Differential space-time modulation (DSTM) has received much attention recent by, since it not only avoids MIMO channel estimation but also can achieve considerably high spatial diversity gain. In order to realize DSTM, the data information needs to be first encoded into differential space-time block codes (DSTBCs). In general, DSTBC is designed to be unitary to simplify the transceiver [34].
In the thesis, we propose a differential STBC-SM system which dose not need CSI knowledge at the receiver and thus outperforms STBC-SM in the presence of channel estimation error. With the need that the DSTBCs should be unitary, it necessitates us to modify the non-unitary Alamouti code-based STBC-SM codewords introduced in the previous section.
Due to the fact that for an NT-transmit-antenna STBC-SM system, only two transmit antennas are selected to transmit symbols and the rest of the antennas are inactive, we
let the number of transmit antennas be even 2 and extend the STBC-SM codeword
can be extended to an unitary matrix by extending the block size B = 4 and letting the unused antennas to transmit additional symbols in time instants 3 and 4. The corresponding DSTBC codeword matrix becomes
XD =
Similar procedures generalized to other value of NT is depicted as follows:
Step 1: Each codeword designed for the NT-transmit antenna STBC-SM system is taken as the first two columns of a DSTBC codeword matrix.
Step 2: To achieve the unitary property, the available transmit antennas at the third and fourth time cannot include the transmit antennas used in the previous tow instants. Therefore, the third and fourth columns (negleting the rows in which the first two columns have nonzero elements) are designed to be the codewords of (NT − 2)-antenna STBC-SM system.
Step 3: Similar process is done to the fifth and sixth columns and the remaining columns by neglecting the occupied rows by the previous steps until all columns are considered.
Since we produce ck = NT − 2(k − 1) 2
2ı
possible combinations at each step k, the spectral efficiency of the proposed DSTBC-SM system is
m = 1 NT
(log2c1+ log2c2+ · · · + log2cNT 2
) + log2M [bits/s/Hz] (5.12)
which is smaller than that of STBC-SM system (5.9).
53
Let each symbol xi be taken from a unimodular ∈ ξD constellation with energy Ex
(e.g. M-PSK, M-QAM, etc). For each codeword XD, it satisfies
XDXHD = 2ExINT, (5.13)
where ξD is the code constructed via the procedure and is of cardinality QNT2
k=1ck. An identity matrix which dose not contain any information is sent to initialize the trans-mission, i.e, VD(0) = INT. By mapping information bits to a DSTBC-SM codeword, the differential encoded codeword matrix of the kth block becomes
VD(k) = ˜VD(k − 1)XD, k ≥ 2 (5.14) where
V˜D(k − 1) = 1
√2Ex
VD(k − 1) (5.15)
denotes the normalized version of ˜VD(k − 1) to ensure constant transmission power, i.e., V˜D(k − 1) ˜VDH(k − 1) = INT.
As a result, the received signals at (k − 1)- and kth block are respectively
Y(k − 1) = H(k − 1)VD(k − 1) + Z(k − 1), (5.16)
Y(k) = H(k)VD(k) + Z(k). (5.17)
For slow time-varying channel, the channel matrices at two consecutive block times are similar, hence H(k − 1) ∼= H(k). The optimal non-coherent detector can be
XˆD(k) = arg min
XD∈ξDkY(k) − 1
√2ExY(k − 1)XDk2. (5.18) In addition, due to the unitary structure of Alamouti code, the transmit data symbols can be estimated individually via the similar approach discussed in (5.8)–(5.7). Therefore, the complexity of the optimal non-coherent detector is further reduced.
5.3 Simulation Results
The performances of the proposed DSTBC-SM are given in this section. In Figure 5.1, we compare the performance of STBC-SM and DSTBC-SM. The transmit and
receive antennas are set to 4, and the slow-tim varying channel is generated by Jake’s model the same as in previous Chapters. The performance of DSTBC-SM with QPSK modulation under the mobile velocity of 40 km/hr outperforms STBC-SM with LS channel estimation error due to the fact that the differential design dose not need CSI at the receiver and can thus avoid the estimation error effect. We also investigate the DSTBC-SM performance under different mobile velocity in Figure 5.2, and it can be seen that the performance degrades with higher mobile velocity.
0 1 2 3 4 5 6 7 8
10−6 10−5 10−4 10−3 10−2 10−1 100
Eb/N
0
BER
DSTBC−SM STBC−SM (CE) STBC−SM (Perfect)
Figure 5.1: Comparison of BER performance for STBC-SM with perfect CSI, DSTBC-SM and STBC-DSTBC-SM with channel estimation error.
55
0 1 2 3 4 5 6 7 8 10−4
10−3 10−2 10−1 100
Eb/N 0
BER
100 km/hr 80 km/hr 50 km/hr 30 km/hr
Figure 5.2: BER performance of DSTBC-SM for different mobile velocity.
Chapter 6 Conclusion
Several issues associated with SM systems are investigated in this thesis. We first propose two channel estimators for time-varying SM channels. The decision-directed estimator gives good error-rate performance when SNR is not too high but exhibits error floor in high SNR regime. To overcome the error propagation effect, we propose a superimposed pilot-aided estimator which not only outperforms the decision-directed method but reduce the pilot overhead.
