1 / 20

Digital Signaling

Digital Signaling. Digital Signaling Vector Representation Bandwidth Estimation Binary Signaling Multilevel Signaling. Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University. Digital Signaling.

silvestri
Download Presentation

Digital Signaling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Digital Signaling • Digital Signaling • Vector Representation • Bandwidth Estimation • Binary Signaling • Multilevel Signaling Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

  2. Digital Signaling • How do we mathematical represent the waveform of a digital signal? • How do we estimate the bandwidth of the waveform? • Example: Message ‘X’ for ASCII computer keyboard - code word “0001101” • What is the data rate?

  3. Digital Signaling Binary (2) Values Binary signal Multilevel signal More than 2 Values • Baud (Symbol Rate) : • D = N/T0 symbols/sec ; N- number of dimensions used in T0 sec. • Bit Rate : • R = n/T0 bits/sec ; n- number of data bits sent in T0 sec.

  4. How to detect the data at the receiver (after transmission over a channel)? • Formal way is to evaluate the orthogonal series coefficient. It is also true that eq. (3-30) is the optimal way of detecting the received signal that is corrupted by AWGN noise. This is known as Match Filtering or Matched Filter Detection.

  5. Vector Representation • Orthogonal function space corresponds to orthogonal vector space :

  6. Vector Representation of a Binary Signal • Examine the representation in next slide for the waveform of a 3-bit (binary) signal. This signal can be directly represented by, . • Orthogonal function approach

  7. Vector Representation of a Binary Signal A 3 bit Signal waveform Bit shape pulse Orthogonal Function Set Vector Representation of the 3 bit signal

  8. Bandwidth Estimation wk takes only BINARY values Waveform: • The lower bound for the bandwidth of the waveform w(t) is given by the Dimensionality Theorem • Binary Signaling: Example: Binary signaling from a digital source: M=256 distinct messages M = 2n = 28 = 256 Each message ~ 8-bit binary words T0=8 ms – Time taken to transmit one message; Code word: 01001110 w1= 0, w2= 1, w3= 0, w4= 0, w5= 1, w6= 1, w7= 1, w8= 0 • Case 1: Rectangular Pulse Orthogonal Functions: : unity-amplitude rectangular pulses;

  9. Bandwidth Estimation (Binary Signaling) The Lower Bound : The actual Null Bandwidth: Bandwidth:  Null BW > lower bound BW • Receiver end: How are we going to detect data? Orthogonal series coefficients wk are needed.Sample anywhere in the bit interval

  10. Binary Signaling Lower bound BW: For N=8 pulses, T0=8 ms => B=500Hz. • Case 2: sin(x)/x Pulse Orthogonal Functions Minimum Bandwidth Where Ts=Tb for the case of Binary signaling. • Receiver end: How are we going to detect data? Orthogonal series coefficients wk are needed.Sample at MIDPOINT of each interval

  11. Binary Signaling 0 1 0 01 1 1 To recover the digital data at the receiver, we sample received wavform at the right time instants (SYNCHRONIZATION) and from the sample values a decision is made about the value of the transmitted bit at that time instant.

  12. Binary Signaling Which wave shape gives lower bound BW? 0 1 0 0 1 1 1 Individual Pulses Total Waveform

  13. Binary Signaling Using Sa Shape 1 0 010

  14. Binary Signaling Using Raised Cosine Shape

  15. Multilevel Signaling • B Reduces, if N Reduces: So wk should take more than 2 values ( 2- binary signaling) • If wk’shave L>2 values Resultant waveform – Multilevel signal • Multilevel data : Encoding l-bit binary data  into L-level :DAC

  16. Multilevel Signaling (Example) M=256-message source ; L=4; T0=8 ms Encoding Scheme: A 2-Bit Digital-to-Analog Converter Binary Input Output Level (l=2 bits) (V) 11 +3 10 +1 00 -1 01 -3 Binary code word - 01001110 w1= -3, w2= -1, w3= +3, w4= +1 Bit rate : k bits/second Different Baud ( symbol rate): k baud Relation :

  17. Multilevel Signaling - Example B=1/Ts=D=500 Hz B=N/2T0=250Hz • How can the data be detected at the receiver? • Sampling at midpoint of Ts=2 ms interval for either case (T=1, 3, 5, 7 ms)

  18. Multilevel Signaling - Example 0 11 01 11 0 -3 +1 +3 +1 Total Waveform Individual Pulses

  19. Binary-to-multilevel polar NRZ Signal Conversion • Binary to multilevel conversion is used to reduce the bandwidth required by the binary signaling. • Multiple bits (l number of bits) are converted into words having SYMBOL durations Ts=lTb where the Symbol Rate or the BAUD Rate D=1/Ts=1/lTb. • The symbols are converted to a L level (L=2l) multilevel signal using a l-bit DAC. • Note that now the Baud rate is reduced by l times the Bit rate R (D=R/l). • Thus the bandwidth required is reduced by l times. Ts: Symbol Duration L: Number of M ary levels Tb: Bit Duration l: Bits per Symbol L=2l D=1/Ts=1/lTb=R/l

  20. Binary-to-multilevel Polar NRZ Signal Conversion (c) L = 8 = 23 Level Polar NRZ Waveform Out

More Related