Lecture 5 Interymbol Interference FDM TDM 1
Time Limited Waveform Time-Limited Signal = Frequency Unlimited Spectrum Square Pule i a Time-Limited Signal Fourier Tranform 0 T S -3/T S -2/T S -1/T S 0 1/T S 2/T S 3/T S The tranmitted pule are filtered to be band-limited (To have a limited frequency pectrum) Effect in Time domain The pule are pread in Time domain 2
Interymbol Interference Interymbol interference (ISI) occur when a pule pread out in uch a way that it interfere with adjacent pule at the ample intant. Example: Aume polar NRZ line code. The channel output are hown a pread (width T b become more than T b ) pule hown (Spreading due to bandlimited channel characteritic). Channel Input Pule width T b Channel Output Pule width 2T b Data 1 T b / 2 0 Tb 3T / 2 T / 2 0 b T b b 3T b / 2 Data 0 T b / 2 0 Tb 3T b / 2 / 2 0 T / 2 T b T b 3 b 3
Inter-ymbol Interference (ISI) Spreading of the pule caue inter-ymbol interference (ISI) ISI reult due to: (1) improper filtering of the pule in the tranmitter to reduce BW. (2) Effect of channel. Effect: Neighboring ymbol affect the meaured value and thi introduce error in the deciion device at the receiver which reult in increaing the bit error rate. How can we retrict BW and at the ame time not introduce ISI? 3 Technique. 4
Combating ISI Three trategie for eliminating ISI: 1-Nyquit Firt Method for Zero ISI Ue a line code that i abolutely band-limited. Would require Sinc pule hape. It i difficult to do thi. 2- Raied Coine filtering Ue a line code that i zero during adjacent ample intant. It okay for pule to overlap omewhat, a long a there i no overlap at the ample intant. Can come up with pule hape that don t overlap during adjacent ample intant. Raied-Coine Rolloff pule haping 3- Equalization Ue a filter at the receiver to undo the ditortion introduced by the channel. 5
Combating ISI h(t) h e (t) Input pule 6
1-Nyquit Firt Method for Zero ISI ISI can be eliminated by uing an equivalent tranfer function, H e (f), uch that the impule repone atifie the condition: k i an integer, h C ( t) 0 T i the ymbol (ample) period i the offet in the receiver ampling clock time C i a nonzero contant e t 0 t T, 2T,... in x Now chooe the function for he ( t) x Sinc function (in time domain) atifie thi condition if it duration in freq. domain i 1/T -2T -T 0 T 2T t 7
1-Nyquit Firt Method for Zero ISI ISI can be eliminated by uing an equivalent tranfer function, H e (f), uch that the impule repone atifie the condition: k i an integer, h C ( t) 0 T i the ymbol (ample) period i the offet in the receiver ampling clock time C i a nonzero contant e, 2T,... in x Now chooe the function for he ( t) x T t 0 t T h e Sinc function (in time domain) atifie thi condition if it duration in freq. domain i 1/T ( t T) Sampling Intant ISI occur but, NO ISI i preent at the ampling intant t 8
1-Nyquit Firt Method for Zero ISI There will be NO ISI and the bandwidth requirement will be minimum (Optimum Filtering) if the tranmit and receive filter are deigned o that the overall tranfer function H e (f) i: 1 f in ft 1 He f he t Where f f f ft T Thi type of pule will allow ignalling at a baud rate of D=1/T =2B (for Binary R=1/T =2B) where B i the abolute bandwidth of the ytem. H e (f) T -T 0 T t 1 2T 0 1 f 2T 1 R The minimum abolute bandwidth W0 where R 2T 2 ignaling i 9 rate
1-Nyquit Firt Method for Zero ISI H e (f) h e (t) T t W 0 1 0 1 W 0 f Sinc pule are not poible to create due to: Sharp tranition band in the frequency domain. 2T 2T The Sinc pule hape can caue ignificant ISI in the preence of timing error. If the received ignal i not ampled at exactly the bit intant (Synchronization Error), then ISI will occur. We eek a pule hape that: Ha a more gradual tranition in the frequency domain. I more robut to timing error. Still atifie Nyquit firt method for zero ISI. 10
2-Raied Coine Filtering Becaue of the difficultie caued by the Sinc type pule hape, conider other pule hape which require more bandwidth uch a the Raied Coine-rolloff filter but they are le affected by ynchronization error. The Raied Coine filter i defined by it rollof factor number r. e R Bandwidth W (1 r) 2 W o ( 1 r) when when r r 0, W 1, W W o 2W o 11
