When co-located dual-polarized in the SM system, information is conveyed by the index of the transmit antenna pair and the specific polarization in that pair used and the symbol transmitted. Hence, m = log2(NTM) bits are transmitted in each channel
35
use. The receiver’s task thus contains the used transmit antenna and polarization index estimation and transmitted symbol detection. The system model is depicted in Figure 4.3. A mapping rule for this SM system with two dual-polarized antenna pairs in both the transmitter and receiver and BPSK or QPSK modulated symbols is suggested in Table 4.1
Polar. Est. Ant. Est.ġ Symbol Det.ġ
Transmitterġ Receiverġ
Figure 4.3: A dual-polarized SM system model.
Three data detection techniques are proposed for the spatial modulated dual-polarized MIMO system. Since we only concentrate on its data detection in this section, CSI ˜Hx
is assumed known at the receiver and block index k is ignored. The received signal corresponding to transmitted signal X can be represented as
Y = ˜HxX + Z. (4.23)
The ML detector is simply
(ˆxi, ˆℓi) = arg min
xi,ℓikyi− ˜hx,ℓixik2, i = 1, · · · , B. (4.24)
Input bits Antenna Index Transmit Symbol Antenna Index Transmit Symbol
Table 4.1: An SM mapping table for the dual-polarized system for 3 bits/transmission
The MF-based detector for (4.24) is similar to the traditional one (2.16)-(2.21) for (2.3) with following procedure: Prior to the introduction of the last detection method, we consider the following.
Since antenna polarization selection bares information for SM system in dual-polarized MIMO system, we shall give a few facts. Based on the Cauchy-Schwarz inequality, for a specific spatial channel i (the ith column of ˜Hx, hi), we have the following due to the mismatch of polarization:
|hHiVhiH|
khiHk ≤ |hHiVhiV|
khiVk = khiVk (4.29)
which agree with our intuition. On the other hand, for two different spatial channel vectors, say hi and hj, the correlation between their portions corresponding to the same polarization outweighs that corresponding to different polarizations, i.e.,
|hHiVhjH|
khjHk ≤ |hHiVhjV|
khjVk ≤ khiVk. (4.30)
37
This is because of the inability of a polarized antenna to receive signal of other polar-izations. In this way, the (horizontal) polarization of a signal passing through hiV can be effective estimated prior to the antenna and symbol detection.
As a result, the polarization used can be detected before ML detection of antenna pair index and symbol. This suboptimal method effectively lower the complexity of detection algorithm with some performance loss. Specifically, first calculate (4.24) and find the MF output of vertical or horizontal polarized transmit antenna of each transmit antenna pair,
where nP is the indicator vector whose position of value 1 represents the detected po-larization in a specific transmit antenna pair and ˆnV and ˆnH count the total number of detected polarization used in all transmit antenna pairs. Based on the majority vote algorithm, the used polarization of the transmit antenna is decided via
P = arg maxˆ
P =V,H {ˆnV nˆH} (4.32)
Based on the result, the ML detector of the antenna pair used and symbol transmitted only needs to search over the specific ˆP -polarized channel vectors,
(ˆxi, ˆℓi) = arg min
xi,ℓi=i ˆPkyi(k) − ˜hx,ℓixik2, i = 1, . . . , B. (4.33) This detection method reserves the high detection performance of the ML detector but needs only about half of the complexity required by the latter. As will be shown later, it outperform the MF-based detector.
4.5 Simulation Results
In this section, we investigate the performance of SM scheme using dual-polarized antenna. For simplicity and the measurement results in [19], we concentrate on the effect
of XPR and CPR. The values of µ and χ are set to 0.7 and 0.1 for all the simulation results except for Figure 4.8 and Figure 4.9, and the parameters of polarized correlation are set to zero. First, the BER performance of 2 × 2 SM comparing to 4 × 4 SM using dual-polarized antenna is given in Figure 4.4 where MF-based detector is used and CSI is assumed known to receiver. We can see from the result that the use of dual-polarized antennas can give the polarization diversity gain.
