Feedback overhead is arose when a receiver transmits feedback signaling to a transmitter, which occupies the uplink transmission resource. Although the larger feedback overhead improves the downlink performance, the portion of feedback overhead in the uplink transmission time or the whole system transmission time should be well balanced so that the uplink throughput performance is significantly suffered.

Design Methodology of Optimal Feedback Overhead Signalling Edit

One of method for designing optimal feedback overhead is to maximize the feedback gain $ \Delta R_\mathrm{dn} $ in the downlink subtracted by the feedback loss $ \Delta R_\mathrm{up} $ in the downlink, which we define as the effective throughput gain $ \Delta R_\mathrm{eff}(T_\mathrm{OS}) = \Delta R_\mathrm{dn}(T_\mathrm{OS}) - \Delta R_\mathrm{up}(T_\mathrm{OS}) $. The optimization criterion is given by

$ T_\mathrm{OS}^* = \max_{T_\mathrm{OS}} \Delta R_\mathrm{eff}(T_\mathrm{OS}). $

This is different from an approach which finds an appropriate amount of feedback signalling overhead for the given target rate. /* effective in the maximization of the duplex throughput.*/

As an example motivated from limited feedback multiuser MIMO system, we assume that $ \Delta R_\mathrm{dn}(T_\mathrm{OS}) = R_\mathrm{dn} - \Delta R_\mathrm{dn,max} + \alpha T_\mathrm{OS} $ and $ \Delta R_\mathrm{up}(T_\mathrm{OS}) = R_\mathrm{up} (T_\mathrm{OS}/T) $. The optimization of the feedback overhead is given by

$ T_\mathrm{OS}^* = \max_{T_\mathrm{OS}} R_\mathrm{dn} - \Delta R_\mathrm{dn,max} + \beta T_\mathrm{OS} $

where $ \beta = \alpha - R_\mathrm{up}/T $ is generally a dependent variable on $ T_\mathrm{OS} $. If we fix the range of the overhead time, we know whether incremental or decremental of the feedback signaling is beneficial for the performance of the limited feedback systems. For example, Jindal shows that the limited feedback ZF-BF system yields approximately [1]

$ \Delta R_\mathrm{dn,max} - \alpha T_\mathrm{OS} = \log_2 \left( 1 + \frac{P}{M} 2^{-\frac{T_\mathrm{OS} R_\mathrm{dn}}{M(M-1)}} \right). $

The right side of the above equation becomes $ \log_2 \frac{P}{M} - \frac{T_\mathrm{OS} R_\mathrm{dn}}{M(M-1)} $ and $ \frac{P}{M} 2^{-\frac{T_\mathrm{OS} R_\mathrm{dn}}{M(M-1)}} $ for high and low SNR range (relying on $ P $), respectively. We see that the lower SNR range, the less sensitive on the throughput performance of the limited feedback system if the feedback overhead increases while the feedback loss in the uplink still linearly increases.


  1. N. Jindal, MIMO Broadcast Channels with Finite Rate Feedback, IEEE Trans. Information Theory, Vol. 52, No. 11, pp. 5045-5059, Nov. 2006.
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