QAM bit error probability calculator

Calculate the M-ary QAM bit error probability with this online calculator. Enter



M E b N 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaala aabaGaamyramaaBaaaleaacaWGIbaabeaaaOqaaiaad6eadaWgaaWc baGaaGimaaqabaaaaaaa@3AC9@ E b N 0  [dB] MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGfbWaaSbaaSqaaiaadkgaaeqaaaGcbaGaamOtamaaBaaaleaacaaI WaaabeaaaaGccaaMe8Uaai4waiaadsgacaWGcbGaaiyxaaaa@3EAA@ Bit error probability p b MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa aaleaacaWGIbaabeaaaaa@37FC@ Start simulation
0.07864960352514244 Start

The bit error probability p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@ of M-QAM over an AWGN channel is given by

p B = 4 n ( 1− 1 M )Q( 3n M−1 ⋅ E B N 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOqaaqabaGccqGH9aqpdaWcaaqaaiaaisdaaeaa caWGUbaaamaabmaabaGaaGymaiabgkHiTmaalaaabaGaaGymaaqaam aakaaabaGaamytaaWcbeaaaaaakiaawIcacaGLPaaacaWGrbWaaeWa aeaadaGcaaqaamaalaaabaGaaG4maiaad6gaaeaacaWGnbGaeyOeI0 IaaGymaaaacqGHflY1daWcaaqaaiaadweadaWgaaWcbaGaamOqaaqa baaakeaacaWGobWaaSbaaSqaaiaaicdaaeqaaaaaaeqaaaGccaGLOa Gaayzkaaaaaa@4D52@

or

p b = 2 ld( M ) ( 1− 1 M )erfc( 3ld( M ) 2( M−1 ) ⋅ E B N 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaGccqGH9aqpdaWcaaqaaiaaikdaaeaa caWGSbGaamizamaabmaabaGaamytaaGaayjkaiaawMcaaaaadaqada qaaiaaigdacqGHsisldaWcaaqaaiaaigdaaeaadaGcaaqaaiaad2ea aSqabaaaaaGccaGLOaGaayzkaaGaamyzaiaadkhacaWGMbGaam4yam aabmaabaWaaOaaaeaadaWcaaqaaiaaiodacaWGSbGaamizamaabmaa baGaamytaaGaayjkaiaawMcaaaqaaiaaikdadaqadaqaaiaad2eacq GHsislcaaIXaaacaGLOaGaayzkaaaaaiabgwSixpaalaaabaGaamyr amaaBaaaleaacaWGcbaabeaaaOqaaiaad6eadaWgaaWcbaGaaGimaa qabaaaaaqabaaakiaawIcacaGLPaaaaaa@5918@ .

See QAM bit error probability for AWGN channel.