New SM schemes for dual-polarized antenna arrays are then presented, along with a modified channel estimator which takes into account the spatial correlations. The corre-sponding signal mapping and MF-based and ML detection techniques are proposed. We also suggest a suboptimal low-complexity detector which achieves near-ML performance.
Looking into the depolarization effect on the performance of these detectors, we find that considerable performance degradation incurs when the CPR value is small. On the other hand, large XPR values cause performance loss on the MF-based and suboptimal detectors but have little or no influence on the ML detector’s performance.
We also propose a differential STBC-SM scheme to relieve the burden of channel estimation requirement. The simulation result shows that it performs well in slow time-varying environments and outperforms the conventional STBC-SM with imperfect CSI knowledge.
Detailed studies on the feasibilities of various SM systems, including cost, complexity
57
and implementation losses have to be performed before the SM technology becomes a realistic design option. As has been mentioned, the spatial channels have to be dissimilar to a certain extent for the receiver to resolve the transmit antenna indices. We think there must be ways to make the equivalent MIMO subchannels as dissimilar as possible by proper signal design.
Finally, we notice that the SM scheme has recently been applied for high speed LED (array) communications where optical on-off keying is used. To enhance the throughput of such optical communication systems, higher-order modulations like PPM or PAM can be employed. In an indoor environment where multiple optical sources coexist, opti-cal interference must be considered and the associated interference-insensitive detection scheme has to be developed if LED communication systems are to become practical.
Appendix A
In order to find a set of basis for the null space matrix that can be used to separate superimposed pilots from data matrix, the choices of basis need to be satisfy a specific form. Since each column of the data matrix X(k) only has one nonzero element, it is not complicated to find the basis of its null space. We give the algorithm to solve this issue as follows.
, and define the B × M matrix Nx which consists of the null space basis of X and M = Nullity(X),
These two matrices satisfy the condition that XNx = 0. This is equal to solve a homogeneous system of linear equations:
nx1,jxi,1+ nx2,jxi,2+ · · · + nxB,jxi,B = 0, j = 1, · · · , M (3) where the bases are found by the rows of matrix X whose nonzero elements are larger than one. For each equation, we set the second variable with nonzero coefficient to 1 and solve the value of the first variable by setting other variables to zero and thus we can get one basis of the null space. Then the second variable with nonzero coefficient is set
59
to 0 and the third nonzero coefficient is set to 1 and solve the value of the first variable to get another basis. The rest can be done by the same manner until all coefficients are solved in one equation. By this way, we can get M basis of the null space for matrix X to form Nx.
For example, when a 4 × 4 BPSK data matrix is used,
X =
the corresponding Nx is
Nx=
Bibliography
[1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005.
[2] ˙I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecom-mun., vol. 10, no. 6, pp. 585–595, Nov., 1999.
[3] E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. V.
Poor, MIMO Wireless Communications., Cambridge University Press, 2007.
[4] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communi-cations, Cambridge University Press, 2003.
[5] V. Tarokh, N. Seshadri, and A. Calderbank, “Space-time codes for high data rate wireless communication: Performance criterion and code construction,” IEE Trans.
Inf. Theory, vol. 44, no. 2, pp. 744–765, Mar. 1998.
[6] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J., vol. 1, no. 2, pp. 41–59, Sep. 1996.
[7] R. Meslsh, H. Haas, S. Sinanovi´c, C. W. Ahn, and S. Yun, “Spatial modulation,”
IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2228–2241, Jul. 2008.
[8] M. D. Renzo and H. Haas, “Performance comparison of different spatial modulation schemes in correlated fading channels,” in Proc. IEEE ICC 2010, pp. 1–6, May 2010.
61
[9] M. D. Renzo, H. Haas, and P. M. Grant, “Spatial modulation for multiple-antenna wireless system: a survey,” IEEE Commun. Mag., vol. 49, no. 12, pp. 182–191, Dec.
2011.
[10] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Space shift keying modulation for MIMO Channels,” IEEE Commun. Mag., vol. 8, no. 7, pp. 3692–3703, Jul. 2009.
[11] F. A. Prisecaru and H. Hass. (2007) Mutual information and capacity of spatial modulation system., school of Engineering and Science Jacobs University, Germeny.
[Online]. Available: http://www.eecs.iu-bremen.de/archive/bsc-2007/prisecaru.pdf [12] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial modulation: Optimal
de-tection and performance analysis,” IEEE Commun. Lett., vol. 12, no. 8, pp. 545–547, Aug. 2008.
[13] M. D. Renzo, R. Meslsh, and H. Haas, “Sphere decoding for spatial modulation,”
in Proc. IEEE ICC 2011, pp. 1–6, Jun. 2011.
[14] M. Biguesh and A. B. Gershman, “Training-based MIMO channel estimation: A study of estimator tradeoffs and optimal training signals,” IEEE Trans. Signal Pro-cess., vol. 54, no. 3, pp. 884–893, Mar. 2006.
