE because the MMSE DFE can deal with the pre-cursor ISI
but the PCMC DFE cannot. Next, the BER performances of the DS-UWB system of 220 Mbps data rate in CM3 and CM4 by using S-Pre-Rake diversity combining and different equalizer types compared with a high complexity equalizer are shown in Figures 4.11 and 4.12 respectively. It is observed that the performance of using a high complexity equalizer gains 2 to 4 dB for a BER of 10-3 compared with the proposed joint design systems. Compared with the 110 Mbps mode, the shorter spreading code will lead system performance to degrade. Under CM3 environment, the high complexity MMSE DFE needs 803+402 complex multipliers to compute tap weights. The S-Pre-Rake diversity combining cooperated with simple MMSE DFE system needs only 163+162 complex multipliers to compute tap weights. The S-Pre-Rake diversity combining cooperated with PCMC DFE system does not need any matrix inversion computation.
4.6 Summary
Due to the ultra short transmitted pulse, the receiver will resolve a ultra long delay spread channel. The average total received energy is distributed over a number of multipath arrivals. Although the equalizer mentioned in Section 3.3 can capture most multipath energy, this will induce high complexity. Furthermore, Rake diversity combining is another technique to effectively capture multipath energy. But the multipath induced ISI which will degrade system performance cannot be eliminated.
Hence, a joint design of S-Pre-Rake scheme at transmitter and simple equalizer at receiver which can achieve both diversity combining and ISI elimination is proposed in this chapter. Computer simulations show that the proposed joint design systems have much lower complexity with insignificant performance degradation.
Figure 4.1 Block diagram of the Rake system
Figure 4.2 Rake combining concept
Figure 4.3 Block diagram of the Pre-Rake system
Transmitted
Signal Channel Output of
Matched filter
Pre-Rake Combining
Input
Figure 4.4 Pre-Rake combining concept
Figure 4.5 A concept of the S-Pre-Rake diversity combining
Figure 4.6 Ratio of desired path power to ISI path power PD/PISI VS finger numbers
l
1α l
L 1α
−s t ( ) s t ( )
r t ( )
Figure 4.7 PCMC DFE structure
(a)
(b)
(c)
(d)
Figure 4.8 MSE of different channel estimation methods under different environments. (a) CM1 (b) CM2 (c) CM3 (d) CM4
Figure 4.9 BER performances of the DS-UWB system of 110 Mbps data rate in CM3 by using S-Pre-Rake diversity combining and different equalizer types compared with high complexity equalizer
Figure 4.10 BER performances of DS-UWB system of 110 Mbps data rate in CM4 by using S-Pre-Rake diversity combining and different equalizer types compared with high complexity equalizer
Figure 4.11 BER performances of DS-UWB system of 220 Mbps data rate in CM3 by using S-Pre-Rake diversity combining and different equalizer types compared with high complexity equalizer
Figure 4.12 BER performances of DS-UWB system of 220 Mbps data rate in CM4 by using S-Pre-Rake diversity combining and different equalizer types compared with high complexity equalizer
Table 4.1 S-Pre-Rake finger numbers requirement for different environments
CM 1 CM 2 CM 3 CM 4
S-Pre-Rake
finger number 5 10 20 40
Table 4.2 Equalizer tap numbers of proposed joint design system for different environments
CM3 CM4
MMSE DFE FFF 16 30
MMSE DFE FBF 16 30
PCMC DFE 16 30
Chapter 5 Conclusion
In this thesis, we propose an IEEE 802.15.3a DS-UWB system incorporating enhanced early-late (EL) code tracking loop and selective-Pre-Rake (S-Pre-Rake) diversity combining schemes. Compared to the conventional DS system, the receiver can resolve a dense and long delay spread channel impulse response due to the transmitted ultra short pulse.
In Chapter 2, concepts of DS system and specification of IEEE 802.15.3a DS-UWB system has been introduced. In Chapter 3, we first introduce the S-V model to form indoor UWB channel environment. Compared with usual narrowband channel model, the clustering phenomenon is the most notable characteristic in the channel. Next, we construct a simulation platform of an IEEE 802.15.3a DS-UWB system using Matlab. Synchronization and equalization algorithms for DS-UWB receiver are established. In particular, the dense and long delay spread multipaths will lead some receiver function blocks to be modified. The dense multipaths will cause the conventional EL code tracking loop to loose accuracy; the proposed EL code-tracking loop with multipath cancellation scheme can effectively overcome this problem. Besides, the channel length is different under different situations (CM1 to CM4), and we have defined different numbers of equalizer tap, respectively.
In Chapter 4, we introduce S-Pre-Rake diversity combining scheme to capture multipath energy without using a high complexity equalizer. Although the equalizer mentioned in Chapter 3 can capture most multipath energy, this will induce extreme high complexity. Furthermore, Rake diversity combining is another technique to effectively capture multipath energy. But the multipath induced ISI which will degrade system performance can not be eliminated. Hence, a joint design of S-Pre-Rake scheme at the transmitter and simple equalizer at the receiver which can achieve both diversity combining and ISI elimination simultaneously is proposed.
Compared with the conventional equalizer, the proposed methods have much lower complexity with insignificant performance degradation.
The study presented in the thesis has thoroughly discussed the transceiver design for an IEEE 802.15.3a DS-UWB system and its efficacy has been rigorously
The study presented in the thesis has thoroughly discussed the transceiver design for an IEEE 802.15.3a DS-UWB system and its efficacy has been rigorously