In this section, the simulation results of the proposed two channel estimation meth-ods are presented. For a 4 × 4 MIMO system, we generate each independent path of the spatial uncorrelated time-varying channels by jake’s model [35]. The carrier frequency is 2GHz and sampling time Ts is 0.1ms of the duration 10s channel paths. Then the time correlation function is defined as
E{hij(t1)h∗ij(t2)} = J0(2πfD(t1− t2)Ts). (3.24) Setting the block length to 4 for the reason that at least 4 symbol times are needed to fully estimate the total number of channel coefficients. The frame size is 5 where the first block consist of pilot signals only. In addition, QPSK constellation is used.
In Figure 3.2 and Figure 3.3, we generate the time-varying channel at mobile velocity 30 km per hour, and compare the bit error rate(BER) and normalized minimum mean square error(NMSE) of decision-directed channel method based on MF-based and ML detector and perfect CSI under the same pilot overhead. It is shown that the performance of decision-directed channel estimation is better than that of only initial pilot estima-tion is used. Moreover, the decision-directed channel estimaestima-tion based on ML detector
outperforms MF-based detector. The BER and NMSE performance of decision-directed channel estimation method via different mobile velocity based on MF-based and ML detector are given in Figure 3.4, Figure 3.5, Figure 3.6, and Figure 3.7. It can be seen that there is error floor in high SNR region.
0 5 10 15 20 25 30
10−3 10−2 10−1 100
Eb/N 0
BER
DD−MF−based perfect CSI Pilot DD−ML
Figure 3.2: BER performance of SM detectors with decision-directed channel estimation.
Superimposed channel estimation method is proposed to improve the error floor performance of decision-directed channel estimation, the energy of superimposed pilot signals affects the BER performance which is shown in Figure 3.8 where the MF-based detector is used and the mobile velocity is set to 30 km/hr. If the energy of superimposed signals is too large, it would cause the serious ICI to receiver and thus degrades the BER performance. However, if the energy is small, it could not have good channel estimation performance. Hence, the optimal energy of the superimposed signal is approximately 2/SNR which is shown in Figure 3.9. The BER performance of superimposed channel estimation method under different mobile velocity based on MF-based and ML detector are shown in 3.10 and 3.11, respectively. In addition, we can see from these simulation results that the use of superimposed signal can get better performance than that of
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0 5 10 15 20 25 30 10−3
10−2 10−1 100
Eb/N 0
BER
DD−MF DD−ML pilot
Figure 3.3: NMSE performance of SM detectors with decision-directed channel estima-tion.
decision-directed channel estimation method in high SNR region and in high mobile velocity.
0 5 10 15 20 25 30
Figure 3.4: BER performance of MF-based detector with decision-directed channel es-timation under various mobility.
Figure 3.5: NMSE performance of MF-based detector with decision-directed channel estimation under various mobility.
25
0 5 10 15 20 25 30 10−5
10−4 10−3 10−2 10−1 100
Eb/N0
BER
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 3.6: BER performance of ML detector with decision-directed channel estimation under various mobility.
0 5 10 15 20 25 30
10−3 10−2 10−1 100
Eb/N0
NMSE
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 3.7: NMSE performance of ML detector with decision-directed channel estimation under various mobility.
0 5 10 15 20 25 30 10−3
10−2 10−1 100
Eb/N0
BER
1/20 Es 1/10 Es 1/5 Es 1/2 Es 1/30 Es
Figure 3.8: BER performance of superimposed channel estimation with different super-imposed pilot symbol energy.
0 5 10 15 20 25 30
10−4 10−3 10−2 10−1 100
Eb/N
0
BER
5/SNR 4/SNR 2/SNR 1/SNR
Figure 3.9: BER performance of different superimposed pilot symbol energy versus SNR.
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0 5 10 15 20 25 30 10−3
10−2 10−1 100
Eb/N0 (dB)
BER
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 3.10: BER performance of superimposed channel estimation method with MF-based detector under different mobile velocity.
0 5 10 15 20 25
10−4 10−3 10−2 10−1 100
Eb/N0
BER
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 3.11: BER performance of superimposed channel estimation method with ML detector under different mobile velocity.
