Tag: Equalizer

A comparison of the input to a symbol-spaced versus fractionally-spaced equalizer
Wireless/SDR

A Classification of Equalization Techniques

We have seen before how a wireless channel distorts the Rx signal. The main task of DSP/comms engineer is to remove the Inter-Symbol Interference (ISI) from the Rx samples and recover the correct symbols. Equalization refers to any signal processing technique that eliminates or reduces this ISI before symbol detection. The output of an equalizer should be a Nyquist pulse for a single symbol case from which digital data can be recovered. A conceptual block diagram of such a process is shown below. The equalizer performs the bulk of the signal processing operations required at the Rx for proper demodulation.

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A composite channel model consisting of a pulse shaping filter, baseband channel and a matched filter
Wireless/SDR

Channel Estimation in Wireless Communication

Channel estimation is a special case of the system identification problem that has a long history in the field of signal processing. The most common method to estimate a channel at the Rx is based on a training sequence (i.e., a data-aided scenario). The strategies below explain the fundamental idea of channel estimation in single-carrier systems that are still used by most advanced channel estimation techniques (aided by fancy mathematical modifications in subsequent steps). Channel estimation in OFDM systems is a topic of another article. System Parameters In this article, the modulation symbols are denoted by $a[m]$ while the channel

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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
Wireless/SDR

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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Pilot contamination problem arises by reusing the same set of pilots in different cells
Wireless/SDR

What is Pilot Contamination in Massive MIMO?

5G NR standard supports both Frequency Division Duplex (FDD) and Time Division Duplex (TDD) modes in massive MIMO systems. For a reasonably pure estimate, it is necessary to make sure that each pilot transmission in a cell occurs in a vacuum, i.e., free from the interference of other pilots in the same time or frequency. This is achieved through orthogonality or separation of training signals in time or frequency slots. As we see now, simple orthogonality is not enough and new problems emerge due to the interaction among different cells in a network. Uplink A set of orthogonal pilots in

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A V-BLAST architecture for 4 Tx antennas
Wireless/SDR

V-BLAST with Successive Interference Cancelation

In the article on Zero-Forcing detector for MIMO receivers, we have seen that the performance of linear detectors is unsatisfactory for actual implementations of conventional MIMO systems. Their main attraction comes from their low computational complexity. To strike a nice balance between performance and complexity, a neat trick is employed by the algorithm known as Successive Interference Cancelation (SIC). The concept was devised by Gerard Foschini from Bell Labs, although it was not a new idea. Successive interference cancelation was already proposed for the detection algorithms in CDMA systems. Again, the fundamental idea was borrowed from decision feedback equalization schemes

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