Results without interference

In this section, we present the results for the resource allocation strategies with different channel models. We simulated 10000 frames for each of the SNR points and MCS values using the OAI unitary LTE PHY link simula-tor and we give the results in terms of the spectral efficiency. For reference purposes, we also give the probability of outage after the first roundP_out,1. The outage probability after the second round P_out,2 is fixed to 1% for all simulations.

AWGN channel

First, we present the case with AWGN channel and no interference. We optimize the allocation of PRBs in the second HARQ round by following the procedure described in section 5.4. We save the number of erroneous transmissions after each round to compute the probability of outage and we use it together with the number of coded bits per codeword to compute the spectral efficiency as in (5.1).

−6 −4 −2 0 2 4 6 8

10⁻² 10⁻¹ 10⁰

SNR [dB]

Pout1 (AWGN, no interf.)

mcs2 mcs3 mcs4 mcs5 mcs6 mcs7 mcs8 mcs9 mcs11 mcs12

Figure 5.4: Probability of Outage after the first round of the HARQ protocol. The channel is AWGN and there is no interference.

Figure 5.4 shows the results for the probability of outage after the first HARQ round. In figure 5.5, the left axis and solid lines show the spectral efficiency depending on the resource allocation chosen. The right axis and dashed lines show the corresponding (optimized) number of PRBs used in the second round. We show the MCS used in each case (for the retransmissions the MCS is fixed to force them to use QPSK), the TBS remains fixed across the HARQ rounds. We also show the spectral efficiency values specified in the LTE standard for terminal feedback signaling (see Table 7.2.3-1 in [7]). If

we look at the lines showing these values, we can see the corresponding MCS that would be used in each case. For example, if we consider the spectral efficiency of0.3770, we would be using MCS3which gives the highest achiev-able spectral efficiency. If we consider the next spectral efficiency0.6016, we would use MCS6. However, for the large number of intermediate values that the protocol can use, one could change the allocation and/or MCS depend-ing on the SNR to maximize the spectral efficiency. This could be done by the base station scheduler based on estimates of the first and second round error probabilities. The latter could be achieved based on the statistics of received ACK/NACK signals. By doing so, one has more liberty to adapt parameters such as PRB allocation or MCS and modulation across rounds to those values that result in a higher spectral efficiency given the latency constraint.

The desired latency of the protocol translates as the probability of outage for the different operating SNR points. For our latency constraint of 10⁻², we can look at different SNR values and see what the best allocation is. If we consider an SNR= 0dB, the corresponding MCS is 3 and the allocation corresponds to18 PRBs in the first round and 3 in the second round. This corresponds to a ratio of dimensions of ρ = 0.8571. If we now consider an SNR= 5dB, the MCS becomes9with6PRBs in the first round and2in the second round (ρ = 0.75). As the SNR gets higher, we use less resources in the second round. Interestingly, if we look at the outage probability after the first round, we see that the second case of MCS9, has a higher probability of outage when compared to the case with MCS 3, which means that in this case, almost all the data transmission occurs at the second round of the HARQ protocol.

Rayleigh Channel

We investigate the effect of the distribution of dimensions across rounds (re-lated to section 4.3.2, Chapter 4) and we look at the results when the channel is Rayleigh distributed giving a worse channel quality than the AWGN case.

This is equivalent to the outdated CQI case with uncorrelated channels pre-sented in section 4.3.2 of Chapter 4.

Figure 5.6 show the probability of outage after the first round of the HARQ protocol. Figure 5.7 shows the spectral efficiency for the different optimized allocations and those specified in the LTE standard. When we consider an SNR of2dB, the best combination of MCS and PRBs allocation is MCS7with8 PRBs in the first round and25in the second round, which gives a ratio of dimensions ρ = 0.2424. However, if we look at high SNR (15dB), the best MCS becomes 16 with3 PRBs in the first round and6 in the second round, withρ= 0.3333.

Chapter5PracticalSchedulerDesignforLTEBaseStations

−5 0 5 10 15 20 10⁻²

10⁻¹ 10⁰

SNR [dB]

Pout1 (Rayleigh, no interf)

mcs3 mcs4 mcs5 mcs7 mcs9 mcs13 mcs15 mcs16 mcs18

Figure 5.6: Probability of Outage after the first round of the HARQ protocol under Rayleigh fading. There is no interference.

Chapter5PracticalSchedulerDesignforLTEBaseStations

−50 0 5 10 15 20

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

SNR [dB]

Spectral eff (Rayleigh, no interf)

mcs3 mcs4 mcs5 mcs7 mcs9 mcs13 mcs15 mcs16 mcs18

1.1758 1.9141

1.4766

0.8770

0.3770 0.6016

0.2344 0.1523

Figure 5.7: Spectral efficiency for different resource allocations under Rayleigh fading. There is no interference.

2 4 6 8 10 12 14 16 18

Figure 5.8: Ratio of dimensions.

We can compare these values with the theoretical example in figure 5.1(b).

For this purpose, in figure 5.8, we plot the ratio of dimensions between first and second round and we also plot the results from figure 5.1(b). The differ-ence in the curves comes from the fact that in the theoretical example, the results were obtained from the Gaussian expressions for mutual information which represent an unconstrained modulation and in the case of the simu-lation results, we study the LTE codes with imperfect channel estimation.

However, we see that the results follow the same trend in both cases withρ becoming higher in the high SNR region. Also, from figure 5.6, we observe that as the SNR becomes higher, the outage probability after the first round becomes higher. The latter is important if we consider that commercial sys-tems are designed to operate in the order of 10⁻¹, but allowing a higher outage probability results in a higher spectral efficiency. We can relate our results to those from the rateless coding schemes with AWGN channels. In this case, more dimensions are used in the first round than in the second since it is possible to overcome errors due to finite block-length (inducing a gap from the Shannon capacity).

Figure 5.9: Scenario.