Lecture 12 - Analog Communication (II)

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1 Lecture 12 - Analog Communication (II) James Barnes (James.Barnes@colostate.edu) Spring 2014 Colorado State University Dept of Electrical and Computer Engineering ECE423 1 / 12

2 Outline QAM: quadrature amplitude modulation SSB: single sideband Lab suggestions Reference: Tretter Chapters 5-8 (On e-reserve), Haykin, Communication Systems, Third Edition Colorado State University Dept of Electrical and Computer Engineering ECE423 2 / 12

3 QAM Basics QAM= Quadrature Amplitude Modulation QAM is both a generic term which encompasses AM, FM, DSB-SC, and SSB ( linear modulation techniques ) and a specific technique for sending two independent messages over one carrier. For AM and SSB with pilot signal, the receiver oscillator can be derived from s(t); for DSB-SC and SSB without pilot signal, the receiver oscillator must be independently created. Colorado State University Dept of Electrical and Computer Engineering ECE423 3 / 12

4 QAM Modulator/Demodulator A picture of QAM commonly used in analog communication is given below. There is an alternate picture which is more useful and common in DSP, which will be shown later. For this representation, using the othogonality of sin(.) and cos(.), it is straightforward to show that the outputs of the LPF blocks are proportional to x(t) and y(t) as shown in the figure. Colorado State University Dept of Electrical and Computer Engineering ECE423 4 / 12

5 Modulation Types For AM, x(t) = A c [1+k a m(t)], y(t) = 0. For DSB-SC, x(t) = A c m(t), y(t) = 0. For SSB, x(t) = m(t), y(t) = ˆ m(t). For QAM modulation, x(t) and y(t) can be independent signals, called in-phase and quadrature respectively. For FM, x(t) = cos(φ(t)), y(t) = sin(φ(t)). Colorado State University Dept of Electrical and Computer Engineering ECE423 5 / 12

6 Complex Baseband Representation of Passband Signals We can picture x(t) and y(t) as being real and imaginary components of a complex baseband signal z(t) = x(t) + jy(t). z(t) can be transformed into a real passband signal and vice-versa. This is modulation and de-modulation. With independent x(t) and y(t), the modulated passband signal will be similar to DSB-SC in bandwidth utilization, but we will send two independent channels in the same bandwidth. If x(t) and y(t) are not independent, but instead y(t) = ±x(t), ˆ ˆ Hilbert tranform, then we can send one channel in either the upper sideband or lower sideband only (SSB), thus using half the bandwidth of DSB-SC and power of DSB-SC. Colorado State University Dept of Electrical and Computer Engineering ECE423 6 / 12

7 Modulation of Complex Baseband Signal Let w(t) = z(t)e jωct, where ω c is the carrier frequency. We know from the Modulation Theorem that W(ω) = Z(ω ω c ). W has only a positive frequency component (is an analytic signal ) and spans a bandwidth of 2B, which is the bandwidth of z(t). We can form a real passband signal by converting w(t) to real: s(t) = 1 2 [w(t)+w(t)], where w(t) is the complex conjugate of w(t). Can easily show that s(t) = z(t)e jωct +z(t)e jωct = x(t)cos(ω c t) y(t)sin(ω c t). Colorado State University Dept of Electrical and Computer Engineering ECE423 7 / 12

8 Demodulation of Complex Baseband Signal Assume the received signal is s(t) (no channel distortion). First put s(t) through a phase splitter filter φ(t) FT Φ(jω) = u(ω), where u(ω) is a frequency step function. The phase splitter discards the negative frequency term in s(t) and we recover w(t) = z(t)e jω ct. Next multiply w(t) by a locally-generated complex exponential e jω ct to recover z(t). Colorado State University Dept of Electrical and Computer Engineering ECE423 8 / 12

9 Recovering Carrier We cannot regenerate the carrier using the quadrature component, as with the Costas receiver. There are two strategies for dealing with this: 1. Free-running at the carrier frequency, with some phase error (distortion). This is tolerable for many applications (voice). 2. Add small DC component to m(t) pilot tone. This requires that m(t) be passband (no DC component). Then s(t) = x(t)cos(ω c t) y(t)sin(ω c t)+pcos(ω c t). This produces a small carrier signal which can be locked onto by a PLL or amplified to create the local oscillator signal. Colorado State University Dept of Electrical and Computer Engineering ECE423 9 / 12

10 SSB Modulation To achieve SSB, the only difference is that we generate the complex baseband signal from a real baseband signal m(t) by passing through a phase splitter. This creates an analytic signal z(t) = m(t)±jm(t) ˆ which has only positive or negative frequency components. This is the positive or negative pre-envelope. When multiplied by e jωct and converted to real, s(t) will have only upper or lower sideband components, depending on the sign in z(t). De-modulation in principle is the same as before. Colorado State University Dept of Electrical and Computer Engineering ECE / 12

11 Practical: Creating a Phase Splitter Remember that H(jω) = jsgn(ω) is the Hilbert Transform. There are cof files for various orders of Hilbert Transformers in the lab support files. How do you multiply by j? 1 r(t) = s(t) + w(t) = s(t) + j (t) -j sgn( ) j Phase Splitter: ( j ) Colorado State University Dept of Electrical and Computer Engineering ECE / 12

12 Practical: QAM Receiver using Pilot Tone received signal -j sgn( ) x Re[ ] BPF DAC x(t) nt o Hilbert Transformer Im[ ] BPF DAC y(t) 1 r 1 2r cos( t ) z c o 1 2 r z 2 Baseband Filters That Remove DC Components 1 r cos( c o t ) z 1 In-phase Carrier rsin( c o t ) z 1 Quadrature Carrier Bandpass Carrier Recovery Filters Colorado State University Dept of Electrical and Computer Engineering ECE / 12

COMM 601: Modulation I

COMM 601: Modulation I Prof. Ahmed El-Mahdy, Communications Department The German University in Cairo Text Books [1] Couch, Digital and Analog Communication Systems, 7 th edition, Prentice Hall, 2007. [2] Simon Haykin, Communication