CHAPTER 4 COMPLEXITY REDUCTION
C. S UMMARY OF THE C LUSTER -B ASED A LGORITHM WITH C OMPLEXITY
Complexity Reduction Version
We summarize the proposed cluster-based algorithm with complexity reduction version in serial of steps as follows:
1) Compute the MMSE output ˆxMMSE and perform phase detection to obtain the candidate nodes in first layer of multilevel tree.
2) For layer = −L 1, , 2
i) Collect the nodes which extended from the candidate node in upper layer as a search set ∏
ii) Compute the radius constraint γ according Eq. (4)
iii) Collect the nodes whose D x( , i) are less than radius constraint by branch and bound search strategy ( B=γ).
iv) Sort the nodes collected by step 2.iii, and select the K best nodes as candidate nodes.
3) For detail matching (=1),
i) Collect the nodes which extended from the candidate node in layer 2 as a search set ∏L
ii) Find the node which has the smallest distance metric by branch and bound search strategy.
Chapter 5
Simulation Results
A typical MIMO-OFDM system is based on IEEE 802.11n Wireless LANs, TGn Sync Proposal Technical Specification [10] which is used as the reference design platform. The simulation model is mainly based on TGn multipath specification of mode E, which is the multipath fast-fading channel model of 15-taps and 100ns Root Mean Square (RMS) delay. The major simulation parameters are shown in Table 1
Table 1 Simulation parameters
Parameter Val ue
Number of antennas 3Tx and 3Rx,
4Tx and 4Rx
Signal bandwidth 20 MHz
Number of subcarrier 52
Subcarier modulation 64 QAM
Packet size 1024 (Bytes)
FEC coding rate 2/3
Channel Model TGn E type
Number of taps 15
RMS delay spread 100 nsec
The proposed cluster-based detection algorithm has two levels in cluster matching and needs to sort cluster candidates in the cluster matching stage. The cluster candidate number is critical for detection complexity and detection precision. Consequently, the approach applies a branch and bound strategy to reduce the number and a sorting
strategy to fix cluster candidate number. The fast phase decision method is another way to reduce cluster candidates number. Since the fast phase decision method has fixed candidate number in the first cluster matching stage, it only needs to select cluster candidate in the second stage. However, the phase decision method suffers from signal distortion in large number of antennas. Thus the proposed cluster-based with three phase decision method can mitigate the error detection. This section compares performance and complexity between different detection methods in MIMO detection.
Note that the performance comparison is considered under packet error rate 0.08 and normalizes to the ML detection methods.
A. Performance Evaluation
For the purpose of performance comparison, the performance of various MIMO detection methods is considered. Fig. 5 and Fig. 6 present the PER for 3 x 3 and 4 x 4 MIMO-OFDM systems. As can be seen from the figure, there is a large gap between the linear and nonlinear MIMO detection methods. The nonlinear detection methods such as the proposed Cluster-based method and K-best sphere decoder maintain SNR degradation within 0.4dB in the Fig. 5 and 0.2dB to 0.45dB in the Fig. 6
The table 2 summarizes the performance and the performance is normalized to ML detection method. The proposed cluster method can maintain performance within 0.45dB such that the method is suitable for practical system.
Table 2 Summaries performance comparison for various detection methods
Method
Fig. 5 PER of various detection methods for 64-QAM modulated 3 x 3 MIMO-OFDM systems
Fig. 6 PER of various detection methods for 64-QAM modulated 4 x 4 MIMO-OFDM systems
PER 0.08
0.4 dB
0.45 dB PER 0.08
Since K-best sphere decoder was accepted as practical, the target of cluster-based detection is complexity reduction and remains performance. For the purpose of complexity comparison between the K-best sphere decoder and the cluster-based methods, we tune K-best parameter: k and cluster parameter: candidate number such that different methods have nearly the same performance.
Fig. 7 and Fig. 8 compare cluster-based detection method and cluster-based phase detection method with K-best sphere decoder.
Observing from the Fig. 7, there is only near 4 dB SNR degradation for cluster-based method, cluster-based with phase decision method and K-best sphere decoding method. To take account of the complexity, the cluster-based with two phase decision method need fewer candidates than the cluster-based with three phase decision method, 8 candidates in phase decision stage and 64 candidates in second level cluster matching stage, to remain the same performance.
Observing from the Fig. 8, cluster-based with two phase decision approach can’t remain performance within 0.45 dB. Therefore, cluster-based with three phase detection method is better candidate for 4 x 4 MIMO-OFDY system.
Fig. 7 PER of phase decision methods for 64-QAM modulated 3 x 3 MIMO-OFDM systems
Fig. 8 PER of phase decision methods for 64-QAM modulated 4 x 4 MIMO-OFDM systems
PER 0.08 PER 0.08
B. Complexity Comparison
The table 3 summarizes the performance and compares sorting operation among these methods. Assume heap sort operation is used and then it needs Nlog2N sorting operations to sort N element. The table shows that sorting operation in cluster-based methods has complexity reduction ranges from 7.37% to 21.5% in 3 x 3 MIMO-OFDM system and 29.76% to 76.8% in 4 x 4 MIMO-OFDM system.
Table 3 Complexity comparison between K-Best SD, CBD, CBD with 2 phase decision and CBD with 3 phase decision
Method
3 x 3 MIMO-OFDM system
ML K-Best SD
4 x 4 MIMO-OFDM system
ML K-Best SD
Chapter 6 Conclusions
This work presents a near ML performance, low-complexity cluster-based MIMO detection design, which use fast phase decision and branch and bound method to reduce the need of system hardware for MIMO-OFDM wireless accesses.
Simulations and measurements indicate that the proposed scheme can achieve 8%
PER with about 0.45 dB SNR loss compared with MLD in frequency-selective fading of TGn E channel [10]. Without any specific preamble, pilot format and STBC coding, this cluster-based MIMO detection method for 4×4 MIMO-OFDM systems can provide near ML performance with relatively low complexity. This study does not only derive an efficient solution for OFDM-based MIMO receivers, but is also well-suited for next-generation wireless LAN discussed in IEEE 802.11 VHT study group.
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