Lecture 22: Digital Transmission Fundamentals

Transcription

1 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals Using Geometri Representation of Digital Modulations Now, that we learned the basis of representing digital pulses in geometri form (in a Cartesian spae), what an we do with this representation? This representation an be used for deteting whih of the original pulses did the transmitter most likely transmit. Choosing a partiular original pulse as the one that was transmitted in a partiular pulse period is done by:. Mapping eah of the original pulses into the Cartesian spae (this produes what we all a onstellation) 2. Mapping the reeived pulse to the Cartesian spae in whih the original pulses are mapped. 3. Computing the distane between the point representing the reeived pulse and all other points representing the original pulses 4. eleting the original pulse with the shortest distane to the reeived pulse as the pulse that was most likely transmitted. Constellations of ome Digital Modulations everal types of digital modulations exist. The three basi types of digital modulations are named:. Amplitude hift Keying (AK) 2. Phase hift Keying (PK) 3. Frequeny hift Keying (FK) (Will not be disussed here) Next we desribe several of these modulations and shown their time domain pulses and their onstellation. Amplitude hift Keying (AK) Binary Amplitude hift Keying (BAK) In AK, the different pulses all have the same phase but different amplitudes. In the binary amplitude shift keying (BAK) modulation tehnique we transmit one of two pulses for eah bit: ) for logi 0, we transmit nothing ( s 0 () t = 0 for 0 t T )

2 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals 2) for logi, we transmit a modulated pulse with magnitude A s () t = A os2π f t for 0 t T ) ( ( ) ine all the pulses have the same phase (you an think of the first signal as ( π ) s0 () t = 0os2 f t for 0 t T ), the onstellation of this modulation tehnique (the representation of the pulses of the modulation algorithm) beomes A Example: A BAK algorithm uses the following pulses to transmit binary data:. s 0 () t = 0 for 0 t (Logi 0 ) 2. ( π ) s ( t) = 5 os 2 f t for 0 t (Logi ) Determine whih bit is the most likely one that was transmitted if the reeived pulse is a. ( π ) rt ( ) = 5 os 2 ft for 0 t To solve this, sketh the onstellation of the modulation algorithm and sketh the reeived pulse on the figure showing the onstellation. 2

3 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals Now, it is simple. The dot in the onstellation of the modulation method that is losest to dot that orresponds to the reeived pulse is the most likely pulse that was transmitted. Therefore, a logi was most likely transmitted. In this example, atually the reeived pulse was exatly equal to one of the pulses of the modulation so it would have been very logial to assume that that pulse was the one that was transmitted from the beginning but this method is a systemi method for determining it. b. ( π ) rt () = 4os2 ft for 0 t Repeating the same proess above, we see that reeived pulse is represented by a dot as shown in the following figure. It is also lear here that most likely s () t was transmitted (but it got attenuated a little). o a logi would be onsidered to be the bit that was transmitted. 3

4 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals. ( π ) rt () = 5sin 2 ft for 0 t Now, this one is a little triky. Your first instint may tell you that s () t was transmitted but it got delayed a little so that the osine pulse beame a sine pulse. But this may not be true. In this example, it is lear that phase of the reeived signal rt () is not the same phase of the signal s () t. In fat, they are 90 out of phase, so the onstellation and the reeived pulse would be as shown in the following figure. Although the reeived signal is far away from both pulses of the modulation algorithm, it is atually loser to the pulse of logi 0, whih is s () 0 t, whih means that a logi 0 was most likely transmitted. d. ( π ) rt () = 5os2 ft+ 60 for 0 t As an exerise, verify that this onfiguration gives the following: 4

5 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals In this ase, the reeived pulse has exatly the same distane from both onstellation points. Here, you may flip a oin and pik one of the pulses to be the one transmitted. You would have a probability of being right equal to 50%. M-ary Amplitude hift Keying (M-ary AK) In this digital modulation tehnique, we transmit one of M pulses, where M is a power of two number suh that M = 2 n. The quantity n here is equal to the number of bits that are arried by eah transmitted pulse. To determine whih pulse to transmit in eah ase, we will have to divide the sequene of information bits into groups of n onseutive bits. The ombination of bits will be one of M = 2 n possible ombinations that will determine the pulse to be transmitted for these n bits. o, in this modulation we will transmit one of the following pulses: ) for bit sequene , transmit s () 0 for t = t T 2) for bit sequene 00..0, transmit 00 0 ( π ) 3) for bit sequene 00..0, transmit 00 0 ( π ) 4) for bit sequene 00.., transmit ( π ) s () t = A os2 f t for 0 t T s () t = 2A os2 f t for 0 t T s () t = 3A os2 f t for 0 t T 00 : : M) for bit sequene.., transmit ( ) ( π ) s ( t) = M A os 2 f t for 0 t T 5

6 EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on Leture 22: Digital Transmission Fundamentals ine all pulses of this modulation tehnique have the same phase, the representation of all pulses in the onstellation fall on a straight line. The onstellation of this modulation algorithm is shown below. Clearly in this ase, the power required for transmitting different pulses is different and the average power of transmission an be obtained easily by averaging all powers assuming that different bit sequenes have equal probabilities. 6