Chapter 4 Applications of the Sphere Decoder in Space-Time-Frequency code
4.4 Space Time Frequency Coding
So, we can decode full diversity SFBC by using the sphere decoder.
4.4 Space Time Frequency Coding
In this section, we will examine space time frequency (STF) codes to see are they suitable for the sphere decoder. Assume the information symbols
I I
x1 1,..., N N
s=⎡⎣s s ⎤⎦∈C and X is the space time frequency codeword comprises
symbols ( )xnµ p with µ∈
[
1,NT]
, n∈[
0,Nx− , and 1]
p∈[
0,Nc− . Where 1]
NT denotes the number of transmit-antenna, N OFDM blocks, and x N subcarriers. c Each STF codeword contains NT x N N symbols. Figure 4.1 shows the STF x cFigure 4.2 Space Time Frequency codes [17]
Assume X denotes X =
[
X(0),X(1),...,X N( c −1)]
∈CN N NT c x and for eachAnd in each subcarrier, the channel is flat fading MIMO channel.
T
And the received matrix Y p( )∈CN NR T with entries
[
Y p( )]
νn = ynµ( )p , we can write the input-output relationship at pth subcarrier as[ ]
For example, there are four subcarriers, two transmit antennas, and two receive-antennas. We can rewire (4.32) into matrix form as:
(0) (0) 0 0 0 (0) (0)
0 is the zero matrix with size 2x2 and we can rewrite (4.33) as Y=HX+W. This can be decoded by the sphere decoder but if the number of subcarriers is too large (512, 1024, 2048) the matrix size is to large to decoded. Therefore, subcarrier grouping STF codes is the way to reduce dimension. Suppose the number of subcarriers is an integer multiple of the channel length.
( 1)
c g
N =N L+ (4.34)
N is the number of groups and L is the channel order. And the information symbol g
used in this group is { }sg g Ng==0g−1 which is divided from original information symbol
1,..., NI T
s= ⎣⎡s s ⎤⎦ . The codeword of the grouped STF code is
( 1)
From (4.36) we can decode grouped STF codes in a smaller dimension by the sphere decoder.
4.5 Discussion
In the chapter, we discuss ST, SF, STF codes at flat fading and frequency selective fading channels and derive the general form of input-output relationship. We find that the sphere decoder can detect the following codes at different channels:
1. Space time block codes at flat fading and frequency selective fading MIMO channel.
2. Space frequency codes on MIMO-OFDM systems at frequency selective fading channel and flat fading channel.
3. Space time frequency codes at frequency selective fading channel.
4. Grouped Space time frequency codes in order to reduce the decoder complexity.
Chapter 5
Conclusion and Future Work
This thesis has analyzed the implementation of the sphere decoder on Quixote DSP board in Rayleigh flat fading MIMO systems. And we compare the implementations of the sphere decoding on DSP, FPGA, and ASIC to find out a suitable hardware structure for our Quixote DSP board. Finally, we discuss the applications of the sphere decoder on space-time-frequency codes in MIMO-OFDM systems. The main conclusions can be summarized as:
The BER performance of the sphere decoder with full precision and brute-force decoder are the same.
This sphere decoder we implemented is faster than brute-force method about 120 times when high SNR and 50 times when low SNR under 2x2 MIMO systems.
The fixed point implement can result BER performance degradation at high SNR.
Since there are one TI DSP chip and one Xilinx Virtex-II FPGA on this Quixote DSP board, we proposed a hardware structure to realize the sphere decoder.(Figure 3.12)
The sphere decoder is suitable to decode space-time-frequency on MIMO-OFDM systems under Rayleigh flat fading and frequency selective fading channel.
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簡歷：
姓名：林帛諺
生日：民國七十一年四月八日 學歷：
國立交通大學電子工程研究所碩士班 畢業 2005.9 ~ 2007.11 國立成功大學工程科學系 畢業 2000.9 ~ 2005.6 台北市立成功高級中學 畢業 1997.9 ~ 2000.6