Maximum ratio merging (MRC) analysis in wireless communication

The maximum ratio merging is the best choice in the diversity merging technique, and the better performance is obtained relative to the combination of select merging and equal gain, and the performance improvement is determined by the higher signal-to-noise ratio brought by array gain, which leads to better BER characteristics.

The implementation of the maximum ratio merge (maximal Ratio combining) is achieved by multiplying the N-way signals of the diversity by a different coefficient wi, i=1,2,......, N, the coefficients are determined with the fading coefficients of the N-way branch HI, i=1,2 ,......, N related. Usually have 650) this.width=650; "src=" Http://s3.51cto.com/wyfs02/M02/6F/12/wKiom1WQ-i6SMG5NAAAeSBSGGk4481.jpg "title= Capture. PNG "alt=" wkiom1wq-i6smg5naaaesbsggk4481.jpg "/>

The following is a proof of why the maximum ratio merger is the optimal merging scheme.

As described above, consider a AWGN channel, wherein the transmit symbol power is ES, the noise power spectral density of N0,n strip path of the fading coefficient is Hi, i=1,2,......, N, the combined weighting coefficient is wi, i=1,2,......, N.

The receiver and the signal-to-noise ratio are

650) this.width=650; "src=" http://s3.51cto.com/wyfs02/M01/6F/12/wKiom1WQ-g2w5oTPAACotDpF2fQ224.jpg "title=" capture. PNG "alt=" Wkiom1wq-g2w5otpaacotdpf2fq224.jpg "/>

If you need the most Snr, you need to take 650) this.width=650; "Src=" http://s3.51cto.com/wyfs02/M02/6F/0E/wKioL1WQ_ D6shvtzaaaohscpppw048.jpg "title=" capture. PNG "alt=" wkiol1wq_d6shvtzaaaohscpppw048.jpg "/> Maxima, which is biased by the SNR to WI and makes the bias 0 available:

650) this.width=650; "src=" http://s3.51cto.com/wyfs02/M02/6F/12/wKiom1WQ-w7CFUDbAAA3K1vgHQA266.jpg "title=" capture. PNG "alt=" wkiom1wq-w7cfudbaaa3k1vghqa266.jpg "/> after simplification, there are the following formulas:

650) this.width=650; "src=" http://s3.51cto.com/wyfs02/M01/6F/0E/wKioL1WQ_UDjQ4eqAAA7MD0ev-4007.jpg "title=" capture. PNG "alt=" Wkiol1wq_udjq4eqaaa7md0ev-4007.jpg "/>

When analyzing I=1 and i=2, two formulas are compared to the difference:

650) this.width=650; "src=" http://s3.51cto.com/wyfs02/M01/6F/12/wKiom1WQ--uhvlZRAABIsNyAVSY871.jpg "title=" capture. PNG "alt=" Wkiom1wq--uhvlzraabisnyavsy871.jpg "/>

Therefore, the maximum ratio of the letter to noise is the combination of MRC merger.

Note: The above content is from Baidu Library "maximum ratio merger can obtain the maximum signal to noise ratio proof"

Continue to analyze at this time and signal to noise ratio snr, may make 650) this.width=650; "Src=" http://s3.51cto.com/wyfs02/M02/6F/0F/wKioL1WQ_ Ghbyqohaaatcj9zwfa723.jpg "title=" capture. PNG "alt=" wkiol1wq_ghbyqohaaatcj9zwfa723.jpg "/>, where C is a constant, so the SNR can be rewritten as:

650) this.width=650; "src=" http://s3.51cto.com/wyfs02/M01/6F/0F/wKioL1WQ_yfSgv6bAADa7JDLvqY534.jpg "title=" capture. PNG "alt=" Wkiol1wq_yfsgv6baada7jdlvqy534.jpg "/>

For each branch of the signal-to-noise ratio of the sum.

This article is from "Miao Han Dahan" blog, please make sure to keep this source http://double4tar.blog.51cto.com/9394773/1669061

Maximum ratio merge (MRC) analysis in wireless communication