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Explain the effects of coefficient quantization in FIR filters

• Generally digital FIR filter are designed such that they have linear phase characteristic in the pass band. If FIR filter are realized using direct from realization then linear phase is maintained even when the quantization of filter co- efficients is done. • That means the quantization does not affect the phase characteristics of FIR filter, but it affects the ,magnitude response. To avoid this effect , the cascade form realization should be used and 12 to 14 bits should be used to represent the co-efficients. Similarly the number of bits per co-efficients must be increased to maintain the same error in the frequency response characteristic of the filter. Let us say each filter coefficients is rounded to (b+1) bits. Then the maximum error in the co efficient value is bounded as, − 2 − ( b + 1 ) < e n ( n ) < 2 − ( b + 1 ) − 2 − ( b + 1 ) < e n ( n ) < 2 − ( b + 1 ) The error in the frequency response can be given as, E M ( w ) = ∑ n = 0 M − 1 e n ( n ) .

Diversity methods

Diversity is a powerful communication receiver that provides wireless improvement at relatively low cost. It requires no training overhead since a training sequence is not required by the transmitter. Diversity exploits the random nature of radio propagation by finding independent signal paths for communication. All diversity decisions are made by receiver and are unknown to transmitter. If one radio path undergoes a deep fade, another independent path may have strong signal. By having more than one path to select from, both the instantaneous and average SNRs at the receiver may be improved by as much as 20db to 30db. Type of diversity methods A. Microscopic diversity:-  Small scale fading is characterized by deep and rapid amplitude fluctuations that occur when mobile moves over a distances of few wavelengths. These fades are caused by multiple reflections from the surroundings in the vicinity of mobile. In order to prevent rapid deep fades from occurring, microscopic diversit

RAKE receiver in CDMA system

Transmitted signal is received at receiver as time delayed multiple versions of transmitted signal due to propagation delay. RAKE receiver combines all multipath components of original transmitted signal in order to improve signal to noise ratio at receiver. It provides separate correlation receivers for each multipath component to combine all multipath components. RAKE receiver is diversity receiver designed for CDMA, where the diversity is provided by the fact that the multipath components are practically uncorrelated from one another when their relative propagation delays exceed a chip period. A RAKE receiver utilizes multiple correlators to separately detect the M strongest multipath components. The outputs of each correlator are weighted to provide a better estimate of the transmitted signal than is provided by a single component. Demodulation and bit decision is based on weighted outputs of the M correlators. Basic idea of RAKE receiver was proposed by Price and Green. In ou