0 2 4 6 8 10 12 14 16 18
10−3 10−2 10−1 100
Eb/N
0
BER
SM−BPSK SM−16 QAM DPSM−BPSK DPSM−16 QAM
Figure 4.4: Comparison of BER performance for SM under conventional MIMO channel and dual-polarized MIMO channel.
We also give a BER performance comparison between SM and V-BLAST and space time code based on Alamouti[4] under dual-polarized channel in Figure 4.5. Based on the same spectral efficiency which is 8 bits/transmission, SM outperforms V-BLAST and Alamouti scheme. V-BLAST in this simulation result uses QR-based detector and Alamouti and SM scheme use ML detector.
Then the normalized mean square error of dual-polarized spatial correlated channel estimation method is shown in Figure 4.6. In this figure, we use the 3GPP SCM model
39
0 5 10 15 20 25 10−5
10−4 10−3 10−2 10−1 100
Eb/N0
BER
V−BLAST 16−QAM 4x2 Alamouti 256QAM 4x2 SM 32 QAM 4x8
Figure 4.5: Comparison of BER performance for SM and VBLAST and Alamouti scheme under dual-polarized channel for 8 bits/transmission.
to generate the co-located dual-polarized spatial correlated channel. Two channels with different angle spread (AS) 2 and 15 with mobile velocity 60 km/hr are adopted in the simulation result. The number of transmit and receive antennas setting to 8, we compare the NMSE performance of conventional MIMO channel estimation methods and modified dual-polarized channel estimation method. It can be seen from this figure that dual-polarized spatial correlated channel estimation method only use half of the basis to achieve the same estimation performance with conventional method.
The BER performance of proposed detectors for SM in dual-polarized system is shown in Figure 4.7. We consider a 4 × 4 MIMO channel using dual-polarized antennas, and QPSK modulated signals. From the result, ML detector performs the best of three detectors and the low-complexity sub-optimal detector outperforms MF-based detector where we assume CSI is known to receiver in this simulation result. We also investigate the influence on the three detectors of depolarization effect caused by propagation chan-nel. From Figure 4.8, fixed parameter χ to 0.5, when the value µ is too small, all the three detectors can not have adequate performance because the horizontal-polarized channel
0 5 10 15 20 25 30
Figure 4.6: NMSE comparison of channel estimation for dual-polarized spatial-correlated MIMO channel with different modelling order, AS=2 and 15.
is too small than vertical and thus cause the signals transmit by horizontal-polarized antenna cannot be successfully detected. The effect of χ which denotes the inverse of XPR value with fixed µ = 0.5 on the detectors’s performance is given in Figure 4.9. The result shows that when the value of χ is too large which means that cross interference between polarization is large, the performance of the MF-based and the suboptimal detector degrade since the large χ value can make the channel vector of vertical- and horizontal-polarized transmit antenna become similar thus the value of MF output of both the vertical and horizontal polarized antenna are approximately equal. Therefore, the MF-based and suboptimal detectors cannot detect the polarization correctly.
The following part, we give the simulation result of different time-varying channel estimation methods in DPSC channel where t and r are assumed to be 0.3, and three detectors are investigated. In Figure 4.10–4.15, the BER and NMSE performance of decision-directed channel estimation method based on MF-based, suboptimal and ML
41
0 2 4 6 8 10 12 14 16 18 10−4
10−3 10−2 10−1
Eb/N0
BER
subopt.
ML MRC
Figure 4.7: Comparison of BER performance of SM for MF-based detector, suboptimal detector and ML detector under perfect CSI.
detector are shown, we can see that using ML or suboptimal detectors can have better performance than that of MF-based detector. In addition, the performance loss increase when the mobile velocity increases. In Figure 4.16, BER performance of superimposed channel estimation method is given. It performs better than decision-directed channel estimation in high SNR and fast varying channel.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10−4
10−3 10−2 10−1 100
µ
BER
MF−based Deteector Sub−ML Detector ML Detector
Figure 4.8: The effect of different mu (inverse of CPR) value with different detectors on BER performance.
