Multipath fading is an important aspect in WSN design and there are many papers in literature . Just GoogleScholar it. One recent paper is below:

http://www.iret.co.in/Docs/IJNTEC/Volume2/Issue2/2.%20Minimum%20Transmitting%20Power%20and%20Other%20Performance%20Metrics%20in%20Regular%20WSN%20In%20Fading%20Environment%20.pdf

Definitely multi-path fading affect the detector output in wireless communication receiver.

Electromagnetics signals are waves, then:  the instantaneous energy depends if the multipath signals are in phase or no, this is the basic idea undelaying fading.

Indeed multipath fading affects the performance of receivers in wireless communications, but if you are interested in energy collection and you're willing to reduce the bit-rate you can collect all the energy in a given symbol period (e.g. by integrating the square root of the received signal). The problems with this non-coherent approach is that is hard to reject interference, and synchronization is also complex (with a non-perfect synchronization the risk is that not all the energy is collected).

An approach typically used to counter multipath fading is the rake receiver, but it's normally used for coherent receivers, not for energy-detection.

Try to obtain a paper "Estimate of Local Average Power of a Mobile Radio Signal" by William C.Y. Lee

It is a cornerstone in all such measurements, and a proper procedure to gather data for propagation modelling of any kind.

Propagation channel in modelled using tapped delay line (TDL) model to take into account the multipath fading. The resulting signal at receiver side depends on the amplitude and the phase of each path. In the literature, you can find can find different power profiles describing various environments (urban or rural and also pedestrian or vehicular depending on the mobile velocity).

Multipath fading affect energy detection in wireless communication receivers as

the signal that reaches the reciever is just not only through LOS but also NLOS hence the path difference leads to the phase difference & thus the receiver receives several replicas of the original signal with varying amplitudes, time & phases causing Inter symbol interference etc.

Multipath fading is achieved in a emulated way in a reverberation chamber  (RC). By an RC are emulated and studied the characteristics of the channels for wireless communications. In an RC the signals for wrireless communications are transmitted and received. You can see the literature on RC; there you find many answers for your question!

Best Regards

Angelo Gifuni

thanks for the above contributions but all of them are lacking the answer to the question. 

Rather strange for a person asking question to comment negatively on all the responses. 

In my opinion, you do not want a contribute that helps you to find the aswer; you want the solution directly. I confirm my previous answer again!

When the questions is "How is energy detection implemented and how the delay spread or inter-arrival times of the echoes of multi-path fading have an effect on the detector output?" and all the answers are basically "multipath affects receivers"!! Then, why mentioning that the answers are not to the point is a bad thing?!

Dear Gifuni Angelo:

Can you please explain in a scientific way how does your answer on reading about reverberation chamber (RC) answer the above question? Basically how does that answer 

i) "How is energy detection implemented" and 

ii) "How the delay spread or inter-arrival times of the echoes of multi-path fading have an effect on the detector output?"

I am very familar with wireless channels and been in wireless research for more than a decade: http://scholar.google.com/citations?user=0uHjG2gAAAAJ&hl=en'

So, just telling me that wireless transmission causes multipath which is harmful to receiver is not any way helpful. 

I think that, the answer can be found experimentally by working with the signal received in an RC when different signals of feeding are used (monochromatic and modulated). The experimental observation helps to find the mathematical model.  

Best Regards

Dr Ramy Abdallah

Nice to see your impressive work on wireless communication.

Not sure whether you had seen the following paper which could be of some use to your work.

Performance of an Energy Detector over Channels

with Both Multipath Fading and Shadowing

IEEE Transactions on Wireless Communication SACTIOACTIONS ON WIRELESS VOL. 9, NO. 12, DECEMBER 2010

http://www.ece.ualberta.ca/~hai1/TWireless_2010_12.pdf

Sorry for some typos in my previous mail.

Read the Reference as

Performance of an Energy Detector over Channels

with Both Multipath Fading and Shadowing

IEEE Transactions on Wireless Communication, Vol. 9, No. 12, December 2010

I've noticed I received a -1 for citing a paper that basically answers 100% of the original question, only to learn that the original poster is a prolific author in a communications field that asks questions on the basics of radio survey. Ramy M. Abdallah, please remind me next time that there is some odd test of yours that I have to pass before I can even aspire to your high standards.

Davor, I am not asking basic radio survey question. I was looking for a mathematical model whereby it shows the effect of ignoring the multi-path echoes in energy detection receivers on BER analysis vs taking all the echoes into account. The effect could be immense on the simplicity of obtaining closed form expressions for outage probability for example. I did not find the answer in the paper you cited. However, I agree that it quite close to the topic. I will take the -1, I apologize, your original post came with few useless posts.

BTW, there is not test except that I am trying to do my part and encourage everybody is that in order for RG to continue as a nice academic portal is to only answer questions with meaningful contributions.    Thanks for your contribution. Yeah, may be my standards are a bit high :) 

Dear Jayaraman V,

this is what am looking for. thanks a lot for pointing out this paper. 

With all due respect, what you mention now is quite different from the original question. I'm not used to read other peoples' minds. Not yet.

Anyway, good luck with your research. There is a lot going on between the antenna and information output. The fair way of observing the resulting BER is a function of a margin added on top of the Shannon limit for a given technology. Energy per bit is the measure you are seeking for, as bulk energy of received signal (indicated in your original question) is not saying a lot about the processing power of your system.

You also never mentioned interference from neighbouring sources. Real life systems performance calculation is not complete without those. I've seen some such calculations heavily abused in marketing, but never replicated in real networks.

It would help a lot if you simply say what system you have in mind.

You can find the answer to your question in the Chapter 5 (section 5.7)  of the book Fundamentals of Statistical Signal Processing_Detection Theory _Vol II by Steven M. Kay