Wireless
Communication
Lecture 14 – Digital
Modulation and pulse shaping
Portfolio
(a) Create a baseband (not modulated) Matlab simulation that creates the impulse train for a BPSK signal. Use at least 8 bits in your impulse train, and make it easy to add more bits. Sample the impulse train Ts/10 apart. Plot the pulse train in time using matlab’s “stem” plotting method.
(b) Compute and plot (1) rectangular, and (2) root raised cosine shaping pulses with samples also Ts/10 apart with alpha = 0.35. Then (3) recomputed the pulse with alpha = 0.5 and compare these results with figure 6.18.
(c) Convolve the impulse train with each shaping pulse and plot the results.
(d) Take the fourier transform of an individual pulse and compare it to Figure 6.17.
(e) Extend your impulse train to 1000 data points and compute the preceding convolutions. Take the Fourier transform of the pulse train and explain it. Is it a better match to Figure 6.17? Why?
(f) Create the “eye” diagram for your system.
a. Create a pulse train with “all possible” combinations of 1’s and 0’s. Your 1000-point data set should cover this. For instance… 11, 01, 10, 00 are every possible combination of 2-bit signals. This will give you the eye diagram for a pulse that has ISI only on the adjacent pulse. For pulses with ISI in more than just the adjacent pulse (like the sinc pulse), you may have to use 000, 001, 010, etc. to get the full eye diagram.
b. Plot each of these pulses in a single window. The width of the window is one pulse width T. You should have several different “lines” within this plot that create the typical “eye” diagram.
Why Digital
Modulation?
Advantages compared to Analog (AM/FM) modulation
· Greater noise immunity
· Robustness to channel impairments and fluxuations
· Easier to multiplex differing forms of data (voice, data, video, etc.)
· Greater privacy / security
· Data can be corrected for errors
o Error-control coding
o Signal conditions and processing
§ Source encoding
§ Encryption
§ Equalization
· Much / Most / All of this can be done in software using digital signal processing chips
Desired attributes of
digital modulation scheme
· Low signal-to-noise ratio (SNR)
· Performs well in multipath/fading
· Uses minimal bandwidth
· Easy and cost-effective to implement
Measures of digital
modulation scheme
· Power Efficiency / Energy Efficiency
o ability to receive signals at low power
o hp = Eb / No
§ hp = Power Efficiency = ratio of signal energy per bit to noise power spectral density at a given probability of error (eg. 10-5)
§ Eb = signal energy per bit
§ No = noise power spectral density
· Bandwidth Efficiency
o Ability to accommodate data in a limited bandwidth (To get more data into a pulse train, you can decrease the width of each pulse. This increases the bandwidth required for transmission.)
o hB = R / B
§ hB = Bandwidth Efficiency = ratio of the throughput data rate per Hz of Bandwidth
§ R = throughput data rate (bps)
§ B = bandwidth of the system (Hz)
o
§ hB = C / B = log2 (1 + S/N)
· hB = Bandwidth Efficiency = ratio of the throughput data rate per Hz of Bandwidth
· C = channel capacity (bps)
· B = bandwidth of the system (Hz)
o Bandwidth (has many definitions)
§ FCC:
· 0.5% of power of the signal is below the allotted band, and 0.5% is above the allotted band. (99% of the power is within the allotted band)
Generic Digital
Communication System Block Diagram
Data Symbols:
· representation of data using either “0” and “1” or “-1” and “1”
· Create a “pulse train”
· Each symbol can have “m” values. There are “n” bits of data per symbol. n = log2 m
o For binary m=2 (values are “0” or “1”), and n = 1 bit/symbol.
o For Quaternary data, m=4, n=2 bits/symbol.
Pulse Trains
· Types of pulse shapes
o Non-return to Zero
§ Unipolar
§ Bipolar
o Return to Zero
§ Unipolar
§ Bipolar
o
§ Uses two short pulses to represent each data bit
· Tradeoffs
o Bipolar codes – better separation between “0” and “1”
o Non-return to Zero
§ Less bandwidth (longer pulses)
§ Poor synchronization abilities (cannot tell where a pulse is if you have +1 and -1)
o Return to Zero
§ Twice the band width of the NRZ codes
§ Better synchronization
o
§ Requires the largest bandwidth
§ Has good synchronization
Pulse Shaping
· Why?
o Channel will corrupt pulse train and induce error in the data
o ISI = Intersymbol interference (when errors from one pulse overlap on another pulse
· How?
o Round edges of pulse to reduce bandwidth
o Increase width of pulses
Pulse Shaping
· Why? Because the rectangular pulse has infinite frequency components. Electronics cannot support this pulse, so it will be inherently filtered, which will corrupt the pulse. Rather than letting this happen at random, we should shape the pulse for maximum efficiency of our system.
Nyquist Criteria for successful digital
transmission:
(1) Intersymbol Interference (ISI): The pulse should be zero when the NEXT (and all subsequent) bits are sampled.
Examples:
Rectangular Pulse
Sinc
Raised Cosine Rolloff
Raised Cosine (RC)
(2) Interchannel Crosstalk: The frequency spectrum of the pulse must be fully contained in the existing channel. BW >= 1/(2T) Hz, where T is the sampling period. This is the same as the “Nyquist sampling theorem” that requires two samples per cycle for full characterization of a signal.
Examples:
Same pulses as above.
Is it possible to have a pulse that is both time and frequency limited? No, not exactly.
Bandwidth:
Absolute consider all frequency components
3dB where frequencies are 3dB down from peak
equivalent where half the power is in the band, and the other half is not
null-to-null distance between first nulls on either side of peak
bounded spectrum specify how much power is “out of bounds”
Power (99%) FCC, .05% above and .05% below.
(3) Overlap Interval: Pulses must all be orthogonal (multiply two pulses, and integrate them over time…. Result must be zero)