Simulation of LTE Downlink Channel Estimation
4.1 Simulation Conditions
The system parameters used in our simulation are listed in Table 4.1. In addition to AWGN which is for calibration purpose, we also simulate SUI-2 (where SUI stand for Stanford Uni-versity Interim),SUI-4, SUI-5, TU (Typical Urban) [10], ITU-VA (International Telecommu-nication Union RadiocommuTelecommu-nication Vehicular A), and an artificial channel model based on ITU-VA [2]. The SUI channels model deal suburban path loss environments in three different types, depending on the tree density and pass loss condition. The three types in suburban area are listed in Table 4.2. SUI1 and SUI2 are Rician multipath channels and the other four are Rayleigh multipath channels; the former two correspond to situations with line-of-sight (LOS) and the latter four non LOS respectively. The Rayleigh channels are more hostile and exhibit a greater root-mean-square (RMS) delay spread. In our simulation, we employ
34
Table 4.1: OFDMA Downlink Parameters (Normal CP)
Parameters Values
Bandwidth [MHz] 5 / 10
modulation type QPSK
Central frequency [GHz] 2
Number of resource blocks 25 / 50
Number of occupied subcarriers 300 / 600
CP time [µs] (first symbol in slot, else) 5.2, 4.7
NF F T 512/1024
Sampling frequency [MHz] 7.68 / 15.36
Subcarrier spacing [kHz] 15
Symbol time [µs] (first symbol in slot, else) 71.8, 71.3
Samples per slot 3840 / 7680
three types of environments, i.e., terrain A, B, and C. We select SUI-2, SUI-4, and SUI-5 as representative for terrain C, terrain B, and terrain A, respectively. For simplicity, we use Rayleigh fading to model SUI-2 instead of Rician fading.
The TU channel model, as its name shows, is a channel model for the urban environment.
The TU channel model is also a Rayleigh channel, but there are 12 taps in it, which is four-times that of SUI channels. The ITU-VA is a channel model for UE in vehicular type of motion. The ITU-VA channel model is a Rayleigh channel. There are 6 taps in it, which is two-times that of SUI channels. In order to see how the proposed technique may perform in various conditions, we choose these quite different channel models to do our simulation.
Artificial ITU-VA [2], the PDP of which is far from exponential PDP, is also chosen to see how the proposed technique may perform when the PDP is totally different from exponential PDP. The PDP of the artificial ITU-VA consists of three copies of ITU-VA’s PDP with intercluster delays of 2 and 4 µs, respectively. The relative power scales of three clusters are 0, 5, and −2 dB, respectively. It has been shown that exponential PDP modeling performs better than uniform modeling [2] when the PDP is Artificial ITU-VA. But the performance is unknown for exponential PDP modeling in the method described in chapter 3. We thus
35
Path gain
0 1 2 3 Sample index
Adjustment required
Adjustment required
Figure 4.1: Tap adjustment.
Table 4.2: SUI Channel Model for Differetn Terrain Types
Terrain type Description SUI channels
A hilly terrain with heavy tree SUI5, SUI6 B flat terrain with heavy tree, hilly
terrain with light tree
SUI3, SUI4 C flat terrain with light tree SUI1, SUI2
simulate this channel model to understand it.
Tables 4.3–4.8 present the characteristics of the models mentioned above. Note that the PDP of each channel model may not have the path delays equal to integer multiples of the LTE sample spacing. Experience with the Matlab channel simulator shows that this situation results in huge amount of memory usage which causes difficulty in simulation of systems where the FFT size is more than 512. To solve this problem, the PDP listed in Table 4.4–4.8 are adjusted by forcing each channel impulse response tap to its nearest sampling point by rounding to preserve the path number as well as path power. The idea is illustrated in Figure 4.1. Expeiments show that the performance with and without tap adjustment is almost the same.
36
Table 4.3: PDP of SUI2
Relative delay Average power
Tap µs sample numbers
(512,1024)
dB normalized dB
1 0 (1, 1) 0 −0.393
2 0.4 (4, 7) −12 −12.393
3 1.1 (9, 18) −15 −15.393
Table 4.4: PDP of SUI4
Relative delay Average power
Tap µs sample numbers
(512,1024)
dB normalized dB
1 0 (1, 1) 0 −1.9218
2 1.5 (13, 24) −4 −5.9218
3 4 (32, 62) −8 −9.9218
Table 4.5: PDP of SUI5
Relative delay Average power
Tap µs sample numbers
(512,1024)
dB normalized dB
1 0 (1, 1) 0 −1.5113
2 4 (32, 62) −5 −6.5113
3 10 (78, 155) −10 −11.5113
4.1.1 Parameter Setting
We now discuss considerations concerning tap number of LMMSE filtering, length of DPSS, time-bandwidth product, and number of DPSS bases.
