Link Adaptation Using Dynamically Allocated Thresholds and Power Control

Abstract

Link adaptation technique, in which the modulation and coding used in a communication system is changed as per the channel conditions is a very well investigated topic for link throughput maximization with widespread application in wireless access networks. Most of the known algorithms dynamically adjust transmitter data rate by comparing instantaneous SNR with pre-defined SNR switching thresholds, in order to maximize throughput while maintaining the desired quality of service. However, the use of incorrect or stale values of these pre-defined switching thresholds often leads to selection of erroneous modulation and coding schemes resulting in unsatisfactory throughput or quality of service. This work introduces a novel scheme which achieves the maximum possible throughput while maintaining the target quality of service by dynamically acquiring the threshold values of different modulation and coding schemes used in the system for a given value of block error rate based on measurement at the receiver. This helps in keeping the threshold look up table up to date, so that proper threshold values for mode switching is present for all channel conditions. Also, a relationship between the throughput and the accuracy of the threshold value calculation is provided so that these can be optimized depending on the user requirements. The performance evaluation shows that the proposed system outperforms the conventional link adaptation in various operating scenarios where pre-determined look up tables are not available.

Appendix

1.1 Derivation of (30)

$$\begin{aligned}&{\frac{\partial \left[ {\lambda \left( Q(\sqrt{m.\bar{\gamma }_{rx}(P_{t}^{i})} )-{\lambda {e}_{th}}\right) }\right] }{\partial P_{t}^{i}}} \\&\quad = \frac{-\lambda }{2}\frac{\partial \left[ erf\left( \sqrt{\frac{m.\bar{\gamma }_{rx}(P_{t}^{i})}{2}}\right) \right] }{{\partial P_{t}^{i}}} \\&\quad = \frac{-\lambda }{2}\frac{\partial \left[ erf\left( \sqrt{\frac{m.\bar{\gamma }_{rx}(P_{t}^{i})}{2}}\right) \right] }{\partial P_{t}^{i}} \\&\quad =\frac{-\lambda }{2}\frac{2e^{\frac{-m.\bar{\gamma }_{rx}(P_{t}^i)}{2}}}{\sqrt{\pi }}\frac{\partial \left[ erf\left( \sqrt{\frac{m.\bar{\gamma }_{rx}(P_{t}^i)}{2}}\right) \right] }{{\partial P_{t}^i}} \\&\quad =\frac{-\lambda }{{\sqrt{\pi }}}{2e^{\frac{-m.\bar{\gamma }_{rx} (P_{t}^i)}{2}}}\frac{\sqrt{m}}{2\sqrt{2\bar{\gamma }_{rx}P_{t}^i}} \\&\quad ={-\lambda {e^{\frac{-m.\bar{\gamma }_{rx}(P_{t}^i)}{2}}}}\frac{\sqrt{m}}{\sqrt{2{\pi }\bar{\gamma }_{rx}P_{t}^i}} \\&\quad =\frac{-\lambda }{\sqrt{\pi }}{2e^{\frac{-m.\bar{\gamma }_{rx}(P_{t}^i)}{2}}}\frac{\sqrt{m}}{2\sqrt{2\bar{\gamma }_{rx}P_{t}^{i}}}. \\&\quad ={-\lambda {e^{\frac{-m.\bar{\gamma }_{rx}(P_{t}^{i})}{2}}}}\frac{\sqrt{m}}{\sqrt{2{\pi }\bar{\gamma }_{rx}(P_{t}^i)}}. \end{aligned}$$

(46)

1.2 Derivation of (34)

We repeat (32) for convenience

$$\bar{e_i} = \dfrac{1}{N_{obs}}\sum _{n=0}^{N_{obs}-1} e_i(n).$$

Let us assume the probability of a packet error event be p.

Now $\sum _{n=0}^{N_{obs}-1} e_i(n)$ denotes a sum of $N_{obs}$ number of independent Bernoulli random variables, each with a mean of $\mathbb {E}[e_i(n)] = p$ and variance $Var[e_i(n)] = p(1-p)$. So mean of this quantity is the sum of these individual means

$$\mathbb {E}\left[ \sum _{n=0}^{N_{obs}-1} e_i(n)\right] = N_{obs}p.$$

Therefore

$$\mathbb {E}[\bar{e_i}] = \mathbb {E}\left[ \dfrac{1}{N_{obs}}\sum _{n=0}^{N_{obs}-1} e_i(n)\right] = p.$$

Combining the above equation with (33) we can write

$$p = e_{th}.$$

Similarly, the variance is also the sum of individual variances. So

$$Var\left[ \sum _{n=0}^{N_{obs}-1} e_i(n)\right] = N_{obs}e_{th}(1-e_{th}).$$

Therefore,

$$Var[\bar{e_i}] = Var\left[ \dfrac{1}{N_{obs}}\sum _{n=0}^{N_{obs}-1} e_i(n)\right] = \dfrac{e_{th}(1-e_{th})}{N_{obs}}.$$

Which is the relation we set out to prove.