Spectrum of the Nyquist pulse and its symbol rate shifted version exhibit a spectral null at 0.5 symbol rate for a 0.5 timing offset

Why the Performance of an Equalizer Depends on Symbol Timing Phase

This post is written on an advanced topic mainly for practitioners and researchers in the design of wireless systems. For learning about wireless communication systems from a DSP perspective (the idea behind SDRs), I recommend you have a look at my book. One of the main questions in the design of a wireless receiver is the interactions among the three main blocks, namely the timing recovery loop, the equalizer and the carrier recovery loop. Life would have been easy if input to any of these blocks was independent of the output from the others. That obviously is not the case.

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Multiple stable lock points in the S-curve of a decision-directed loop

Resolving Phase Ambiguity through Unique Word and Differential Encoding and Decoding

In the context of carrier synchronization, we have discussed the Costas loop and other techniques before. Today, we discuss the significance of differential encoding and decoding for phase ambiguity resolution. Keep in mind that this topic is different than differential detection. In the former case, the data bits are encoded before modulation and decoded after demodulation in a differential manner. Nevertheless, the demodulation is still coherent (i.e., it requires carrier synchronization). In the latter case, the data symbols are detected during demodulation through differential operations, thus canceling the effect of channel phase and eliminating the need for carrier synchronization. Let

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The effect of symbol timing offset on an OFDM symbol

Effect of Timing Mismatch in OFDM Systems

Timing synchronization is one of the most fascinating topics in the field of digital communications. The impact of symbol timing offset has been discussed in the context of single-carrier systems before. The intuition behind how an OFDM system works is also presented in a previous article. However, the problem of timing synchronization is quite different in OFDM systems as compared to single-carrier systems due to the nature of the waveform. Let us explore how a timing error impacts the demodulated waveform in such a scenario. To avoid using many indices, we skip the OFDM symbol index $m$ in the following

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Converging towards angle 30

Coordinate Rotation Digital Computer (CoRDiC)

Digitial Signal Processing (DSP) plays a crucial role in algorithm implmentation for building digital and wireless communication systems. A common theme in all those algorithms is that they can be implemented with the following simple operations: addition multiplication shift In fact, these are the basic principles on which a digital signal processor is constructed. However, when it comes to implementation of real-time systems in hardware such as FPGAs, we find ways to reduce the complexity even further. Which operation (out of the above three) do you think is the most demanding in computations? It is the multiplications. Therefore, it is

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A description of a real space-time code

Understanding Space-Time Codes: Alamouti Scheme

In major cellular and wireless networks today, space diversity is employed with the help of multiple Tx antennas and/or multiple Rx antennas giving rise to Multiple Input Multiple Output (MIMO) systems. There are three different modes in which multiple antennas can be deployed: Beamforming Spatial Multiplexing Space-Time Coding In this article, we discuss space-time coding that achieves Tx diversity through multiple antennas at the Tx and simple linear processing at the Rx. This simplicity made this technique quite suitable for the past generations of cellular and other infrastructure based networks. There are two main kinds of space-time codes: Space-Time Block

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