It is known that the coherent bandwidth, denoted as Bc herein, is inversely proportional
37
Table 4.6: PDP of TU
Relative delay Average power
Tap µs sample numbers
(512,1024)
dB normalized dB
1 0 (1, 1) −4 −10.3582
2 0.1 (2, 3) −3 −9.3582
3 0.3 (3, 6) 0 −6.3582
4 0.5 (5, 9) −2.6 −8.9582
5 0.8 (7, 13) −3 −9.3582
6 1.1 (9, 18) −5 −11.3582
7 1.3 (11, 21) −7 −13.3582
8 1.7 (14, 27) −5 −11.3582
9 2.3 (19, 36) −6.5 −12.3582
10 3.1 (25, 49) −.6 −14.9582
11 3.2 (26, 50) −11 −17.3582
12 5.0 (39, 78) −10 −16.3582
Table 4.7: PDP of ITU-VA
Relative delay Average power
Tap µs sample numbers
(512,1024)
dB normalized dB
1 0 (1, 1) 0 −3.14
2 0.31 (3, 6) −1 −4.14
3 0.71 (6, 12) −9 −12.14
4 1.09 (9, 18) −10 −13.14
5 1.73 (14, 28) −15 −18.14
6 2.51 (20, 40) −20 −23.14
to the RMS delay spread denoted τrms, that is [10],
Bc ∝ 1
τrms. (4.1)
The proportionality constant in (4.1) may vary with the definition of coherence bandwidth or other considerations. For instance, if the coherence bandwidth is defined as bandwidth
38
Table 4.8: PDP of Artificial ITU-VA
Relative delay Average power
Tap µs sample numbers
(512,1024)
Table 4.9: RMS Delay of Channel after Tap Adjustment with FFT size = 512
Channel Model SUI-2 SUI-4 SUI-5 TU ITU-VA Artificial
ITU-VA RMS delay
spread (sample)
1.485 9.794 21.92 7.905 2.726 9.437
RMS delay spread (µs)
0.193 1.275 2.854 1.03 0.355 1.229
with correlation of 0.9 or above in channel frequency response, then we have
Bc≈ 1 50τrms
. (4.2)
In case the coherence bandwidth is defined as bandwidth with correlation of 0.5 or above in 39
channel frequency response, it is given as
Bc≈ 1
5τrms. (4.3)
Here we consider the latter definition. In this case, if τrms is equal to 2 µs, which is a relatively large RMS delay spread, then the coherence bandwidth is equal to 100 kHz. On the other hand, if τrms is equal to 0.2 µs, which is a relatively small RMS delay spread, then the coherence bandwidth is equal to 1 MHz. The use of pseudo RR as discussed in chapter 3 makes the spacing between adjacent RSs equal to 45 kHz in LTE and LTE-A. Considering both the large and small RMS delay spread environments, it appears that 4 is a proper number of LMMSE filter taps.
Now consider the other parameters, namely, length of DPSS, time-bandwidth product, and number of DPSS bases. We may intuitively expect that a longer length of the DPSS should result in better performance. But longer DPSS imply grater latency and grater mem-ory requirement. We let it be 7 slots plus 1 symbol, i.e., about 3.6 ms in our simulation, which is a relatively arbitrary choice. The time-bandwidth product is related to the nor-malized Doppler frequency, which is not estimated in this thesis. But as shown in (3.15), the product has to be rounded in determining the dimensions used, which means there is a high tolerance to error in the assumed normalized Doppler frequency. Our simulation results show that DPSS for higher normalized Doppler frequencies can be used in cases with lower normalized Doppler frequencies with some small degradation. Thus we choose a set that corresponds to about 150–300 km/h for the 0-300 km/h operating environment when the carrier frequency is equal to 2 GHz. The number of DPSS bases, where each basis sequence corresponds to a different eigenvalue, is determined by simulation. We find that eigenvalues lower than 0.001 can be discarded with little degradation. And the lowest eigenvalue should be in the interval [0.01, 0.001] for the best performance. So here we preserve 7 DPSS bases, where the 7th eigenvalue is 0.0034 and the 8th is 0.00018.
40