Authors: Beneyam B Haile Jyri Hämäläinen
Publish Date: 2015/04/05
Volume: 84, Issue: 3, Pages: 1855-1875
Abstract
In literature various limitedfeedback beamforming methods applied in colocated and distributed antenna systems have been proposed for enhancing wireless link spectral efficiency and reliability We focus on practical limitedfeedback methods and introduce a hierarchical feedback structure whereby colocated/distributed transmit antennas are organized into two or more groups To facilitate robust and flexible use of channel state information we apply independent feedback to antenna groups and between the groups This structure provides additional implementation flexibility under practical constraints particularly for coordinated multipoint CoMP systems For the presented methods with hierarchical control structure we compute closedform expressions for the signaltonoise power ratio gain the fading figure and the average biterrorprobability Although hierarchical structure leads in some cases to suboptimal methods results show that performance loss against upper bound given by transmitter equal gain combining is negligible even when number of feedback bits is small Thus it is concluded that the hierarchical feedback that is robust against errors can be effectively used when antennas form natural groups like in eg CoMP transmissionIn recent years various limitedfeedback beamforming methods have been proposed and studied in order to improve the robustness and data rate of wireless link 1 2 3 4 5 6 7 Some of these methods have been adopted to practical systems for instance into the 3rd generation partnership project 3GPP high speed packet access HSPA and long term evolution LTE systems to be used in either colocated or distributed transmission modes In the colocated scenario closelyspaced antennas transmit the same information exploiting channel state information CSI to maximize the received signaltonoise ratio SNR 8 9 10 11 12 For the distributed beamforming scenario techniques such as coordinated multipoint CoMP joint transmission JT have been introduced and incorporated into the practical systems mainly to improve link reliability and data rate of celledge users 13 14 15 16 17Feedback There is a tradeoff between amount of CSI available at the transmitter side and link performance improvement In general the more there is feedback capacity the better the link performance see eg 4 5 12 17 18 19 The performance degradation due to feedback errors is presented in 20 while 21 shows that it is possible to design efficient codebooks even under imperfect feedback system Furthermore mechanisms to mitigate negative impact of feedback errors and delay are proposed in 22 while achievable rate analysis for JT CoMP under imperfect feedback is presented in 23 24Backhaul To reach the expected performance intersite JT CoMP methods set strict backhaul capacity and latency requirements 15 We note that the CoMP methods studied and incorporated in 3GPP release 11 assume ideal backhaul with infinite capacity and zero latency 13 The 3GPP methods may work with highcapacity and low latency wireline backhaul eg fiber However the capacity and latency requirements need to be relaxed while using less ideal backhaul technologies As a result various CoMP methods under nonideal backhaul has been recently studied 25 26 While 26 presents two algorithms that can significantly reduce backhaul capacity requirements 25 focus on 3GPP release 12 CoMP assuming nonideal backhaulIn what follow we also mathematically analyze the performance of the proposed hierarchical system when combining two practical beamforming methods the socalled quantized cophasing QCP which is applied in HSPA and LTE and transmit selection combining TSC We note that these methods have different performance and feedback requirements 20 We derive closedform expressions for the expected SNR fading figure and average bit error probability BEP when assuming different combinations of QCP and TSC methods While exact expressions for the expected SNR and the fading figure are obtained we deduce tight approximations for the average BEP using distributions based on calculated exact moment expressions While the SNR gain provides insight on the benefit obtained from the coherent combining results on the fading figure and the average BEP demonstrate the amount of achieved diversity gainThe rest of the paper is structured as follows Section 2 presents the system model and the limited feedback precoding methods Section 3 recalls definitions of the applied performance metrics and respective expressions for the reference methods In Sects 4–6 we analyse the hierarchical methods and present the mathematical formulations for the SNR gain the fading figure and the average BEP Analytical results are validated in Sect 7 and discussion on the results is carried out Finally Sect 8 concludes the paper highlighting the core contributionsFigure 2 illustrates the structure of transmission system with 2times 2 antennas The model can be easily generalized to larger group and number of antennas but for simplicity we have focused on the case of 2times 2 antennas We have assumed flexible feedback structure where antenna pairs can be either on separate base station sites or colocated on the same site In former case mobile receiver use two separate control channels to send precoding feedback Thus precoding information for the first base station indicates the preferred transmit beamforming vector mathbfw 1=w 11w 12 and weight v 1 that is used to adjust the sum signal from first pair of antennas against the sum signal from the second pair of antennas Similarly precoding information is provided for the second base station to select beamforming vector mathbfw 2=w 21w 22 and weight v 2 If all antennas are colocated on the same base station site then the same precoding information is sent through single control channel towards serving base station We note that the introduced hierarchical feedback structure is flexible so that it can be used for both cooperative multipoint transmission from separate twoantenna base stations and for fourantenna transmission from a single base station
Keywords: