3. Uplink Search-Based Direction-of-Arrival (DoA) Estimation 77
4.1. Downlink Inter-Cell Interference in Multiple-User MIMO
4.1.2. Interference Compensation
In the previous section, sum spectral efficiency degradation due to inter-sector interference is shown.
Thereby, T = 20 randomly selected users are spatially multiplexed. In this section, the impact of inter-sector interference on user selection is studied. Then, an additional low overhead feedback is proposed to compensate sum spectral efficiency losses from interference.
The impact of unknown interference on the sum spectral efficiency is shown over the number of available users ˜Kl in Fig. 4.3a. Upward and downward pointing triangles represent random user selection in the homogeneous and heterogeneous scenario, respectively, while right- and left-hand pointing triangles represent sum spectral efficiency maximizing projection based zero forcing (PBZF)3 user selection in the homogeneous and heterogeneous scenario, respectively. In case of the random scheduler the number of selected streams is constraint by the minimum of the number of available users and streams in the first-stage precoder Bl given by N( ˜Ω) such that4
T = minN( ˜Ω),K˜. (4.4)
With parameters from Table 4.1 maximum T = 32 streams can be scheduled. This is shown in Fig. 4.3b, where the number of selected streams T over the number of available users ˜K is given. This constant number of scheduled streams is also the reason for the approximately constant sum spectral efficiency with
3See Section 2.3.4 for details on the PBZF user selection algorithm.
4See Section 2.4.4 on hybrid precoding for details.
Table 4.1.: Parameter assumptions for multiple-sector simulations.
Parameter Value
Scenario 3GPP three dimensional (3D) Urban
Macro NLoS, [3GP17e]
Center frequency 4 GHz
Number of multi-path componentsL(MPC) 21
OFDM RB Bandwidth 180 kHz
Number of RBs 50
Utilized bandwidth 9 MHz
Cyclic prefix overhead 7 %
SINR bounds,γ(min), γ(max) γ(min)=−5 dB ,γ(max)= 40 dB
Number of BSsL 7
Inter-side distance 500 m
Sectorization Three per BS location
User distribution Uniform random in hexagons according to Fig. 4.1a
Number of available users ˜K [20,100]
Homogeneous: N(α), N(β), N 10,10,100
Heterogeneous: ˜N(α),N˜(β),N˜ 2,2,4
First stage precoder Bl Sub codebook splitting with values below N(α)(Ω), N(β)(Ω), N(Ω) 16,16,256
α(CW,min), α(CW,max) −50◦,50◦
β(CW,min), β(CW,max) −40◦,8◦
N(α)(Ω,SCB), N(β)(Ω,SCB), N(Ω˜) 8,4,32
N(SCB) 8, according to Algorithm 4
Second stage precoderPl
Minimum mean square error based on first-stage precoded channels and multiple-input single-output feedback
according to Section 2.2
Scheduler Random or PBZF according to
Section 2.3.4
(a) Sum spectral efficiency over the number of available users ˜Kcomparing random and PBZF scheduling for homogeneous and heterogeneous scenario.
20 40 60 80 100
Number of available users ˜K 10
15 20 25 30 35
NumberofScheduledStreamsT
Random,T = min(N( ˜Ω),K)˜ PBZF
(b) Number of scheduled streams T over the number of available users ˜K.
Figure 4.3.: Performance of homogeneous and heterogeneous multiple-sector scenario.
random selection for ˜Kl > 30 in Fig. 4.3a. The gap between homogeneous and heterogeneous scenario is approximately constant over ˜K.
With the PBZF scheduler the sum spectral efficiency gain is less than 15 % for ˜K = 60 with respect to K˜ = 20, achieved in the homogeneous scenario. For ˜K > 60 the sum spectral efficiency is decreasing due to the unknown inter-sector interference and no further scheduling gains are realized. The gap between homogeneous and heterogeneous scenario increases for the PBZF scheduler because the received interference power in the heterogeneous scenario is larger, see Fig. 4.2.
Fig. 4.3b shows that for PBZF the number of scheduled streams constantly increases along with the number of available users, but without gain in sum spectral efficiency. This is due to the unknown interference situation of the users, which is not taken into account in the scheduling decision and precoder design. Note that this observation is independent of TDD or FDD systems. In [KRTT13] the same observation for second stage precoding using maximum ratio transmission (MRT), signal to leakage and noise ratio (SLNR) and zero forcing (ZF) is described. First stage precoding is not considered in [KRTT13] corresponding to Bl=INl in this work.
The results in Fig. 4.3 confirm that the interference situation at the mobile users is essential for massive MIMO multiple-user downlink transmission5, otherwise spatial multiplexing gains are limited. In [KTH14b]
the author of this thesis and others proposes to include the interference power received at the mobile users in the regularization matrix of the minimum mean square error (MMSE) precoder. This proposed scheme and corresponding details are presented in the next paragraphs.
In (2.37) the regularization matrix R(MMSE) ∈ CTl×Tl is introduced as diagonal matrix with elements hR(MMSE)i
t,t = z(IF,i)k . The term zk(IF,i) reflects the level of interference at user k that is known at the BS and is defined in Eq. (2.37) for i ∈ [0,1,2]. For the sake of readability these three cases are briefly summarized again.
• i= 0 corresponds to the case that only noise variance and no interference knowledge is considered.
5Actual, the knowledge about interference is essential not only for massive MIMO transmission, however the emphasis here is on massive MIMO because the spatial multiplexing gain is the main advantage of massive MIMO and a large portion of it is rendered useless by the unknown interference.
