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Digital Modulation Techniques Digital modulation The process by which digital symbols are transformed into waveforms that are compatible with the characteristic of the channel. Bandpass modulation Process whereby the amplitude, frequency, or phase of an RF carrier, or a combination of them, is varied in accordance with the information to be transmitted.

Digital Bandpass Modulation A carrier signal has three parameters which can be used for impressing: s( t) = θ ( t) = ω t s( t) = A( t) cosθ ( t) 0 + φ( t) A( t) cos[ ω t 0 + φ( t)] Amplitude Frequency Phase

Digital Bandpass Modulation If the amplitude, V of the carrier is varied proportional to the information signal, a digital modulated signal is called Amplitude Shift Keying (ASK) If the frequency, f of the carrier is varied proportional to the information signal, a digital modulated signal is called Frequency Shift Keying (FSK)

Digital Bandpass Modulation If the phase, θ of the carrier is varied proportional to the information signal, a digital modulated signal is called Phase Shift Keying (PSK) If both the amplitude,v and the phase, θ of the carrier are varied proportional to the information signal, a digital modulated signal is called Quadrature Amplitude Modulation (QAM)

Amplitude Shift Keying (ASK) ASK demonstrates poor performance, as it is heavily affected by noise and interference. Used in radio telegraphy in the early 1900s

Amplitude Shift Keying (ASK) General Analytic Expression The amplitude term values The phase,ϕis an arbitrary constant. The parameter E is symbol energy T is symbol time duration will have M discrete

Amplitude Shift Keying (ASK) M has to be chosen equal to 2, so it is corresponding to two waveform types. Also know as Binary ASK signaling (also called on-off off keying)

Amplitude Shift Keying (ASK)

Frequency Shift Keying (FSK) Bandwidth occupancy of FSK is dependant on the spacing of the two symbols. A frequency spacing of 0.5 times the symbol period is typically used. FSK can be expanded to a M-ary scheme, employing multiple frequencies as different states.

Frequency Shift Keying (FSK) The general analytic expression: The frequency term ωi has M discrete values The phase ϕ is an arbitrary constant.

Frequency Shift Keying (FSK) M has chosen equal to 3, corresponding to the 3 waveform types (3-ary). Emphasize the mutually perpendicular axes. The signal set is characterized by Cartesian coordinates, such that each of the mutually perpendicular axes represents a sinusoid with a different frequency. Such mutually perpendicular vectors are called orthogonal signals.

Frequency Shift Keying (FSK)

Phase Shift Keying (PSK) Phase Shift Keying (PSK) demonstrates better performance than ASK and FSK. PSK can be expanded to a M-ary scheme, employing multiple phases and amplitudes as different states. Filtering can be employed to avoid spectral spreading. Widely used in both military and commercial communications system.

Phase Shift Keying (PSK) General analytic expression: The phase term, ϕ ϕi (t), will have M discrete values With ϕi(t) given as:

Phase Shift Keying (PSK) M is chosen as 2, and it is called binary PSK (BPSK) The modulating signal shifts the phase of the wave si(t) to one of two states, either zero or π (180º). For the BPSK example, the vector picture illustrates the two 180º opposing vectors. Signal sets that can be depicted with such opposing vectors are called antipodal signal sets.

Phase Shift Keying (PSK)

Phase Shift Keying (PSK) Constellation of two-level PSK

Phase Shift Keying (PSK) Excellent performance of 2-PSK encourages us to go with 4-PSK, also called quadrature PSK (Q-PSK)

Phase Shift Keying (PSK) 4-PSK has more efficient usage of bandwidth than 2- PSK, because each signal unit has two bits. For the same bandwidth, the data bit rate doubles.

Example 1 Find the bandwidth for a 4 PSK signal transmitting at 2000 bps. Transmission is in half-duplex mode.

Phase Shift Keying (PSK) The idea can be extended to 8-PSK, 16-PSK, 32- PSK,. The limitation is the ability of equipment distinguish small differences in signal s phase. to 8 PSK

BPSK Modulator Binary PSK (BPSK) modulation can be accomplished by simply multiplying the original signal d(t) (which is a binary random sequence) by the carrier signal, which is an analog sinusoidal oscillation. After multiplication a bandpass filter is required

QPSK Modulator

Example 2 Given a bandwidth of 5000 Hz for an 8-PSK signal, what are the baud rate and bit rate?

Quadrature Amplitude Modulation (QAM) Combination of ASK and PSK which helps making a contrast between signal units. The number of amplitude shifts should be lower than the number of phase shifts due to noise susceptibility of ASK.

Quadrature Amplitude Modulation (QAM)

Bit and Baud Rate Comparison

Example 3 Compute the bit rate for 1000 baud 16 QAM signal.

Summarize

Demodulation/ Detection A binary bandpass system will transmit one of two waveforms, denoted s1(t) and s2(t). Si(t) is used as a generic designation for a transmitted waveform. The received signal r(t) degraded by noise n(t) and is rewritten as n(t) assumed to be a zero mean AWGN process. (degradation caused by unavoidable thermal noise)

Demodulation/ Detection Demodulation- Recovery of a waveform (to an undistorted pulse) Detection- decision making process of selecting the digital meaning of that waveform.

Demodulation/ Detection Step 1: Frequency down-conversion Frequency translation for signals operating at some radio frequency (RF) Receiving Filter (matched filter) To recover a pulse with the best possible signal to noise ratio (SNR), free of any ISI Equalizing Filter Compensate for the distortion caused by both the transmitter and the channel.

Demodulation/ Detection Predetection Point Sample / test statistic z(t) that has a voltage value directly proportional to the energy of the received symbol and that of the noise. Step 2: Threshold Comparison Decision is made regarding the digital meaning of that sample.

Demodulation/ Detection Coherent Detection When the receiver exploits knowledge of the carrier s phase to detect the signals. Noncoherent Detection When the receiver does not utilize such phase reference information to detect the signals.

Coherent Detection of PSK Consider the following binary PSK (BPSK) ϕ=arbitrary constant E= signal energy per symbol T = symbol duration.

Coherent Detection of PSK Convert the antipodal case into single basis function, ψ1(t) as Thus, express the transmitted signal, si(t) in terms of ψ1(t) and the coefficients ai1(t) as follows:

Coherent Detection of PSK For detection, the correlation receiver can be drawn as two product integrators, one of which is matched to s1(t), and the other is matched to s2(t)

Coherent Detection of PSK Assume that s1(t) was transmitted. Then the expected values of the product integrators as in Figure 5.1 with reference signals ψ1(t), are found as E{.} denotes the expected value.

Coherent Detection of FSK A typical set of FSK signal waveforms as below: E is the energy content of si(t) over each symbol duration T Assuming that the basis functions ψ1(t), ψ2(t),..ψn(t) form an orthonormal set, the most useful form for {ψj(t)} is

Coherent Detection of FSK The linear combination of N orthogonal waveforms ψ1(t), ψ2(t),.. ψn(t) These relationships are expressed in more compact notation as where

Coherent Detection of FSK The amplitude normalizes the expected output and can write as: Therefore, The ith prototype signal vector is located on the ith coordinate axis at a displacement from the origin of the signal space.

Coherent Detection of FSK Partitioning the signal space for 3-ary FSK signal The distance between any two prototype signal vectors si and sj is constant:

Noncoherent Detection of Differential PSK The term DPSK, refers to a detection scheme often classified as non coherent because it does not require a reference in phase with the received carrier. No attempt is made to determine the actual value of the phase from the incoming signal. Therefore, if the transmitted waveform is

Noncoherent Detection of Differential PSK The received signal can be characterized by α is arbitrary constant and is typically assumed to be a random variable uniformly distributed between zero and 2π n(t) is an AWGN process ( noise). If we assume that α varies slowly relative to two period times (2T), the phase difference between two successive waveforms, θj(t1) and θk(t2) is independent of α; ; that is,

Noncoherent Detection of Differential PSK To send the ith message (i= 1,2, M), the present signal waveform must have its phase advanced by ϕi= 2πi/M radians over the previous waveform. The detector measures the angle between the currently received signal vector and the previously received signal vector Figure: signal space for DPSK

Noncoherent Detection of FSK The detection hardware must be configured as an energy detector, without exploiting phase measurement In-phase (I) Quadrature (Q)

Noncoherent Detection of FSK The incoming signal will partially correlate with the cos (ω1t) reference and partially correlate with the sin (ω1t) reference. The noncoherent receiver require I and Q branch for each candidate signal in the signaling set. There are product integrators and squaring operation to prevent the appearance of any negative values. Each signal will be added from I and Q channel respectively. The final stage which the test statistic z(t) will be chosen based on which pair of energy detectors yield maximum output.