In this article, we describe the impact of multipath caused by the wireless channel on the signal arriving at the receiver from a constellation viewpoint. Recall that an eye diagram, a transition diagram and a scatter plot are the stethoscopes of a communication system and hence it is imperative to bring in that perspective for a Tx signal convolved with the channel impulse response. This is because a wireless channel can be seen as a Finite Impulse Response (FIR) filter with the result that the sampled Rx signal is a convolution between taps of this FIR filter and the Tx
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Wireless communications and Software Defined Radio (SDR)
Why Digital Communication is Superior to Analog Communication
At the beginning, the history of wireless communication revolved around analog communication systems for several decades. Amplitude Modulation (AM) and Frequency Modulation (FM) were the most widely used techniques during this time. Gradually, however, a transition towards digital transmission occurred in wireless systems as well, a phenomenon that was in sync with digital revolution in the society as a whole. So what are the main benefits of digital technology that made it much superior to its analog counterpart? Let us analyze some of them below [1]. Performance Analog signals suffer from distortion and noise, even if they are small. Although
Continue readingWhat is Carrier Phase Offset and How It Affects the Symbol Detection
In case of Quadrature Amplitude Modulation (QAM) and other passband modulation schemes, Rx has no information about carrier phase of the Tx oscillator. Let us explore what impact this has on the demodulation process. Constellation Rotation To see the effect of the carrier phase offset, consider that a transmitted passband signal consists of two PAM waveforms in $I$ and $Q$ arms denoted by $v_I(t)$ and $v_Q(t)$ respectively and combined as \begin{equation}\label{eqRealWorldQAMPhaseOffset} s(t) = v_I(t) \sqrt{2} \cos 2\pi F_C t – v_Q(t) \sqrt{2}\sin 2\pi F_C t \end{equation} Here, $F_C$ is the carrier frequency and $v_I(t)$ and $v_Q(t)$ are the continuous versions
Continue readingFree Space Propagation in mmWave Systems
In this article, we describe the free space propagation in mmWave systems. During the discussion, we dispel a common myth that the received power at any distance decays with increasing carrier frequency. We will see that the received power is in fact independent of the carrier frequency for suitably designed systems such as those at mmWave frequencies. Instead, it is only after including the atmospheric effects such as water vapors, oxygen, rain and penetration loss in materials that the carrier frequency plays a substantial role in establishing the link budget. Suppose that a Tx transmits $P_{\text{Tx}}$ watts of power uniformly
Continue readingThe Fundamental Problem of Synchronization
We have seen in the effect of phase rotation that the matched filter outputs do not map back perfectly onto the expected constellation, even in the absence of noise and no other distortion. Unless this rotation is small enough, it causes the symbol-spaced optimal samples to cross the decision boundary and fall in the wrong decision zone. And even for small rotations, relatively less amount of noise can cause decision errors in this case, i.e., noise margin is reduced. In fact, for higher-order modulation, the rotation becomes even worse because the signals are closely spaced with each other for the
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