[15] P. Zhang, I. Dey, S. Sugiura and S. Chen, “Semi-blind adaptive space-time shift keying systems based on iterative channel estimation and data detection,” IEEE VTC 2011-Spring, pp. 1–5, May 2011.
[16] S. Sugiura, C. Xu, S. X. Ng, and L. Hanzo, “Reduced-complexity coherent versus non-coherent QAM-aided space-time shift keying,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3090–3101, Nov. 2011.
[17] T. Weichse and P. Eggers, “Simultaneous characterization of polarization matrix components in pico cells,” IEEE VTC 1999-Fall, vol. 3, pp. 1361–1365, Sep. 1999.
[18] A. S. Y. Poon and D. N. C. Tse, “Degree-of-freedom gain from using polarimetric antenna elements,” IEEE Trans. Inf. Theory, vol. 57, no. 9, pp. 5695–5709, Sep.
2011.
[19] C. Oestges, B. Clerckx, M. Guillaud, and M. Debbah, “Dual-polarized wireless com-munications: From propagation models to system performance evaluation,” IEEE Trans. Commun., vol. 7, no. 10, pp. 4019–4031, Oct. 2008.
[20] C. Oestges, V. Erceg, and A. J. Paulraj, “Propagation modeling of MIMO mul-tipolarized fixed wireless channels,” IEEE Trans. Veh. Technol., vol. 53, no. 4, pp.
644–654, May 2004.
[21] M. Coldrey, “Modeling and capacity of polarized MIMO channel,” IEEE VTC-Spring, pp. 440–444, May 2008.
[22] C. Degen and W. Keusgen, “Performance evaluation of MIMO systems using dual-polarized antennas,” in Proc. IEEE ICT 2003, vol. 2, pp. 1520–1525, Feb. 2003.
[23] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen,
“A stochastic MIMO radio channel model with experimental validation,” IEEE J.
Sel. Areas Commun., vol. 20, no. 6, pp. 1211–1226, Aug. 2002.
[24] W. Weichselberger, M. Herdin, H. ¨Ozcelik, and E. Bonek, “A stochastic MIMO channel model with joint correlation of both link ends,” IEEE Trans. Commun., vol.
5, no. 1, pp. 90–100, Jan. 2006.
[25] A. M. Sayeed, “Deconstructing multiantenna fading channels,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 2563–2579, Oct. 2002.
[26] W. Weichselberger, M. Herdin, H. ¨Ozcelik, and E. Bonek, “A stochastic MIMO channel model with joint correlation of both link ends,” IEEE Trans. Commun., vol.
5, no. 1, pp. 90–100, Jan. 2006.
63
[27] Y. C. Chen and Y. T. Su, “MIMO channel estimation in correlated fading environ-ments,” IEEE Trans. Commun., vol. 9, no. 3, pp. 1108–1119, Mar. 2010.
[28] E. Ba¸sar, ¨U. Ayg¨ol¨u, E. Panayırcı, and H. V. Poor, “Space-time block coded spatial modulation,” IEEE Trans. Commun., vol. 59, no. 3, pp. 823-832, Mar. 2011.
[29] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall PTR, 1998.
[30] G. Taricco and E. Biglieri, “Space-time decoding with imperfect channel estima-tion,” IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 359–383, Feb. 2002.
[31] L. Zheng and D. N. C. Tse, “Communication on the Grassman manifold: A ge-ometric approach to the noncoherent multiple-antenna channel,” IEEE Trans. Inf.
Theory, vol. 48, no. 2, pp. 359–383, Feb. 2002.
[32] F. B. Gross, “New approximation to ..0 and ..1 Bessel functions,” IEEE Trans.
Antennas Propag., vol. 43, no. 8, pp. 904–907, Aug. 1995.
[33] A. D. R. McQuarrie and C.-L. Tsai, Regression and Time Series Model Selection.
World Scientific, World Scientific, 1998.
[34] Tarokh V and Jafarkhani H, “A differential detection scheme for transmit diversity,”
IEEE J Sel. Areas Commun., vol. 18, pp. 1169–1174 , Jul. 2000.
[35] W. C. Jakes, Microwave Mobile Communications, New York: Wiley, 1974.
Autobiography
I graduated from National Chiao Tung University in Taiwan. Both my
Master’s and Bachelor’s degrees are in Communications Engineering. From a happy middle class family, my father is a civil servant and my mother is a house wife. My brother studies EE in National Sun Yat-Sen University in Taiwan.
For the past six years, I have studied well on some courses which have given me a foundation in several areas, such as Coding Theory, Wireless Communication, and Mobile Computing. Among those courses, I am most interested in signal
processing and communication systems.
During the two years of Master’s degree, I did my research in “Transmission and Networking Technologies Lab”, learning the advanced knowledge of
communication systems with Prof. Yu T. Su. When doing research, the most valuable thing I got was the skill of how to find useful resources efficiently, and solve
problems by myself.
After all, I am truly grateful to all the members of lab 811 and Prof. Yu T. Su . Without them, my life would not be so colorful.