Decentralising Multicell Cooperative Processing: A Novel Robust Framework

In the case of quantized limited feedback, for each user there is a quantization codebook consisting of vectors of unit norm, where is the number of feedback bits. This codebook is known both by the user and by the scheduling entity. Each MS after obtaining an estimate of its channel vector (in this paper we assume a perfect estimate) quantizes its direction to the vector from the codebook that best approaches it, which is the one leading to the smallest angle separation [19‐21]. Therefore

where results from the inner product rule. The quantity determining the efficiency of quantization is the quantization error defined as . The codebook should be user specific in order to avoid multiple users quantizing their channel direction to the same vector.

After quantization, MS i feeds back to the system the index k in binary form which corresponds to the quantization vector that best describes its channel direction. Therefore this piece of information is defined as Channel Direction Information (CDI). The more the feedback bits are, the larger the quantization codebook is, which leads to a better approximation of the MS's channel direction. Apart from CDI, the scheduling entity needs some information regarding the channel quality of each user in order to be able to make user selection decisions; this is defined as Channel Quality Information (CQI). In this paper we consider the unquantized channel norm as the fed back CQI which does not capture the interuser interference. This is because we are interested in investigating the precoding performance and not the efficiency of scheduling; therefore the consideration of more complex CQI metrics is unnecessary.

A random codebook has been considered as optimization of the codebook design is beyond the scope of this paper. Thus the codebook is comprised of unit norm complex Gaussian random vectors, and .

Hence the concatenated quantized channel matrix of the system is . The binary indices corresponding to the CSI vectors (lines of ) are fed back to the scheduling entity through one or several radio channels, depending on the MCP framework, that introduce errors. Therefore the concatenated channel possessed by the scheduling entity is , where is a function of the errors introduced by the feedback channel.

When quantized feedback is employed, each MS feeds back a sequence of bits, , . These bits are the index of the vector in the employed codebook that best describes the CDI of a user in binary form. It is assumed that each transmitted bit is received in error with probability . Therefore

The probability of bit errors is considered to be identical and independent across different radio links. The received feedback can be protected from errors by the use of appropriate error correction techniques requiring the addition of a number of bits in the fed back sequence. However such consideration is beyond the scope of this paper which aims at examining the impact of feedback errors in the worst case scenario, when no error detection or correction schemes are employed.

When quantized feedback is employed, the number of feedback bits determines the performance of precoding. Notably the number of bits should increase linearly with the SNR and the number of transmit antennas [21]. However, the more the employed bits are the greater the probability of errors in the received CSI. This can be seen in Figures 5 and 6 where the ergodic capacity of the system with round-robin scheduling and limited feedback as a function of the available bits is plotted. This is for System SNR of 10 dB and 20 dB, respectively, and when random codebook is employed. Without any feedback errors, when system SNR is set to 10 dB, 16 bits provide a good approximation of the perfect CSI, whereas for system SNR equal to 20 dB (high power regime) 20 bits are approximately needed. Notably, MCP with quantized feedback needs more quantization bits compared to the conventional limited feedback multiuser MIMO systems since it is crucial that the achieved ergodic capacity is sufficiently above the capacity of the single-cell processing case.

Feedback errors inevitably degrade performance of both frameworks because some useful information is lost by the intervention of bit errors in the fed back CSI. This is because scheduling performance is degraded due to the corrupted CSI information, and also precoding matrix design is affected due to the same corrupted CSI. The decentralised framework can be more sensitive to scheduling degradation as imperfect CSI might result in a selection of different users by some of the cooperating BSs, depending on the scheduling algorithm employed, which will inevitably increase interuser interference. However, round-robin scheduling is robust to CSI feedback errors as scheduling decisions are not made based on CSI. This scheduling algorithm is selected for the present evaluation which focuses on the impact of feedback errors on the design of precoding matrices. Note that with the absence of feedback errors the performance of the two frameworks under any kind of scheduling and transmission strategy coincides.

In Figures 7 and 8 the ergodic capacity is plotted against the probability of bit errors when MSs are scheduled in a round-robin fashion for system SNR of 10 and 20 dB, respectively. When the system SNR is 10 dB, 16 bits are chosen for feedback whereas at 20 dB, 20 feedback bits are considered. This increase in bits is justified by the higher power regime of operation which demands larger codebooks for guaranteeing low interuser interference. It can be seen that feedback errors have a much greater impact in the case of 20 bits which is justified by (16) and (17). Furthermore in the case of 20 bits the performance gap between the decentralised and centralised frameworks is increased, an increase justified by the greater probability of CSI discrepancy (18). Therefore a more intelligent codebook design can lead to a reduced number of feedback bits for the same performance targets and also provide better robustness against feedback errors. Generally, the centralised framework is a little more robust to feedback errors than the decentralised one, although for a bit error probability less than the difference is negligible. Furthermore the presented results reflect the case where no error detection/correction schemes have been employed. These schemes can significantly reduce the bit error probability ; thus, they have the potential to eliminate the impact of feedback errors.