Coding for Large Antenna Arrays in MIMO Networks

• US 20090262852A1
• Filed: 09/17/2008
• Published: 10/22/2009
• Est. Priority Date: 01/16/2008
• Status: Active Grant

• Current Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Inventors: Orlik, Philip V., Matsumoto, Wataru, Zhang, Jinyun, Molisch, Andreas F., Tao, Zhifeng
• Granted Patent: US 8,179,990 B2
• Time in Patent Office: Days
• US Class Current: 375/267
• CPC Class Codes: H04L 1/0606 Space-frequency coding
• CPC Class Codes: H04L 1/0631 Receiver arrangements
• CPC Class Codes: H04L 1/0662 Limited orthogonality systems
• CPC Class Codes: H04L 1/1816 with retransmission of the same, encoded, message
• CPC Class Codes: H04L 1/1819 with retransmission of additional or different redundancy
• CPC Class Codes: H04L 1/1845 Combining techniques, e.g. code combining

Abstract

A method transmits a sequence of symbols in a multiple-input multiple-output (MIMO) network including a transmitter having a set of transmit antennas and a receiver having a set of receive antennas. The sequence of symbols is represented by a vector S=[S₁ S₂ S₃ S₄]^T of individual symbols, where T is a transpose operator. The individual symbols are transmitted as a transmit matrix

$S=\left[\begin{array}{cccc}{S}_1& -S_2^{*}& S_1& -S_2^{*}\\ S_2& S_1^{*}& S_2& S_1^{*}\\ S_3& -S_4^{*}& -S_3& S_4^{*}\\ S_4& S_3^{*}& -S_4& -S_3^{*}\end{array}\right],$

where * is a complex conjugate, and wherein each column of the matrix S represents the symbols transmitted at each transmission interval, and subscripts index the set of transmit antennas.

Claims

1. A method for transmitting a sequence of symbols S, in a multiple-input multiple-output (MIMO) network including a transmitter having a set of transmit antennas and a receiver having a set of receive antennas, comprising the steps of:

representing the sequence of symbols by a vector S=[S₁ S₂ S₃ S₄] of individual symbols, where T is a transpose operator; and

transmitting the individual symbols as a transmit matrix is

$S=\left[\begin{array}{cccc}{S}_1& -S_2^{*}& S_1& -S_2^{*}\\ S_2& S_1^{*}& S_2& S_1^{*}\\ S_3& -S_4^{*}& -S_3& S_4^{*}\\ S_4& S_3^{*}& -S_4& -S_3^{*}\end{array}\right],$

where * is a complex conjugate, and wherein each column of the matrix S represents the symbols transmitted, and subscripts index the set of transmit antennas.

3. The method of claim 1, further comprising:

detecting and decoding after all columns of symbols have been received at a receiver.

4. The method of claim 1, wherein the receiver has a channel matrix

$H=\; <li></li>\left[\begin{array}{cccc}{h}_{1,1}& h_{1,2}& h_{1,3}& h_{1,4}\\ h_{2,1}& h_{2,2}& h_{2,3}& h_{2,4}\\ h_{3,1}& h_{3,2}& h_{3,3}& h_{4,4}\\ h_{4,1}& h_{4,2}& h_{4,3}& h_{3,4}\end{array}\right],$

where elements h_i,j are channel coefficients from the j^th transmit antenna to the i^th receive antenna.

5. The method of claim 4, wherein a received signal r is

$\hspace{1em}$

r = 

HS + n = 

[ h 1 , 1 h 1 , 2 h 1 , 3 h 1 , 4 h 2 , 1 h 2 , 2 h 2 , 3 h 2 , 4 h 3 , 1 h 3 , 2 h 3 , 3 h 3 , 4 h 4 , 1 h 4 , 2 h 4 , 3 h 4 , 4 ] 

[ S 1 - S 2 * S 1 - S 2 * S 2 S 1 * S 2 S 1 * S 3 - S 4 * - S 3 S 4 * S 4 S 3 * - S 4 - S 3 * ] + n ,

where noise n is

$n=\left[\begin{array}{cccc}{n}_{1,1}& n_{1,2}& n_{1,3}& n_{1,4}\\ n_{2,1}& n_{2,2}& n_{2,3}& n_{2,4}\\ n_{3,1}& n_{3,2}& n_{3,3}& n_{3,4}\\ n_{4,1}& n_{4,2}& n_{4,3}& n_{4,4}\end{array}\right].$

6. The method of claim 5, further comprising:

setting a received signal

$r=\left[\begin{array}{cccc}{r}_{1,1}& r_{1,2}& r_{1,3}& r_{1,4}\\ r_{2,1}& r_{2,2}& r_{2,3}& r_{2,4}\\ r_{3,1}& r_{3,2}& r_{3,3}& r_{3,4}\\ r_{4,1}& r_{4,2}& r_{4,3}& r_{4,4}\end{array}\right],$

and

the first symbol S₁ is

$\left[r_{1,1}<br><br><br><br>r_{1,2}^{*}<br><br><br><br>r_{1,3}<br><br><br><br>r_{1,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{1,1}^{*}\\ h_{1,2}\\ h_{1,1}^{*}\\ h_{1,2}\end{array}\right]+\left[r_{2,1}<br><br><br><br>r_{2,2}^{*}<br><br><br><br>r_{2,3}<br><br><br><br>r_{2,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{2,1}^{*}\\ h_{2,2}\\ h_{2,1}^{*}\\ h_{2,2}\end{array}\right]=2<br><br>\left({<br><br>h_{1,1}<br><br>}^2+{<br><br>h_{1,2}<br><br>}^2+{<br><br>h_{2,1}<br><br>}^2+{<br><br>h_{2,2}<br><br>}^2\right)<br><br>S_1^{*}+n_1^{\mathrm{\prime <br><br>}}$

