very good with strong distorted cahnnel where noise

very good with strong distorted cahnnel where noise is also
amplified with symbols at higher frequencies resulting in Inter symbol
Interference (ISI). To over come these limitations DFEs are used. DFEs use the
feedback of the received symbol to produce the estimated channel output. Thus
DFE is fed with detected symbols and produces an estimated output which is
subtracted from the output of linear equalizer.


Fig.2 Reformulated DFE for 2nd
order FBF

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2 shows the architecture of conventional adaptive DFE. It consists of two FIR
filters namely Feef forward Filter and Feedback FIlter. L and N are their
orders respectively.The operation of DFE can be explained with the following
sets of equation:


= fnTxn ?




= ? n ?






= Q?n






fn +  µenxn





= bn + µ  endn




where n is the current time
instance, xn is the vector of received samples, dn is the
vector of detected samples fn if FFF coefficient vector, bn
is the FBF coefficient vector.The critical path of DFE is shown by the dashed
line which consists of multipliers two adders and a reduce the
computational complexity two adders are replaced by the carry save full adder
and two input adder.Using TSMC 90nm CMOS standard the values od computational
delay of multipler, adder and slicer are found to be 1.54ns,0.74ns and 0.05ns
respectively.In this case the critical path estimated as 1.20 ns which is below
the throughput requirement of 5G. to overcome this limitation relaxed lookahead
DFE is used.It is similar to conventional DFE but it has an extra register in
the decision feedback loop to speedup the architecture by the factor of 2.The
architectural diagram of relaxed look ahead DFE is shown below.

Architectural diagram with relaxed look ahead DFE



            To reduce the computational complexity the feedback and
feedforward filter coefficients are stored in separate LUT and rapidly updated.
This process is done in two stages, hence it is called two stage precomputation
DFE. In first stage only few FBF coefficients are precomputed and saved in
separate LUT1 which reduced the multiplier complexity. In case of
PP-DFE (partially precomputed DFE) it is found that the remaining multipliers
are still high and occupies more area. This can be solved by precomputing and
storing the remaining multiplier coefficients in another LUT2 at
stage 2. Thus hardware and computational complexities are reduced.


            In this method first the LUT1 and LUT2
are transformed and then the proposed architecture is rescaled and unfolded to
achieve the higher throuhput.Now the content of LUT2 is reduced to
half the size by rescaling.This is done with the sign reversal operation for
the remaining content.Now the contents of LUT1 will disturb the
symmetry. Now by adding the FFF output minor symmetry can be achieved. Now
similar to LUT2 ,LUT1 is transformed.Thus the LUT of
stage 1 and 2 are reduced to combining these LUT with DFE our proposed
architechture is obtained.The iteration bond of the proposed architechture
decreases with the larger order of the filter.Thus it reduces the hardware
complexity.Generally it is difficult to store the output of FFF in LUT since
the LUT has to be dynamically updated and the output is larger which consumes
more power and time. But by adding the FFF output outside the LUT in our
proposed mrthos these limitations are overcomed.

            Fig.4. Proposed