OFDM Maximal ratio combining

Hello all:

I want to know more about how Maximal ratio combining is done in an
OFDM based system. I have some IEEE references but cannot get an
insight as to how this is to be implemented. I am particularly
interested as to how to cophase the signals on the two channels and
then combine them. What sort of circuitry can be used to do this, say
in a 802.11a WLAN system.


Here are some of the references

Postdetection Maximal Ratio Combining Diversity Receiver with Scalar
Phase Signals
- Tomoaki Kumagai and Kiyoshi Kobayashi

Receive Diversity for Mobile OFDM Systems
- A. A. Hutter I, J. S . Hammerschmidt I , E. de Carvalho 2, J. M.
Cioffi

Pre-DFT Combining Space Diversity Assisted COFDM
- Minoru Okada and Shozo Komaki,

Optimal Maximal Ratio Combining With Correlated Diversity Branches
- Xiaofei Dong, Member, IEEE, and Norman C. Beaulieu, Fellow, IEEE

Optimal Antenna Diversity Combining for IEEE
802.1 la System
- Xuemei Ouyang, Monisha Ghosh and Joseph P. Meehan

Optimum Combining for Indoor Radio Systelms
with Multiple Users
- Jack Winters 


Thanks
-IM

IM 쓴 글:
> Hello all:
> 
> I want to know more about how Maximal ratio combining is done in an
> OFDM based system. I have some IEEE references but cannot get an
> insight as to how this is to be implemented. I am particularly
> interested as to how to cophase the signals on the two channels and
> then combine them. What sort of circuitry can be used to do this, say
> in a 802.11a WLAN system.

For simple explanation, assume that we have two receive antenna 
branches. Two brance yields two recevied signals x1(t) and x2(t)
and two pilot signals p1(t) and p2(t). The pilot signals are equivalent 
to the channels, c1(t) and c2(t), between the transmiter and each 
received branch, respectively, except they includes the unnecessary 
noise, n1_p(t) and n2_p(t). That is, the received pilot signals are 
represented as

p1(t) = c1(t) + n1_p(t) ~= c1(t),
p2(t) = c2(t) + n2_p(t) ~= c2(t).

Assuming that s(t) is transmitted information, the recevied signals are 
given by

x1(t) = c1(t)*s(t) + n1(t),
x2(t) = c2(t)*s(t) + n2(t)

where n1(t) and n2(t) are the noise signals. From the theory of maximal 
ratio combine (MRC), the combined signal is obtained as

x(t) = c1(t)'*x1(t) + c2(t)'*x2(t)

which maximize the signal to noise ratio before detecting the 
transmitted information, such as

s_dec(t) = dec( x(t))

where dec(.) is a decision function. For BPSK without channel coding, 
dec( x) is given by

dec( x) = {0 for x > 0, and 1 for x < 0}.

I have omitted the detailed theory to proof the optimality of MRC and an 
example which considers OFDM modulation at this note.

-James G.

HI James:

Thanks for the info.

Here's my understanding.

In the case of the OFDM,  I would have to do the above for each and
every carrier. Considering the 2 path case as you mentioned above we
have

x_m(t) = c1_m(t)*x1_m(t) + c2_m(t)*x2_m*(t).

where m represents the carrier number, i.e. 1_m representing antenna 1
data corresponding to carrier m and
2_m representing antenna 2 data corresponding to carrier m.

Combining should be done before channel decoding and decision making,
hence just after equalization. What bothers me is '+'
sign during combining in x_m(t) = c1_m(t)*x1_m(t) + c2_m(t)*x2_m*(t).