the second symbol S₂ is

$\left[r_{1,1}<br><br><br><br>r_{1,2}^{*}<br><br><br><br>r_{1,3}<br><br><br><br>r_{1,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{1,2}^{*}\\ -h_{1,1}\\ h_{1,2}^{*}\\ -h_{1,1}\end{array}\right]+\left[r_{2,1}<br><br><br><br>r_{2,2}^{*}<br><br><br><br>r_{2,3}<br><br><br><br>r_{2,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{2,2}^{*}\\ -h_{2,1}\\ h_{2,2}^{*}\\ -h_{2,1}\end{array}\right]=2<br><br>\left({<br><br>h_{1,1}<br><br>}^2+{<br><br>h_{1,2}<br><br>}^2+{<br><br>h_{2,1}<br><br>}^2+{<br><br>h_{2,2}<br><br>}^2\right)<br><br>S_2+n_2^{\mathrm{\prime <br><br>}}$

the third symbol S₃ is

$\left[r_{3,1}<br><br><br><br>r_{3,2}^{*}<br><br><br><br>r_{3,3}<br><br><br><br>r_{3,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{3,3}^{*}\\ h_{3,4}\\ -h_{3,3}^{*}\\ -h_{3,4}\end{array}\right]+\left[r_{4,1}<br><br><br><br>r_{4,2}^{*}<br><br><br><br>r_{4,3}<br><br><br><br>r_{4,4}^{*}\right]<br><br>\left[\begin{array}{c}{h}_{4,3}^{*}\\ h_{4,4}\\ -h_{4,3}^{*}\\ -h_{4,4}\end{array}\right]=2<br><br>\left({<br><br>h_{3,3}<br><br>}^2+{<br><br>h_{3,4}<br><br>}^2+{<br><br>h_{4,3}<br><br>}^2+{<br><br>h_{4,4}<br><br>}^2\right)<br><br>S_3+n_3^{\mathrm{\prime <br><br>}}$

and the fourth symbol S₄ is

7. The method of claim 5, wherein the sequence of symbols is

S=[S₁ S₂ S₃ S₅ S₆ S₇ S₈], and the transmit matrix is

$S=$

[ S 1 - S 2 * S 5 - S 6 * S 2 S 1 * S 7 - S 8 * S 3 - S 4 * S 6 S 5 * S 4 S 3 * S 8 S 7 * 

S 1 - S 2 * S 5 - S 6 * S 2 S 1 * - S 7 S 8 * - S 3 S 4 * S 6 S 5 * - S 4 - S 3 * - S 8 - S 7 * ] ,

and

the received signal is

$\hspace{1em}<br><br>\begin{array}{c}r=<br><br>\mathrm{HS}+n\\ =<br><br>\left[\begin{array}{cccc}{h}_{1,1}& h_{1,2}& h_{1,3}& h_{1,4}\\ h_{2,1}& h_{2,2}& h_{2,3}& h_{2,4}\\ h_{3,1}& h_{3,2}& h_{3,3}& h_{3,4}\\ h_{4,1}& h_{4,2}& h_{4,3}& h_{4,4}\end{array}\right]\\ <br><br>\left[\begin{array}{cccc}{S}_1& -S_2^{*}& S_5& -S_6^{*}\\ S_2& S_1^{*}& S_7& -S_8^{*}\\ S_3& -S_4^{*}& S_6& S_5^{*}\\ S_4& S_3^{*}& S_8& S_7^{*}\end{array}<br><br>\begin{array}{cccc}{S}_1& -S_2^{*}& S_5& -S_6^{*}\\ S_2& S_1^{*}& -S_7& S_8^{*}\\ -S_3& S_4^{*}& S_6& S_5^{*}\\ -S_4& -S_3^{*}& -S_8& -S_7^{*}\end{array}\right]+n^{\mathrm{\prime <br><br>}}\end{array}$

where noise is

$n=\left[\begin{array}{ccccccc}{n}_{1,1}& n_{1,2}& n_{1,3}& n_{1,4}<br><br>n_{1,5}& n_{1,6}& n_{1,7}& n_{1,8}\\ n_{2,1}& n_{2,2}& n_{2,3}& n_{2,4}<br><br>n_{2,5}& n_{2,6}& n_{2,7}& n_{2,8}\\ n_{3,1}& n_{3,2}& n_{3,3}& n_{3,4}<br><br>n_{3,5}& n_{3,6}& n_{3,7}& n_{3,8}\\ n_{4,1}& n_{4,2}& n_{4,3}& n_{4,4}<br><br>n_{4,5}& n_{4,6}& n_{4,7}& n_{4,8}\end{array}\right].$

8. The method of claim 1, wherein each successive column is transmitted at each transmission interval.

9. The method of claim 1, wherein each successive column is transmitted on adjacent sub-carriers using space-frequency block coding.

2. The method of claim 2, wherein the columns are transmitted as a stream of symbols before any feedback from a receiver is expected.