0 0.2 0.4 0.6 0.8 1
10−4 10−3 10−2 10−1
χ
BER
MF−based Detector Sub−ML Detector ML Detector
Figure 4.9: The effect of different chi (inverse of XPR) value with different detectors on BER performance.
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0 5 10 15 20 25 10−2
10−1 100
Eb/N 0
BER
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 4.10: BER performance of decision-directed channel estimation method with MF-based detector in DPSC channel under different mobile velocity.
0 5 10 15 20 25
10−2 10−1 100 101
Eb/N 0
NMSE
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 4.11: NMSE performance of decision-directed channel estimation method with MF-based detector in DPSC channel under different mobile velocity.
0 2 4 6 8 10 12 14 16 18 20
Figure 4.12: BER performance of decision-directed channel estimation method with low complexity ML detector in DPSC channel under different mobile velocity.
0 2 4 6 8 10 12 14 16 18 20
Figure 4.13: NMSE performance of decision-directed channel estimation method with low complexity ML detector in DPSC channel under different mobile velocity.
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0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1
Eb/N0
BER
30 km/hr 40 km/hr 50 m/hr 60 km/hr 80 km/hr 100 km/hr
Figure 4.14: BER performance of decision-directed channel estimation method with ML detector in DPSC channel under different mobile velocity.
0 2 4 6 8 10 12 14 16 18 20
10−2 10−1 100 101
Eb/N0
NMSE
30 km/hr 40 km/hr 50 km/hr 60 km/hr 80 km/hr 100 km/hr
Figure 4.15: NMSE performance of decision-directed channel estimation method with ML detector in DPSC channel under different mobile velocity.
0 5 10 15 20 25 30 10−4
10−3 10−2 10−1
Eb/N0
BER
30 km/hr ML 60 km/hr ML 80 km/hr ML 100 km/hr ML 30 km/hr MF 60 km/hr MF 80 km/hr MF 100 km/hr MF 30 km/hr Suboptimal 60 km/hr Suboptimal 80 km/hr Suboptimal 100 km/hr Suboptimal
Figure 4.16: BER performance of superimposed channel estimation method based on three detectors in DPSC under different mobile velocity.
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Chapter 5
Space-Time Block-Coded Spatial Modulation (STBC-SM) System
5.1 STBC-SM System
Conventional space-time block codes (STBCs) offer an excellent way to exploit the potential of MIMO systems because of the improvement of transmission reliabil-ity, obtaining both diversity and coding gain. Redundant copies of the data stream transmitted through multiple transmit antennas via STBC. As a result, different copies of the data are received and hence can provide the more reliable information. More-over, STBC schemes are simple to implement and decode. However, the symbol rate of unitary STBCs is upper-bounded by 1 symbol per channel use. Therefore, space-time block-coded SM (STBC-SM) system is introduced to improve the spectral efficiency of conventional STBCs [28].
In the STBC-SM scheme, both STBC symbols and the indices of the transmit an-tennas by which these symbols are transmitted carry information. The famous STBC proposed by Alamouti [4] suggests that the system transmits two symbols, drawn from the constellation, by the two transmit antennas respectively at a time. During the first time slot, the symbols x1 and x2 are simultaneously transmitted by the first and second transmit antennas, respectively, then, in the next time slot, −x∗2 and x∗1 are transmitted
by the respective transmit antennas. In other words, the codeword is given by
X = [x1 x2] = x1 −x∗2
x2 x∗1
. (5.1)
The above Alamouti codeword matrix is extended to the antenna domain for the STBC-SM system where the selection of two out of NT antennas to transmit the two symbols introduce additional carried information. The spectral efficiency is shown to be superior to the conventional STBC or SM system in [28]. We first give an example of STBC-SM systems in the following [28].
