AWGN Channel

AWGN ChannelAWGN ChannelNEuWb GroupDIET

AWGN ChannelOutlineChannel modelSimulation time!Results

AWGN ChannelChannel modelOutlineChannel modelSimulation time!Results

AWGN ChannelChannel modelFramework (1/3)Channel model hypothesis◮ multipath-free◮ AWGN (and any other gaussian interference)◮ attenuation formula: α = c 0 / √ D γ , so α ≡ c 0 @ D = 1[m].Optimum receiver (for AWGN channels)◮ Correlator: it correlates r(t), the rx noisy signal (input), withthe orthonormal waveforms (ψ i ) N−1i=0of the signal space basis,giving a vector Z ∈ R N of decision variables (output).◮ Detector: it decides which wf was transmitted applying theML criterion, i.e. maximizing p(Z|s(t)).

AWGN ChannelChannel modelFramework (2/3)Two decision detection strategies may be used in case ofmulti-pulse signals:◮ SOFT: only one decision based on the whole multi-pulsesignal (SNR mp = N s SNR sp );◮ HARD: firstly N s independent decisions (with errorprobability p), then the final decision is obtained by applying amajority criterion, leading to:P e =∑N sk=N s/2( ) Nsp k (1 − p) Ns−k .k

AWGN ChannelChannel modelFramework (3/3)MOD_TXsTXTransmitterAttenuation1Channel Delay1zNoise1det_dataoutcorrML detectorZZcorrCorrelatorsRXn

AWGN ChannelSimulation time!OutlineChannel modelSimulation time!Results

AWGN ChannelSimulation time!SchematicReceiversRXwnmasksmp_freqdataNsTsnBitsRXestBERMOD_RXProductAWGN Channel SimulationMask generationrefsmp_freqNsdPPMmaskMOD_corr_maskMOD_TX(BPPM_TH, BPAM_DS)num_bitsNssmp_freqTcTsNpNhdPPMIR_dtaupowdBmdatacodesTXrefMOD_TXChannel attenuationsTXc0dgammasRXapathlossAWGNsRXwonSNRpnum_pulses_totsRXwnnoisegnoiseExN015gamma14d13c012avg_pow11wf_shape_factor10wf_time_duration9dither8code_max_val7code_length6frame_time5chip_time4smp_freq3num_pulses_per_bit2num_bits1

AWGN ChannelSimulation time!Routines (1/2)We shall write three routines:◮ [sRX, a] = pathloss(sTX, c0, d, gamma)It implements the pathloss formula (as we’ve looked atpreviously).◮ [sRXwn, noise] = gnoise(sRXwon, SNRp, num pulses tot)It adds noise with suitable power to attain the desired SNRp:if N s > 1, then SNR p = E x /N 0 = E b /(N s N 0 ).◮ mask = corrmask(ref, smp freq, num pulses tot, dPPM)It generates the mask with which correlates the receivedsignal.

AWGN ChannelSimulation time!Routines (2/2)◮ To implement the first block, you have to use the old routinefor the generation of PPM signals.◮ To implement the last block, you can use the already writtenroutine[det data,BER] = MOD receiver(...mod, rx, mask, smp freq, data, nBits, Ns, Ts)

AWGN ChannelResultsOutlineChannel modelSimulation time!Results

AWGN ChannelResultsQuestionsYou should be able to answer to the following questions:1. What is the effect of N s on P e ?2. What are the performance difference btw soft and harddecisions?We invite you to highlight the hypotesis under which,according to you, this conclusion is true.

AWGN ChannelResultsThe main result10 0 SNR xN s=1N s=3, HARDN s=3, SOFT10 −1Pr e10 −210 −310 −40 1 2 3 4 5 6 7 8 9 10