CONCLUSION

 

The capacity of a typical digital communication system following the principle of synchronized detection was derived under the assumption that the system operates on a flat fading MIMO channel and uses an interleaver to combat bursty error events. This is a frequently used model which underlies many practical communication systems, because most well-known channel codes have been devised to combat statistically independent errors. The interleaver plays a crucial role in the derivation of the capacity, since it completely breaks up the channel memory. This assumption leads to uncorrelated received data symbols, and consequently to a channel model which lends itself to the computation of capacity. It must be mentioned that, exactly because the correlation between received data symbol vectors is not used, some information is "thrown away''. Differently phrased, communication systems which exploit that additional information will offer higher capacities, an issue which we are currently investigating.

The interleaver framework was then used to calculate the optimal channel sampling period L for flat fading channels with normalized Doppler frequencies ranging from 0.005, ¼, 0.05. It was shown that especially for low Doppler frequencies a proper choice of L is very important in order to limit any capacity losses. Furthermore, the results for the 4 ×4 MIMO system demonstrate that for low Doppler frequencies capacity scales almost linearly with the number of antenna pairs, whereas for increasingly higher Doppler frequencies capacity eventually degrades substantially. This degradation is a direct result of the growing need for pilots when the number of transmit antennas is increased. Considering that the percentage of the data rate which is dedicated to pilots grows linearly with the number of transmit antennas, it becomes clear that, for a large amount of antennas and a rapidly varying channel, DA channel estimation becomes problematic. At the higher Doppler frequencies and higher SNRs this leads to the fact that capacity continuously increases right up to the Nyquist sampled channel, an observation which led us to examine the case of an undersampled channel more closely. It turned out that, at least for the setup considered here, undersampling did not result in an increased capacity. This is due to the fact that once aliasing occurs, the MSE of the channel estimate increases sharply, and thus further reduces the capacity, even though fewer pilot symbols are used.

We would like to remark that there do exist some cases in which undersampling leads to a capacity increase (e.g. for very low SNRs or for small symbol alphabets). In such a case, or when a high Doppler frequency leads to intolerable degradations, coherent detection with DA channel estimation proves inefficient. Perhaps differential space-time modulation strategies which were recently published in [15] and [ name="CITEhochwald" rtekeep="1">16] constitute a remedy. For small symbol alphabets, another alternative might be to employ blind channel estimation schemes, which exploit the structure inherent in the modulation. The larger the symbol alphabet, though, the more it lacks this inherent structure and therefore blind channel estimation schemes are not a sensible alternative for large symbol alphabets.

APPENDIX
Mutual Information of a Flat Fading Channel with Interleaver/Deinterleaver

 

If the chain rule for information [2] is applied to equation (8) it can be rewritten as

 
 
I(z;A | AP , zP) =
 
 
 
 
  ND-1
Ã¥
j=0
  ND-1
Ã¥
k=0
I( zj ; Ak | z0 ¼zj-1,A0 ¼Ak-1, AP , AP )
(34)
 

Furthermore, it is assumed that the interleaving/de-interleaving operation has completely broken up the channel memory. Consequently, a received symbol vector zk does not convey any information about Aj ¹ k. Thus, for j ¹ k we have that

 
 

ND-1
Ã¥
j=0
  ND-1
Ã¥
k=0

j ¹ k
I( zj ; Ak | z0 ¼zj-1,A0 ¼Ak-1, AP , zP ) = 0
 
(35)

Likewise, since any zk or Ak do neither depend on z0, ¼, zk-1 nor on A0, ¼, Ak-1, for k=j, we arrive at

 
 
 

ND-1
Ã¥
j=0
  ND-1
Ã¥
k=0

j = k
I( zj ; Ak | z0 ¼zj-1,A0 ¼Ak-1, AP , zP ) =
 
 
 
 
  ND-1
Ã¥
k=0
I( zk ; Ak | z0 ¼zk-1,A0 ¼Ak-1, AP , zP ) =
 
 
 
 
ND-1
Ã¥
k=0
I( zk ; Ak | AP , zP )
(36)
 

The flat fading channel with interleaver/de-interleaver is therefore completely characterized by the distribution p(zk | Ak,AP,zP).

Contact

Jens Baltersee, Gunnar Braun, Meik Dörpinghaus

References

References

 

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