$5.$ Alamouti Coded OFDM Consider an Alamouti$-$coded OFDM system with two transmit and one receive antennas. Consider symbols X $1,2$ respectively on the k th $1($k$),$ X $2($k$)$ loaded onto transmit antennas subcarrier of the OFDM system in the first OFDM symbol. Consider a frequency$-$selective channel with channel taps h$(0),$ h$(1),...,$h$($L $1).$ Answer the questions that follow. $($a$)$ Describe the operation of the Alamouti$-$coded OFDM system above, i$.$e$.,$ the transmission on each subcarrier and the decoding operation at the receiver. $($b$)$ If the transmitpower is P per subcarrier, noise power $2$ n $,$ findtheinstantaneousreceive SNRexpression for each symbol. OrthogonalFrequency$-$DivisionMultiplexing $265($c$)$Consideringthechannel tapstobeIIDRayleighrandomvariablesofaveragepower unity,derivetheaverageSymbolErrorRate$($SER$)$expressionsforBPSKand$16-$PSK modulation. $($d$)$ComputetheaverageSERaboveforbothBPSKand$16-$PSKforP$=35$dB$,$number ofsubcarriersN$=128,$L$=5,$andnoisepower$2$ n$=3$dB$.($e$)$ConsideringthechanneltapstobeindependentRayleighrandomvariablesofaverage power$2$ l $,0$l$$L$1,$derivetheaverageSERexpressionsforBPSKand$16-$PSK modulation. $($f$)$ComputetheaverageSERaboveforbothBPSKand$16-$PSKforP$=35$dB$,$number ofsubcarriersN$=128,$$2$ l $=$ldBfor$0$l$4$andnoisepower$2$ n$=3$dB$.$