Wireless Data Networks, TLEN 5520/ECEN 5032Homework #2M. Heusse, Spring 2009Due In Class: February 4thConsiders four methods for sending packets across a 1 Mbps wireless link.1. No coding. A packet is sent without any error correcting codes (ECC) or CRC.2. Lower rate. A packet is sent at 1/2 the rate.3. ECC with interleaving. A packet is sent with a rate 1/2 code applied to the header anddata. After encoding the data is sent through an interleaver matrix. The interleaverwrites the packet in rows that are 20 bits long and reads out the columns.4. CRC. A packet is sent with a 4 byte CRC applied to the header and data. Everypacket received has an ACK sent back. The ACK is equivalent to a packet with 0 datapayload (note the 4 byte CRC is applied to the ACK header). The ACK is sent 10µsec after the Data packet is received.A packet consists of 20 bytes of synchronization and 20 bytes of header, followed by thedata payload. Errors in the synchronization bits are not significant. The ECC corrects upto 3 errors in any block of 20 bits otherwise errors are not corrected. If errors are random(or if they are relatively spread out), the probability of the ECC failing to correct all theerrors in a B byte packet is:PP E∼=2000 B P4BERwhere PBERis the channel bit error rate (see eq. 7.126 in Rappaport if you want to knowmore). Note B is the size of the packet after ECC. Without the ECC, the probability of anerror is the probability that no bit is corrupted.If the data or ACK packet has an error, then the exchange fails and the exchange isretried.If the errors come in bursts, then the errors are specified by a burst length LBand aburst gap LG. For a packet of time duration τ, the probability of a burst appearing duringthat packet is PB= 1 − e−τ/LG(This is the probability that there is no event given a Poissonprocess of intensity 1/LG). If a burst occurs, it causes LB/2 errors (remember a noisychannel has half the bits in error). For simplicity, let the probability of a burst occurring beindependent from packet to packet.1Every data packet sent (or data/ACK exchange) is followed by a τw= 50µsec wait periodwhether the packet is successfully received or not (the reason will become apparent in laterdiscussions). The time to send a packet without acknowledgements is given byτs= τins+ τwwhere τinsis the packet insertion time.The time to send one data/ACK exchange isτe= τins+ τprop+ τwa+ τprop+ τinsA+ τwwhere τpropis the propagation delay which is 1µsec here, τwais the wait time before sendingan ACK, and τinsAis the insertion time of an ACK.The throughput, T , is calculated as the data payload per packet divided by τcyc, thecomplete cycle time to send one data packet. τcyc= τsfor a non-acknowledgement schemeand τcyc= τeNEin a data/ACK scheme.The goodput is G = T (1 − PP E). PP Efor the CRC case is the probability that at theend of an exchange a packet is accepted because the CRC failed to detect the error.We consider several combinations of packet size, performance metric, and channel model.There are two packet data payload sizes: 10, and 1000 bytes. There are three performancemeasures: probability a packet is accepted when it is in error, PP E; the goodput, G; and thedelay, τcyc. There are four channels: the first is an additive white Gaussian noise channel(AWGN) which has random errors with probability PBER= 10−3; the second is a burstyRayleigh fading channel with LB= 2µs and LG= 1ms; the third is a bursty Rayleigh fadingchannel with LB= 1ms and LG= 500ms, the last is an error free channel. All the channelswith errors have the same average error rate, PBER= 10−3. This is a high error rate but itrepresents the channel at the fringe of coverage.For the case of reducing the channel rate by half, see the handout showing the BER as afunction of Eb/N0(aka SNR). Estimate the reduction in average BER of adding 3dB to theSNR for the AWGN and Rayleigh channels. In the AWGN case reduce PBERappropriately.In the Rayleigh case reduce LBappropriately.The solution to this problem should consist of 3 tables, one for each performance mea-sure. One such table is illustrated below. For each combination of channel and packet size,highlight the coding scheme that is most effective. While there are a lot of values to computein this problem, it can be done with a small C, java, perl or python program (or matlab,R. . . ).FramePayload(Bytes) Coding SchemeChannel 1(Random)Channel 2(Short Burst)Channel 3(Long Burst)Channel 4(Error Free)no ECC10 no ECC12rateECC with interCRC with ACKno ECC1000 no ECC12rateECC with interCRC with ACK2Based on your analysis answer the following questions.1. Under which channel model did goodput increase as the packet size increased?2. Comment on the relative merits of each of the methods for sending a packet.3. Which method worked best with each channel model?4. Which method would most likely support voice traffic across the different channels?5. In which channel cases would ECC without interleaving be effective or