Figure 3.6: The structure of the proposed Constrained TST-MUSIC
3.4 Simulation
Some simulations are conducted in this section to assess the proposed approach.
Assume two users are in this system, which are transmitted through four rays and one rays, respectively, and received by a five-element uniform linear array. In the basic setup, the DOAs of the first user are set to be [−43
o
,27o
,−40o
,30o
], and the propagation delays are set to be [.03, .1, .86, .94]Ts
, where Ts
is the chip period whereas the DOA and delay of the other user are 0o
and 0.5Ts
, respectively. The average fading amplitudes of the all rays are equal and normalized to 0 dB.Three algorithms are carried out for comparison, including the tree-structured MUSIC in [14], the algorithm in [13] and the proposed one, constrained TST-MUSIC, referred to as the CTST. For a clear illustration, only the average of the root-mean-square-error (RMSE) of the DOA and the delay estimates for all of the users are provided, as shown in Figs. 3.2 and 3.3. 250 symbols are employed to estimate the temporal and spatial covariances. For each specific SNR, 200 Monte Carlo trials are carried out.
We can note from Figs. 3.7 and 3.8 that the proposed CTST outperforms [14]
in both of the DOA and delay estimates in all of the scenarios. The is due to the fact that the constrained filtering approach, which designs the filters in a statistical approach, enables the tree-structured algorithm to be more robust against the
propagation errors. The improvement is most pronounced in the DOA estimates as the employed delays in the S-MUSIC is the roughest one and the inaccuracy of such estimates will substantially influence the succeeding DOA estimates. Also, the proposed one outperforms [13] in most of the scenarios, but slightly inferior for high SNR cases. This can be explained by the fact that the dimension of the covariance matrices employed is much smaller than that of [13]. It has been observed that there will be less degradation as the number of antennas increases. The new algorithm thus provides an appealing candidate for the joint DOA-delay estimation problem in view of the superior performance it can offer and the computational complexity it calls for.
In order to alleviate the computational complexity, we conduct the ESPRIT algorithm instead of the MUSIC algorithm. Thus we have the constrained TST-ESPRIT algorithm. In addition, we can also consider the constrained STS algo-rithm which perform the DOA estimation first. Fig 3.9 and Fig 3.10 illustrate the comparison of the various algorithms. These algorithm include constrained TST-MUSIC(CTST-MUSIC), constrained TST-ESPRIT(CTST-ESPRIT), constrained STS-MUSIC(CSTS-MUSIC) and constrained STS-ESPRIT(CSTS-ESPRIT). We get that the STS algorithms outperform the TST algorithm. The reason is that the Vandermonde structure of spatial signature is better than the counterpart of temporal signature under our scenario.
Fig 3.11 and Fig 3.12 illustrate the comparison of the CTST-ESPRIT and JADE-ESPRIT. We can observe that the more antennas the array consists, the better the performance gets. And it’s can be seen that the CTST-ESPRIT out-perform JADE-ESPRIT for both DOA and delay estimation. We have the idea that when the pointing error is small, orthogonal projection filtering will perform better than constrained filtering. But when the pointing error become remark-able, the constrained filtering method will outperform the orthogonal projection filtering due to its inherited robustness for pointing error.
-2 0 2 4 6 8 10 12 10 -4
10 -3 10 -2 10 -1
SNR(dB)
RMSE(rad)
[2] [5]
CTST
Figure 3.7: Comparison of the DOA estimation for various algorithms
-2 0 2 4 6 8 10 12
10 -3 10 -2 10 -1 10 0
SNR(dB)
RMSE(Tc)
[2] [5]
CTST
Figure 3.8: Comparison of the delay estimation for various algorithm
9 : : :
Figure 3.9: Comparison of the delay estimation for various algorithm
¾9¿ ¾qÀ ¾HÁ ¾q à  Á À ¿ Äà ÄÅÂ
Figure 3.10: Comparison of the DOA estimation for various algorithm
ë9ì ëqí ëHî ëqï ð ï î í ì ñð ñòï
Figure 3.11: Comparison of the delay estimation for various algorithm
#%$ #'& #)( #'* + * ( & $ ,-+ ,.*
Figure 3.12: Comparison of the DOA estimation for various algorithm
Chapter 4
CONCLUSIONS
Theoretically, the tree-structured algorithm can surely proceed infinitely, but we observed that three layers are in general yield sufficient precise estimates. In this project addresses a tree-structured MUSIC, which employs two T-MUSIC algo-rithms and one S-MUSIC algorithm aletrnatively along with a temporal filtering process and a spatial beamforming process to assist isolating the incoming rays into appropriate groups to enhance the estimation accuracy of the MUSIC algorithms.
The simulation results show that the new approach offers comparable performance as previous ones but the computational complexity is substantially reduced.
In downlink (base station to mobile) scenario, all users’ symbol are com-bined into a path. The downlink model is blind because each mobile knows only its spreading code. As such, the S-MUSIC algorithm can still work well, but the T-MUSIC algorithm will deteriorate due to insufficient information for all users’
spreading code. If we conduct T-MUSIC first, the symbols (temporal structure) will be impaired first, and the succeeding procedure will degrade. Hence the per-formance will deteriorate a bit due to partial information. In order to get better performance, we user the STS-MUSIC algorithm in downlink model instead of TST-MUSIC counterpart. Thus we can conclude that the STS-MUSIC algorithm will provide better performance in the downlink model due to the S-MUSIC algo-rithm first will not impair the symbol structure.
The tree-structured based algorithm concepts therefore can be extended to different fields. Further research can be done by extending the propsed tree-structured approach to the joint estimation of the directions of arrival (DOAs) and frequencies of arrival (FOAs) in wireless communication systems.
We can also apply the tree-structured based algorithm concepts to two-dimensional (2-D) directions of arrival (DOAs) problem. The 2-D DOA problem has the inherited essentials which is similar to joint DOAs and FOAs problem as mentioned above. In addition. In another application, the arrival directions and the polarizations of incoming plane waves with a uniform linear array of crossed dipoles can also tried to be estimated by the tree-structured based algorithm.
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