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the sake of simplicity in SDR implemetations. Nonetheless noise from all the antenna branches can be combined according to MRC. 3 Obtain LLR corresponding to i th subcarrier from Y MRC ( i ) and scale them using σ 2 Avg ( i ) , which is i th element of the vector σ 2 Avg , as follows: ( i , l ) = min z Z l 0 Y MRC ( i ) ( | H X 1 ( i ) | 2 + | H X 2 ( i ) | 2 ) z 2 σ 2 Avg ( i ) min z Z l 1 Y MRC ( i ) ( | H X 1 ( i ) | 2 + | H X 2 ( i ) | 2 ) z 2 σ 2 Avg ( i ) (15) For a dual antenna WiFi receiver, the schematic of MLSC is illustrated in Fig. 8 . 3 Proposed method Since our major focus in this work is to implement our interference mitigating methods using SDR and test their practical applicability, in this section, we chose and ana- lyze easy to implement alternatives of MLSC without compromising with the performance. 3.1 Soft-bit maximal-ratio combiner The idea behind the usage of MRC in MLSC is to achieve diversity gain apart from interference mitigation. Conven- tional MRC, as discussed in Section 2.2.2 , is a Symbol Level Diversity Combiner where the bit metrics are gen- erated after the complex samples are combined from different antenna branches. Although, simulation results in [ 10 ] showed the effectiveness of MLSC; however, a working module of MRC for WiFi is not available in GNU Radio WiFi package [ 35 ]. A somewhat different but simpler way to perform diversity combining, which is more popular in distributed systems, is soft-bit maximal-ratio combining (SBMRC) [ 36 , 37 ]. In contrast to the conventional MRC which combines complex samples obtained from the different antenna branches, an SBMRC combines the LLRs from individual antenna branches. In SBMRC, the combination of bit metrics from different antenna branches, applying maximum likelihood decoding, is performed according to [ 36 , Eq. 11 ] as follows: S p , l , i min z Z l p ( || Y 1 ( i ) H X 1 ( i ) z || 2 ) σ 2 (16) + min z Z l p ( || Y 2 ( i ) H X 2 ( i ) z || 2 ) σ 2 where S p , l , i is the combined bit metrics corresponding to i th subcarrier of l th bit and p could be 0 or 1. Expres- sion of Eq. 16 is nothing but an addition of bit metrics of l th bit corresponding to i th subcarrier from the two antenna branches. Hence, diversity combining can be real- ized by adding the LLRs from the two antenna branches, i.e, ( i , l ) SBMRC = ( i , l ) 1 + ( i , l ) 2 (17) where ( i , l ) 1 and ( i , l ) 2 are LLRs of l th bit and i th OFDM subcarrier corresponding to antenna branch 1 and 2, respectively. ( i , l ) SBMRC is further fed to SDVD. Achieving diversity combining by just adding the LLRs simplifies the way it can be implemented in SDR software. In the simulation section, we see that the performance of SBMRC is equivalent to MRC for all the experimented Fig. 8 Schematic of proposed MLSC for 2-antenna WiFi receiver
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Kumar et al. EURASIP Journal on Wireless Communications and Networking (2019) 2019:224 Page 10 of 21 WiFi MCS under the same channel conditions. The reason being MRC attempts to maximize the SNR of the com- plex samples obtained from multiple antennas which in turn makes LLRs more strong; in contrast, SBMRC tries to maximize the LLRs directly as explained in [ 36 ]. In the fol- lowing, we discuss our method to implement MLSC using SBMRC.
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  • IEEE 802.11, Diversity combining

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