2-Raied Coine Filtering Now filtering requirement are relaxed becaue abolute bandwidth i increaed. Clock timing requirement are alo relaxed. The r=0 cae correpond to the previou Minimum bandwidth cae. e Bandwidth W 1 2T R 2 (1 r) (1 r) W W if if r r 1, then W R 0, then W W 0 12 R 2 =
2-Pule-Shaping with Raied-Coine Filter The tail of h e (t) are now decreaing much fater than the Sinc function. h e (t) Impule repone -3T -2T -T T 2T 3T ISI due to ynchronization error will be much lower. He(f) T S : ymbol interval R S : ymbol rate r: roll-off factor Raied Coine Filter Bandwidth = R S (1+r)/2 13
3-Equalization for Wirele Channel x(t) Channel h(t) y(t) Equalizer G( f ) xˆ ( t) In time domain : y( t) h( t)* x( t) h( t) i theimpulereponeof In frequency domain : Y( f ) H ( f ) X ( f ) Xˆ ( f ) G( f ) Y( f ) H Equalizer G( f ) H 1 thechannel ( f ) H( f ) X ( f ) X ( f ) 1 ( f ) Receiver Equalizer invere the effect of the channel 14
Multiplexing 15
Frequency Diviion Multiplexing (FDM) FDM i a technique for tranmitting multiple meage imultaneouly over a wideband channel. Each uer ha a pecified frequency band and between thee band, there i a Guard interval. Guard band 16
Frequency Diviion Multiplexing (FDM) The diadvantage of thi ytem i the limitation of the uer due to the limitation in the frequency band. The advantage of thi ytem i that all the channel are available for all the uer all the time. 17
Example: Five channel, each with a 100-kHz bandwidth, are to be multiplexed together. What i the minimum bandwidth of the link if there i a need for a guard band of 10 khz between the channel to prevent interference? Solution For five channel, we need at leat four guard band. Thi mean that the required bandwidth i at leat 5 100 + 4 10 = 540 khz, a hown in the following Figure. 18 6.18
Time Diviion Multiplexing (TDM) TDM i the time interleaving of ample from everal ource o that the information from thee ource can be tranmitted erially over a ingle communication channel. 19
Time Diviion Multiplexing (TDM) The following Fig. how the concept of TDM a applied to three analog ource that are multiplexed over a PCM ytem. At the receiver, the ample from individual channel are eparated and ditributed by another ampler (rotary witch called ditributer). The ample from each channel are filtered to reproduce the original meage ignal. 20
Time Diviion Multiplexing (TDM) Sec. Sec. 21
Time Diviion Multiplexing The diadvantage of thi ytem i the delay caued epecially in cae of large number of uer. The advantage of thi ytem i that all the frequency band i available for all the uer. 22
Example: 23 6.23
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d. The frame rate i alway the ame a any input rate. So the frame rate i 1,000,000 frame per econd. Becaue we are ending 4 bit in each frame, we can verify the reult of the previou quetion by multiplying the frame rate by the number of bit per frame. 25
Application of TDM In modern telephony a remote concentrator i a unit to which Subcriber' analogue telephone line are connected to it. They have the following main function, namely: Digitize, that i, turn voice from analogue into a digital form. Multiplex, interleaving many call together on a ingle wire or optical fiber. Only a few hundred telephone line attach to each remote concentrator. 26
Application of TDM (Cont.) When a uer pick up their phone, the concentrator produce the dial tone. When the uer dial, the concentrator read the tone. Once the uer ha completed dialing, the concentrator' microcomputer end the dialing data to the central witch, which allocate a time lot for the dialing phone on the wire pair that pa through the concentrator and through the central witch. After the central witch tell the concentrator which time lot to ue, the concentrator "open" a time-lot on the loop to a local phone. 27
The allocated time lot on the wiring out of the concentrator (with the ame time lot number) carrie data from the local phone to the remote phone. To arrange a connection, the central witch jut complete the circle between the uer' phone and the remote phone. It interchange the data from one to the other. In thi limited ene, telephone "exchange" i exactly correct terminology Telephone operator manually connecting call with cord pair at a telephone witchboard A modern central office 28