**7.2. Results**

In addition to interference alignment2 , we also run the reference scheme single-user MIMO. In this scheme two spatial streams are transmitted from each source using its two transmitter antennas. Two versions of the single-user MIMO is used. In one version one source is active at a time. This version is naturally called TDMA. In another version of single-user MIMO all links are active at the same time. This scheme will work well if the inter-link interference is weak. We call this approach *full-reuse MIMO*. Finally, we also include a scheme called *full-reuse SIMO*. In this approach all sources transmit at the same time but using only a single-antenna at the sources. The difference between this scheme and interference alignment is the beam‐ forming at the sources and the channel state feedback. All other aspects of the signal processing are identical. The performance of the system were investigated in 43 different locations for each of the three destination terminals. Half of the locations were in the corridor and half in the adjacent rooms, see Figure 5. In each location the performance was investigated with the frequency domain granularity parameter, Ng set sequentially to the values 1, 2, 4, 8, 15, 38. No person or object was moving in the environment and all schemes were run in rapid sequence thus making it possible to reliably compare the results. The results are shown in Figure 8. The dashed lines are the results obtained without the feedback compression while the solid lines are with compression (although the frequency domain granularity is still applied). The results

<sup>2</sup> By interference alignment we are here referring to the modified form of interference alignment known as Max-SINR, see Section 3.3. However, measurements we have performed have shown that the performance difference between the original interference alignment and Max-SINR is neglible in our scenario.

25

show negligible performance loss from the quantization. However, using a too high frequency domain granularity, Ng > 8 or 2.5 MHz, do incur some loss. Note that the result for full-reuse MIMO is very poor showing that the interference is strong. The gain of interference alignment over the best reference scheme (TDMA MIMO) is 27%. We may also note that interference alignment provides a gain over full-reuse SIMO which proves that the transmitter beamform‐ ing is making a difference. "Book˙Chapter˙MFZNS" — 2014/10/14 — 15:09 — page 25 — #25

The elements of **Λ**[k] are divided by the noise standard deviation. The so obtained value can be regarded as the SNR of a corresponding stream. The reporting of these SNRs is done separately per stream, and is done in two steps. In the first step, the average SNR in dB over the whole frequency band, i.e. for all singular values of the narrowband channels for which SNR is reported, is fed back to S*k*. This value is uniformly quantised with 8 bits in the range from 10 dB to 53.75 dB. In the second step, the difference in dB between the SNR of the reported sub-carrier and the average SNR is computed and is uniformly quantised with 4 bits in the range from 8 dB to 7 dB. In S*k*, the SNRs of all the reported sub-carriers are first reconstructed. Then, linear interpolation (in dB) is deployed to obtain the SNR for all the sub-carriers for

is fed back. With these two entities at hand, the channel matrices **H**[k] are recon‐

, we also run the reference scheme single-user MIMO.

structed and used to compute the desired pre-coders. For the sub-carriers where there is no feedback available, the pre-coding of the nearest reported sub-carrier is utilized, i.e. no matrix

A practical problem which occurred during the early experimentation was that the SNR sometimes exceeded 53.75 dB. This happened due to the high transmission power and short range. First this was handled by reporting the maximum value 53.75 dB whenever this happened. However, this resulted in making the reconstructed channel at the transmitter highrank although the estimated channel at the receiver were in fact low-rank-which was very detrimental to the performance. To circumvent this problem, an offset is subtracted from SNR

In this scheme two spatial streams are transmitted from each source using its two transmitter antennas. Two versions of the single-user MIMO is used. In one version one source is active at a time. This version is naturally called TDMA. In another version of single-user MIMO all links are active at the same time. This scheme will work well if the inter-link interference is weak. We call this approach *full-reuse MIMO*. Finally, we also include a scheme called *full-reuse SIMO*. In this approach all sources transmit at the same time but using only a single-antenna at the sources. The difference between this scheme and interference alignment is the beam‐ forming at the sources and the channel state feedback. All other aspects of the signal processing are identical. The performance of the system were investigated in 43 different locations for each of the three destination terminals. Half of the locations were in the corridor and half in the adjacent rooms, see Figure 5. In each location the performance was investigated with the frequency domain granularity parameter, Ng set sequentially to the values 1, 2, 4, 8, 15, 38. No person or object was moving in the environment and all schemes were run in rapid sequence thus making it possible to reliably compare the results. The results are shown in Figure 8. The dashed lines are the results obtained without the feedback compression while the solid lines are with compression (although the frequency domain granularity is still applied). The results

2 By interference alignment we are here referring to the modified form of interference alignment known as Max-SINR, see Section 3.3. However, measurements we have performed have shown that the performance difference between the

original interference alignment and Max-SINR is neglible in our scenario.

which **F**[*k*]

**7.2. Results**

interpolation method is used.

72 Contemporary Issues in Wireless Communications

values when this condition happens.

In addition to interference alignment2

**Figure 8.** Measured sum throughput. The dotted line are the results without compression

to provide better FER/BER performance (16QAM code rate 0.5), than an implementation without power control. The results using the modified IEEE802.11ac feedback scheme, show that interference aligment can bring an improvement in throughput when considering the loss of bandwidth needed for feedback of the channel state information even for channels with realistic indoor mobility. IX. ACKNOWLEDGMENTS When the channel is changing the performance of interference alignment will inevitably be degraded due the channel mismatch between the channel at the feedback time and the channel at the actual transmission. The amount of degradation depends on the time delay and the level of movement in the environment. In [26] using measurements we showed that the throughput of interference alignment dropped 6.4% when two passers-by were walking in the measure‐ ment environment and the feedback delay interval was 23 ms. With this delay interval the overhead of performing the feedback scheme above with Ng=8 is 2.5%, assuming that the feedback scheme of IEEE802.11ac is used.

Fig. 8: Measured sum throughput. The dotted line are the results without compression

The research leading to these results has received funding from Swedish Foundation for Strategic Research (SSF) under RAMCOORAN project and ACCESS Linnaeus Center under graduate course wireless experimentations. The measurements were performed within the framework of the HIATUS The channel may also change due to the existence of the users at the destinations. This effect was studied by measuring the performance with and without a user located close to the destination nodes. The results were obtained using eight destination positions. The perform‐ ance of interference alignment dropped 4.9% while the performance of single-user MIMO was unaffected.

project. The project HIATUS acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission under FET-Open grant number: 265578. These results show that interference alignment can still deliver a net performance gain of sum throughput some 15% over single-user MIMO in a WiFi scenario with three access points and three users, even when feedback overheads and mobility is taken into account.

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[3] Maddah-Ali, M. A., Motahari, A. S. & Khandani, A. K. Communication over MIMO X channels:

[4] Cadambe, V. R. & Jafar, S. A. Interference alignment and degrees of freedom of the K-user interference

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