Consider a MIMO system with four transmit antennas (NT = 4), a STBC code ξ is designed to be of the following form:
ξ1 = {X11, X12} = where the codebooks ξ1and ξ2contains two codewords Xij, j = 1, 2 that do not interfere with each other. A codebook is constructed by grouping a codewords satisfying XHijXik = 02×2, j, k = 1, 2, j 6= k, and θ is a rotation angle to be optimized for a given modulation scheme. With this STBC-SM codebook design, coding gain and diversity gain of the scheme can be maximized. A mapping rule of this example with BPSK modulation symbols is given in Table 5.1.
When there are more than two codebooks, multiple rotation angles shall be imple-mented. The optimization of these rotation angles in the STBS-SM system is done by maximizing the minimum distance in the code. For detail, see [28].
Noted that the number of transmit antennas in the STBC-SM scheme needs not be an integer power of 2 as is restricted in SM scheme and thus provides design flexibility.
A design procedure to generalize STBC-SM system to NT antennas is given in the following:
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Table 5.1: STBC-SM mapping table for 2 bits/transmission
Polar. Est. Ant. Est.ġ Symbol Det.ġ
ġ ġ
Step 1: Find the number of possible combinations of two out of NT transmit anten-nas. This number c = ⌊ N2T⌋2ı, where ı is a positive integer, should be a power of 2 to carry information bits by antenna selection.
Step 2: To make codewords in i codebook do not interfere with each other, their nonzero rows have to be nonoverlapping. Therefore, we can calculate the number of codewords in a codebook and total number of codebooks to be a = ⌊N2T⌋ and n = ⌈ac⌉, respectively.
Step 3: Construct the STBC-SM codewords starting from ξ1 which contains a non-interfering codewords as
ξ1 = {[X 02×(NT−2)]T, [02×2 X 02×(NT−4)]T, · · · , [02×2(a−1) X 02×(NT−2a)]T}, (5.3)
where X is defined as (5.1). The other codebooks, ξi, 2 ≤ i ≤ n, are created sequentially in a similar manner, where every codebook ξi should contain non-interfering codewords of different transmit antenna combinations and must be composed of codewords that were never used in the previous codebooks ξj, j ≤ i.
Step 4: Determine the optimal θi of each codebook ξi by maximizing the minimum distance where i = 1, · · · , n. Code ξ = {ξ1, ξ2, · · · , n} is determined.
Since there are c antenna combinations, the spectral efficiency of STBC-SM is
m = 1
2log2c + log2M [bits/s/Hz], (5.4) where the factor 12 is due to the normalization by the block size B = 2. With codeword Xξ(k) drawn from this determined code, the received signal at time k can be denoted as
Y(k) = H(k)Xξ(k) + Z(k), (5.5)
where Xξ(k) is an NT × 2 STBC-SM codeword matrix. While the conventional ML detector needs an exhaustive search over cM2 metrices, i.e.,
Xˆξ(k) = arg min
Xξ∈ξkY(k) − H(k)Xξk2, (5.6) the unitary property of Alamouti code suggests a simpler ML detector. Specifically, the received signal can be replaced by a 2NR× 1 vector [4]
y(k) = Hξ(k) x1(k) x2(k)
+ z(k), (5.7)
where Hξ(k) is the 2NR× 2 equivalent channel matrix corresponding to the different realizations of STBC-SM codewords. In the case of NT = 4, there are c = 4 possible
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realizations for Hξ,
where ϕ = ejθ and time index k is neglected for the moment. The ML detector (5.9) can be simplified and decoupled into two independent ML symbol detectors due to the column-orthogonality in every Hℓi, i.e,
(ˆℓi, ˆxj,ℓi(k)) = arg min
ℓi,xj∈γky(k) − hℓi,j(k)xjk2, j = 1, 2. (5.9)