FM Range Calculation

Transcription

1 FM Range Calculation Thi heet i to etimate of the range that can be epected from an FM or ASK modulated ytem. Chri Haji-Michael It ue a modified-verion of the Fri tranmiion equation. It tart by calculating the minimum ignal trength in dbm that i required in the receiver. It ue three probability-error-function curve, the firt one i for FSK with average white gauian noie (AWGN), a econd one i form ASK and the third i for FSK with Raleigh fading. Many of the RF equation are adapted from Pozar, Microwave & RF Deign of Wirele Sytem. The propagation equation were found on and The error function calculation are from "Wirele Communication", by Andrea Goldmith. := 5, Probability Error Function for coherent FSK The probability error function curve for coherent FSK can be ued to calculate BER for different Eb/No. Thi equation i found in "An Intro to Analogue & Digital Communication" by Simon Haykin and Andrea Goldmith equation 5.4 & table 6. where i in db. := Given PEF fk = 0.5erfc EbNo_FSK_dB PEF fk ( ) Find := ( ) EbNo_FSK_dB ( 0.) =.55 EbNo_FSK_dB ( 0.0) = PEF fk ( ) := 0.5erfc Probability Error Function for coherent ASK The probability error function curve for level puled amplitude modulation (alo called amplitude hift keying or on/off keying). Thi equation i from Andrea Goldmith 5.4 & table 6. for MPAM where i in db := Given PEF ak = erfc log(, ) EbNo_ASK_dB PEF ak ( ) Find := ( ) EbNo_ASK_dB ( 0.00) =.345 PEF ak ( ) := erfc log(, )

2 Probability Error Function for coherent FSK with fading A real ignal i likely to be ubjected to fading of which the mot evere verion i Raleigh fading. Thi i bet repreented a an alternate Error Function Curve and i calculated here according to "Wirele Communication", by Andrea Goldmith, equation y y := Given PEF fk_fad = 0.5 y EbNo_FSK_fad_dB PEF fk_fad + ( ) Find y EbNo_FSK_fad_dB ( 0.) = := ( ) PEF fk_fad ( ) := y :=, Error Function Curve for Coherent FSK 0. PEF fk ( y) PEF ak ( y) PEF fk_fad ( y) y Eb/No RED curve i with average white gauian noie for FSK (frequency hift keying) BLUE curve with average white gauian noie for ASK (amplitude keying or on/off keying) GREEN curve i with Raleigh fading for FSK

3 Required receiver bandwidth for FSK FM ytem require a receive bandwidth which depend on the deviation and bit period. Thi i called the Caron'. More advanced FM receiver that ue a PLL to track the input ignal effectivly reduce thi bandwidth. Remember, the bigger the bandwidth the more noie i een by the receiver and the wore the receive enitivity. BT( fm_dev, bit_period) := fm_dev bit_period Caron_( fm_dev, bit_period) := bit_period + fm_dev Limit of enitivity for FSK in AWGN The limit of enitivity for FM ytem ue the PEF curve and add to thi the noie floor (-74dBm/Hz) and noie you would get with the bandwidth you pecify, a well a the noie-figure of the receiver. There i alo an adjutment for the BT which i a meaure of how large the eye. A low data rate ha a large eye ize and i eaier to receive. In advanced receiver that ue a PLL a the demodulator, thi effectivly reduce the noie bandwith. The IF bandwidth need to be greater than the Caron' bandwidth. The reult here can be directly compared to the receiver meaurement. min_detect_ignal_fk_dbm( BER, fm_dev, bit_period, r_nf_db, ) := 74 + log + EbNo_FSK_dB ( BER) + r_nf_db log( BT( fm_dev, bit_period) ) Hz ( ) min_detect_ignal_fk_dbm BER, fm_dev, bit_period, r_nf_db, min_detect_ignal_fk_w ( BER, fm_dev, bit_period, r_nf_db, ) := Caron_ 0kHz, Caron_ 30kHz, Caron_ 35kHz, Caron_ 37.5kHz, min_detect_ignal_fk_dbm 0.00, 0kHz min_detect_ignal_fk_dbm 0.00, 30kHz min_detect_ignal_fk_dbm 0.00, 35kHz min_detect_ignal_fk_dbm 0.00, 37.5kHz,, 5, 0kHz,, 5, 0kHz 000,, 5, 0kHz 5000,, 5, 0kHz 500 = 9 = 4 = 8 = Thee figure how that the enitivity and for different deviation and bit period. The for the bit period becaue the ytem i mancheter encoded. The enitivity limit i for AWGN Note the i the noie bandwidth and not the 3dB bandwidth

4 Limit of enitivity for FSK in Raleigh Fading A imilar analyi can be carried out for the fading environment, but of coure we cannot meaure thi directly. min_detect_ignal_fkfad_dbm( BER, fm_dev, bit_period, r_nf_db, ) := 74 + log + EbNo_FSK_fad_dB ( BER) + r_nf_db log( BT( fm_dev, bit_period Hz ( ) min_detect_ignal_fkfad_dbm BER, fm_dev, bit_period, r_nf_db, min_detect_ignal_fkfad_w ( BER, fm_dev, bit_period, r_nf_db, ) := min_detect_ignal_fkfad_dbm 0.00, 37.5kHz,, 7, 0kHz 500 = Required receiver bandwidth for ASK An ASK ytem require an IF bandwith that i equal to twice the maimum data rate. Thi i le than the required for FSK, where the deviation i very much greater than the modulation, then ASK give a big reduction in the required RX which will help with limiit of enitivity. ASK_( bit_period) := ASK_ bit_period = 40 khz Limit of enitivity for ASK in AWGN A imilar analyi can be carried out for the AWGN environment with ASK min_detect_ignal_ak_dbm( BER, bit_period, r_nf_db, ) := 74 + log + EbNo_ASK_dB ( BER) + r_nf_db Hz ( ) min_detect_ignal_ak_dbm BER, bit_period, r_nf_db, min_detect_ignal_ak_w ( BER, bit_period, r_nf_db, ) :=

