Early research[ edit ] MIMO is often traced back to s research papers concerning multi-channel digital transmission systems and interference crosstalk between wire pairs in a cable bundle: In the mids Jack Salz at Bell Laboratories took this research a step further, investigating multi-user systems operating over "mutually cross-coupled linear networks with additive noise sources" such as time-division multiplexing and dually-polarized radio systems. Space-division multiple access SDMA uses directional or smart antennas to communicate on the same frequency with users in different locations within range of the same base station.
Transmit pulse shaping filter — rectangular and sinc Nyquist by Krishna Sankar on April 14, In the previous post on I-Q modulator and de-modulatorwe had briefly mentioned that the a baseband PAM transmission can be modelled aswhere is the symbol to transmit, is the transmit filter, is the symbol index and is the output waveform.
In this post, the objective is to understand the properties of the transmit filter i. The sequence of transmit symbols maybe visualized as follows.
Transmit symbols for baseband PAM transmission To recover the symbols fromone may sample the waveform at multiples of symbol interval. The sampled waveform can be. Breaking the above equation into two parts, From the above equation, it is intuitive that for ensuring no inter symbol interference ISIthe second term in the above equation should be zero i.
Rectangular filter The most simplest filter is the zero-order hold filter, i. Mathematically, the filter can be represented as. The filtered waveform can be as shown below. Baseband PAM transmisison with rectangular filtering Though there is no ISI with rectangular filtering, we will show later that this filtering is not be optimal from the bandwidth perspective.
Filtering with sinc shaped pulses From our textbooks, we may recall that sinc shaped pulses have have a band limited rectangular spectrum. For example, consider the sinc pulse of width. Time domain response of sinc filter As desired, the above filter has zeros at and non-zero value at time.
The corresponding frequency response is a rectangular pulse bandlimited from Hz to Hz. The frequency response is as shown below: Frequency response of sinc shaped filter Infact, the above sinc shaped pulse satisfies the Nyquist criterion and is called Nyquist pulse Refer Sec 5.
It follows that with the sinc shaped pulse also called Nyquist pulse used for transmit filtering: Click here to download. The observed spectrum is as shown below. Transmit spectrum with rectangular and sinc shaped pulse shaping filter Summary 1. From the above spectrum plot, the sinc shaped filter does not result in perfectly bandlimited spectrum from from Hz to Hz.
This is because, by theory, the sinc pulse exists from to. However, for simulations the sinc pulse is truncated for a finite duration.
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This results in negligible less than dB spectral content present outside Hz. The above discussion does not present why the sinc shaped filtering is optimal for ensuring minimum bandwidth.
For the theoretical understanding, one may refer Sec 5.Millimeter-Wave MIMO Architectures for 5G Gigabit Wireless Akbar M. Sayeed Wireless Communications and Sensing Laboratory Electrical and Computer Engineering.
In the previous post on I-Q modulator and de-modulator, we had briefly mentioned that the a baseband PAM transmission can be modelled as, where.
is the symbol period, is the symbol to transmit, is the transmit filter, is the symbol index and. is the output waveform.
Selected IEEE Journal Papers: M. Zheng, C. Ling, Wen Chen, and heartoftexashop.com, "Polar Coding Strategies for the Interference Channel with Partially-Joint Decoding," IEEE Transactions on Information Theory, F.
Wei, Wen Chen, Y. Wu, J. Li and Y. Luo, "Towards 5G air Interface Technology: Sparse Code Multiple Access," IEEE Vehicular Technology . International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research. Tutorial 22 – Orthogonal Frequency Division Multiplex (OFDM, DMT) - Description: Orthogonal Frequency Division Multiplex (OFDM, DMT) Download: heartoftexashop.com