Page 88 - Kaleidoscope Academic Conference Proceedings 2021

2021 ITU Kaleidoscope Academic Conference

Figure 1 – Comparison of MSE vs. SNR for the proposed Figure 2 – MSE performance vs. SNR for the proposed
SBL, LS and BCS. SBL with optimal pilot design and the proposed SBL with
non-optimal pilot.
%×" ! is an arbitrarily unitary matrix. Based on
where V ∈ C
the procedure in [21], the resulting A needs to be scaled up
¢
by

r
? A
Z = . (24)
Tr A ¢) A ¢
In order to satisfy the power constraint of (17). The steps to
obtain optimal pilot design is summarized in the following
algorithm.

The Proposed Optimal Pilot Design Algorithm
1. Inputs: ? A , U 1 , W , H 1 ;
¢
2. Solve (20) to attain L ;
¢
¢
3. Execute the eigen-value decomposition of L as L = QΛQ ;

√ √ √
4. A = V diag{ _ 1 , _ 2 , · · · , _ ! } Q ;
¢

q
5. Z = ? A ;
Tr(gA ¢) A ¢ )
6. Outputs: A ← Z A .
¢
¢
ˆ
Thus, the new estimate of the channel and the MSE with the Figure 3 – MSE performance vs. pilot length for the proposed
h
¢ SBL with optimal pilot design and the proposed SBL with
optimal pilot design can be obtained by substituting A in
(11) and (12) , respectively. non-optimal pilot.
5. SIMULATION RESULTS
proposed method can enhance the estimation accuracy much
In this section, we conduct experiments to evaluate the further. Thus, we can achieve better estimation accuracy
performance of the proposed algorithm and compare it with the appropriate pilot length, and as a result of that,
to existing methods. The simulation parameters can be the pilot overhead problem of FDD massive MIMO systems
summarized as follows, " = 100 antennas, # = 10 users, can be addressed with proper design for the pilot length.
! = 10 taps and = 128 subcarriers. The simulation results Figure 3 investigates the robustness of the proposed method
are obtained by averaging over 1000 channel realizations. against the pilot length for the proposed SBL with optimal and
Figure 1 compares the MSE versus SNR for the proposed non-optimal design, where the average power ? A is set to be
SBL, the conventional Least Square (LS) estimation and 25 dB. The results demonstrate the efficacy of the proposed
Bayesian Compressed Sensing (BCS) [22]. The results show optimal design approach of reducing the pilot length.
that the proposed method can achieve the lowest MSE values
by better exploiting the channel priors of the channel sparsity 6. CONCLUSION
and the temporal correlation. Figure 2 shows the MSE versus
the SNR for the proposed SBL algorithm with non-optimal In this paper, we proposed an ML-based channel estimation
design against the SBL algorithm with optimal pilot design. algorithm for FDD massive MU-MIMO systems. The
It can be observed that by employing the optimal pilot, the simulation results revealed that the ML-based channel

– 26 –