Chapter 4
Spatial Modulation Using
Dual-Polarized Antenna Arrays
4.1 Dual-Polarized MIMO Channel Models
In MIMO wireless communication systems, antenna spacings are usually required to be at least half a wavelength at subscriber units and ten wavelengths at base stations to achieve satisfactory performance. This condition restricts the implementation of MIMO systems on some space-limited devices. However, since orthogonal polarization can decrease the correlation of transmit antennas or receive antennas, the usage of co-located dual-polarized antennas can be a space- and cost-effective alternative. Figure 4.1 depicts a co-located dual-polarized MIMO system with antennas grouped into pairs.
For ideal dual-polarized antennas, cross-polar transmissions, from a vertically-polarized transmit antenna to a polarized receive antenna or from a horizontally-polarized transmit antenna to a vertically-horizontally-polarized receive antenna, equal to zero.
Practically, there are two depolarization mechanisms that can cause polarization in-terference: cross-polar isolation (XPI) due to use of imperfect antennas and the depo-larization caused by the propagation channel which can be identified by the existence of cross-polar ratio (XPR). The interplay between both effects forms the global cross-polar discrimination (XPD) which quantifies the separation between two channels of different
29
ڭ ġ
Figure 4.1: A co-located dual-polarized MIMO system model.
polarizations. Besides, vertically-polarized electromagnetic wave is vulnerable to electric current on the ground, so co-polar ratio (CPR) can be taken into consideration in some cases. Figure 4.2 shows the depolarization mechanisms discussed above.
We first consider one dual-polarized transmit-receive antenna pair, Let pij
def= |hij|2(i, j ∈ {V, H}) be the instantaneous dual-polarized channel gain. The channel is a 2×2 matrix,
HP =
hV V hV H
hHV hHH
, (4.1)
and depolarization parameters can be defined as (1) Cross-polar isolation:
Transmitter : XPIT def
= E{pii}
E{pij} (4.2)
Receiver : XPIRdef
= E{pii}
Analytically, XPI effect at transmitter and receiver can be respectively modelled with coupling matriceswhere χa,t and χa,r are the inverse of XPI at transmitter and receiver, respectively. If the used dual-polarized antennas are in perfect condition, these scalars will equal to zeros. Note that this depolarization mechanism affect line-of-sight (LOS) and scattered components whereas XPR exists only in non-line-of-sight components.
While the above definitions concentrate only on the channel gains, to get a thorough understanding of the depolarization effect, the dual-polarized channel can be characterize by the correlation matrix E{vec(HHP)vec(HHP)H}. The diagonal terms of this 4×4 matrix are the average channel gains of each channel coefficient and the off-diagonal ones include the cross-polar correlations (XPC) between hiiand hij or hji, co-polar correlation (CPC)
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between hvvand hhh, and anti-polar correlation (APC) between hvh and hhv. This model is verified by several measurements to be a good approximation to the real dual-polarized channels. The corresponding parameters to various environment settings are given in [19] and references therein.
In the following, one dual-polarized antenna pair is extended to a MIMO system.
As the measurement result [19] shown, in Rayleigh fading environment, the spatial correlation properties are independent of the polarization, i.e., beam pattern are similar for all antennas, the parameters concerning the polarization and spatial correlation can be decoupled in our model. It is especially true when the system is implemented in macrocells or microcells. It is explained in the following.
An NR× NT dual-polarized MIMO fading channel consists of NT/2 and NR/2 co-located dual-polarized transmit and receive antenna pairs. If all dual-polarized antennas are identically oriented, the joint transmitter-to-receiver direction spectrum would be equivalent for all co-located antennas. The matrix can thus be written as
H˜x = HNR
2 ×NT2 ⊗ MrWM˜ t (4.8)
where HNR/2×NT/2 is the spatial correlated Rayleigh fading channel and ˜W is the de-polarization matrix which is separated from the spatial correlation parameters. Matrix W models the differential attenuation and the correlated phase shifts between the dual-˜ polarized channels. Specifically,
where µ and χ represent the inverse of CPR and XPR, σ and ϑ are the receive and transmit correlation coefficients between polarization vv and hv, hh and hv, vv and vh or hh and vh. δ1 and δ2 are respectively co- and anti-polar correlation coefficients. The last term,
where Φk’s are uniformly distributed in [0, 2π).
As a result, a dual-polarized MIMO channel can be formed into
H˜x=
where Hi,j is the dual-polarized channel matrix of the jth transmit and ith receive antenna pairs:
where each entry hiPijPj is the channel coefficient between the Pi-polarized ith transmit antenna pair and Pj-polarized jthe receive antenna pair. In addition, we define the column vectors of ˜Hx as