5 min_detect_ignal_ak_w ( BER, bit_period, r_nf_db, ) ASK_ ASK_ ASK_ ASK_ = 40 khz min_detect_ignal_ak_dbm 0.00 = 0 khz min_detect_ignal_ak_dbm 0.00 = khz min_detect_ignal_ak_dbm 0.00 = 5 khz min_detect_ignal_ak_dbm 0.00,, 5, 50kHz,, 5, 50kHz 000,, 5, 0kHz 5000,, 5, khz 500 = = = 6 = 9 Thee figure how that the enitivity and for different data rate. The in the data rate for the bit period becaue the ytem i mancheter encoded. The enitivity limit i for AWGN Note the i the noie bandwidth and not the 3dB bandwidth Thi plot how the receive enitivity curve for FSK (with and without fading) and for ASK without fading Thi part i a bit confuing, it plot the PEF curve in a comple way becaue it weep ignal tength on the -ai to get the Bit Error Rate (BER) rather than the other way around. It doe thi by having a tarting BER to make the convergence work, I have put 0.0 here but it doe not matter. A ueful plot to tet receiver in FSK i to ue the RED curve. A ueful plot to tet receiver in ASK i to ue the BLUE curve. offet_fk( BER, fm_dev, bit_period, r_nf_db, ) := min_detect_ignal_fk_dbm( BER, fm_dev, bit_period, r_nf_db, ) EbNo_FSK_dB ( BER) offet_ak( BER, bit_period, r_nf_db, ) := min_detect_ignal_ak_dbm( BER, bit_period, r_nf_db, ) EbNo_ASK_dB ( BER) offet_fk 0., 0kHz,, 5, 0kHz = 9.0 offet_ak 0.,, 5, 40kHz = 3.0 RED curve i receiver enitivity curve for FSK 0KHz dev, 5u bit period, 5dB NF with average white gauian noie BLUE curve i receiver enitivity curve for ASK, 5u bit period, 5dB NF with average white gauian noie. GREEN curve i receiver enitivity curve for FSK 0KHz dev, 5u bit period, 5dB NF with Raleigh Fading Note, the ASK curve ue a reduced

6 Receiver enitivity curve 5u bit period 0. ( ( )) PEF fk ig offet_fk 0.0, 0kHz, 5µ, 5, 0kHz ( ( )) PEF ak ig offet_ak 0.0, 5µ, 5, 40kHz ( ( )) PEF fk_fad ig offet_fk 0.0, 0kHz, 5µ, 5, 0kHz ig RF input ignal level (dbm) Calculate the epected range Uing a modified form of the Fri equation from Rappaport & Theodore. N i the propagation coefficient, refer to the picture below. Thee range calculation ue both the Raleigh fading model and non Raleigh fading. freq := 860 MHz n :=.5 The Frii equation i modified according plot from (RT) Rappaport, Theodore., Wirele Communication - Principle & Practice, IEEE Pre, 996. In thi heet I have et n=.5 a communication i ame floor.

7 antenna_gain_db t_power_dbm antenna_gain( antenna_gain_db) := t_power_w ( t_power_dbm) := RangeRT_fad( t_power_dbm, BER, fm_dev, bit_period, r_nf_db, antenna_gain_db, ) := RangeRT( t_power_dbm, BER, fm_dev, bit_period, r_nf_db, antenna_gain_db, ) := p p m freq m freq antenna_gain( antenna_gain_db) t_power_w ( t_power_dbm) min_detect_ignal_fkfad_w ( BER, fm_dev, bit_period, r_nf_db, ) antenna_gain( antenna_gain_db) t_power_w ( t_power_dbm) min_detect_ignal_fk_w ( BER, fm_dev, bit_period, r_nf_db, ) n The range i calculated with the TX power in dbm and required BER for Rappaport & Theodore, with Raleigh fading on the left, non Raleigh on the right. I would epect communication to work reliably to the Raleigh limit, with decreaing performance to the higher limit Summary Range 6dBm TX, 5dB NF, 0kHz dev, 0kHz air data rate, average antenna gain -5dB, 00bit without error, no FEC. Range TX 6dBm TX, : FEC, reduce the data rate by quarter, no Mancheter. RangeRT( tpower( dbm), BER, dev, bitperiod, NF, Antennagain( db), ) Thi range i calculated with the TX power in dbm for Rappaport & Theodore. Note, the bit period i divided by a the data i Mancheter encoded over the air. AWGN on the left, Raleigh fading value on the right. The range i between the two value. RangeRT 6, 0.005, 0kHz,, 5, 5, 0kHz RangeRT 6, 0., 0kHz,, 5, 5, 50kHz 5000 = 8 m RangeRT_fad 6, 0.005, 0kHz,, 5, 5, 0kHz = 435 m RangeRT_fad 6, 0., 0kHz,, 5, 5, 50kHz 5000 = 30 m = 8 m Improvement. The ASK ha not been included in the range calculation becaue thi work need to be double checked and need to be compared to meaurement. The FSK curve and plot are correct and have been checked and are in the range calculation. Thi work i ongoing but provide quite a ueful heet a it i.