 Intuitively I feel that the we would need to weigh a signal based on
how strong the power of the signal is
on an antenna path since I would be better off trusting the signal on
the higher powered path.
So In the 2 antenna case, say signal x1_m(t) and x2_m(t) are the output
of the equalizers for carrier m in path 1 and path 2 respectively. I
would
combine by
x(t)  = w1*x1_m(t) + w2*x2_m(t);

where w1 and w2 are weights that maximize x(t) in such way as to
maximize SNR. Now if x1_m is the higher powered signal (based on RSSI
measurements), then w1 > w2 and w1 + w2 = 1; w1 and w2 should probably
be calculated based on RSSI of path 1 and path 2.
The combining occurs. But the signals x1_m and x2_m could be out of
phase. How to take care of this phase difference. Having separate
equalizers
for each path won't help, We would need information from one path that
can be used by the other path to offset the phase difference
(cophasing)?
How can that be done?
So does it make sense to do the combining after decision making, the we
sort of put off the cophasing issue?

Please comment.

IM wrote:
> I would combine by
> x(t)  = w1*x1_m(t) + w2*x2_m(t);
> 
> where w1 and w2 are weights that maximize x(t) in such way as to
> maximize SNR. Now if x1_m is the higher powered signal (based on RSSI
> measurements), then w1 > w2 and w1 + w2 = 1; w1 and w2 should probably
> be calculated based on RSSI of path 1 and path 2.
> The combining occurs. But the signals x1_m and x2_m could be out of
> phase. How to take care of this phase difference. Having separate
> equalizers
> for each path won't help, We would need information from one path that
> can be used by the other path to offset the phase difference
> (cophasing)?
> How can that be done?
> So does it make sense to do the combining after decision making, the we
> sort of put off the cophasing issue?

I am not good at 11n but I have seen 16e a little bit. So, I'll explain 
the combining techniques based on the 16e OFDM structure. Assuming that 
carrier n is located close enough to carrier m, the  pilot signal, 
p1_n(t) and p2_n(t), transmitted through carrier n can be used for 
determining the weight. Therefore, for MRC, w1 = p1_n*(t) and w2 = 
p2_n*(t) can be used where * is the conjugate operator.

In addition, the power constraint on weights is |w1|^2 + |w2|^2 = 1, 
which is usually applied for simplification.

- James G.

Thanks again James.

It is begining to make sense to me now.
All I know about 16e PHY is that it is OFDM based. Does the 16e talk
about the cophasing?

Thanks

IM wrote:
> Thanks again James.
> 
> It is begining to make sense to me now.
> All I know about 16e PHY is that it is OFDM based. Does the 16e talk
> about the cophasing?
> 
> Thanks
> 

To simplify the diversity combine, we can use equal gain combining (EGC) 
insead of maximal ratio combining (MRC) although the pilot singal exists 
per each coherence group of subcarriers. Moreover, as you said there are 
two different diversity combining methods which are post-decoding 
combining and pre-decoding combining. In the diversity system which 
considers post-decoding combining, the decoded bits from two antenna 
branches are combined after the bit is decoded based on the effective 
signal to noise ratio (SNR) of each bit. In this case, selection 
combining (SC) is more preperable than the others because of its easy 
applicability.

- James G.

>IM wrote:
>> Thanks again James.
>> 
>> It is begining to make sense to me now.
>> All I know about 16e PHY is that it is OFDM based. Does the 16e talk
>> about the cophasing?
>> 
>> Thanks
>> 
>
>To simplify the diversity combine, we can use equal gain combining (EGC)

>insead of maximal ratio combining (MRC) although the pilot singal exists

>per each coherence group of subcarriers. Moreover, as you said there are

>two different diversity combining methods which are post-decoding 
>combining and pre-decoding combining. In the diversity system which 
>considers post-decoding combining, the decoded bits from two antenna 
>branches are combined after the bit is decoded based on the effective 
>signal to noise ratio (SNR) of each bit. In this case, selection 
>combining (SC) is more preperable than the others because of its easy 
>applicability.
>
>- James G.
>

Hi, 
After I have measured the SNR of the pilot signal on each branch, in what
way I should calculate the weight of this path? What is the formula of
this factor w?

thanks