• i = 1 corresponds to the case that interference power is available per user on a per RB granularity, labeled henceforth as “Per RB”. This can be seen as the “upper bound” for the proposed wideband feedback in i= 2.
• i = 2 is the proposed scheme and corresponds to the case that the expectation of the interference power over all RBs is available per user, henceforth labeled as “wideband”.
An estimate of the interference power at userkcan be obtained by subtracting the power of the transmitted signals of the serving BS l from the power of the complete receive signal such that
zk(IF,est)= 1
where M is the number of receive antennas, Vl is the precoding matrix, and Fl is the diagonal power allocation matrices following the definitions in Section 2.2 below Eq. (2.1) for the general downlink receive signal description. The separation of the signal from serving BS l and other BSs in Eq. (4.5) assumes that orthogonal pilots are used. Note, different to the assumption in (2.37), where the noise power is considered, in Eq. (4.5) an instantaneous realization of the noise power is included. Yet, in an interference-limited system the assumption is that zHkzk nHknk such that the impact from the noise becomes negligible and zk(IF,1) ≈ zk(IF,est). In this work, zk(IF,2) is obtained as the average over all RBs in frequency while in real system the expectation value may also be obtained by additional averaging in time. A practical problem is, that additional to the data, a known reference signal has to be transmitted for each stream in order to estimate and subtract signals of serving BS l from the complete receive signal. In LTE and 5G new radio (NR) these signals are available and called demodulation reference signals (DM-RS), see Section 9 in [3GP14] and Section 5 in [3GP18c], respectively. However, the demodulation reference signals from BSland the other BSs m6=lmay not be completely orthogonal and thus an unknown error is included inzk(IF,est)in real systems. Thus, the above mentioned averaging in the frequency domain over all RBs reflects to some extend these errors. By using an averaged value the interference power estimate on some RBs is larger or lower than the actual interference.
Fig. 4.4a shows the homogeneous scenario and there is approximately the same sum spectral efficiency for
“wideband” and “per RB” interference regularization according to Eq. (2.37). In contrast to Fig. 4.3a the sum spectral efficiency is negligibly increasing with ˜Kl resulting in 60 % gain at ˜Kl= 100. The performance of the random scheduler remains approximately constant and the gain compared to no interference knowledge zk(IF,0) in Fig. 4.3a is more than three times. In Fig. 4.4b the sum spectral efficiency for the heterogeneous scenario is shown. The difference between “per RB” ,zk(IF,1) and wideband zk(IF,2) is significantly larger compared to the homogeneous scenario. Especially with the PBZF scheduling heuristic the gap becomes larger with increasing ˜Kl. The sum spectral efficiency gains, due to the additional interference regularization in the MMSE precoder, are larger in the heterogeneous scenario compared to the homogeneous scenario.
The reasons for this is the larger received inter-cell interference power in heterogeneous scenarios, e.g. the gain for PBZF is more than a factor of two at ˜Kl = 100 and more then four for random scheduling.
The additional feedback that is required consist of scalar power values, in case of “Per RB” there are N(RB) values, and in case of “wideband” there is a single value. Considering 10 bit for quantization per power value this results in 500 bit and 10 bit additional feedback for “per RB” and “wideband”, respectively. In case of the homogeneous scenario, the sum spectral efficiency degradation from “per RB” to “wideband” is <1 %.
By sending the interference power feedback on a larger time-scale than the channel state information (CSI) feedback the additional overhead is neglectable compared to the CSI feedback.
(a) Homogeneous scenario.
30 40 50 60 70 80 90 100
Number available users ˜Kl
10 20 30 40 50 60 70
SumSE˜C(sum) lin[bit/s/Hz]
Random,z(IF,0), noise Random,z(IF,1), per RB Random,z(IF,2), wideband PBZF,z(IF,0), noise PBZF,z(IF,1), per RB PBZF,z(IF,2), wideband
(b) Heterogeneous scenario.
Figure 4.4.: Effective sum spectral efficiency comparing user scheduler and MMSE precoding with and with-out interference power regularization according to Eq. (2.37). PBZF is a sum spectral efficiency maximizing scheduler as described in Section 2.3.4. The label “z(IF,0), noise” means that no interference, only noise variance is taken into account. The label “z(IF,1), per RB” means that the interference power per RB is taken into account. The label “z(IF,2), wideband” means that the average interference power over all RBs is taken into account.
4.1.3. Conclusions
It is shown that inter-sector interference is limiting the downlink sum spectral efficiency for massive MIMO multiple-user spatial multiplexing, assuming a practical number of antennas. A homogeneous and heteroge-neous scenario is considered in this section and it can be observed that the impact from interference is less in the homogenous scenario. This confirms findings that, according to the law of large numbers, the probability of orthogonal channels increases with the number of antennas. However, even with the N = 100 antenna elements at all BSs, considered in the homogeneous scenario, the loss from single BS to six interfering BSs is more than a factor of four.
Independent of TDD or FDD, without knowledge about the interference situation at the users, spatial multiplexing gains from single-cell scenario can vanish or even result in sum spectral efficiency degradation.
An interference power feedback metric is proposed, which requires very low additional feedback overhead of 10 bit per feedback interval. Furthermore, it is shown that by including this metric in the MMSE precoder massive MIMO spatial multiplexing gains can also be utilized in interference-limited scenarios. Results in this section indicate that in the homogeneous massive MIMO scenario a wideband interference power feedback is sufficient and additional gains with “per RB” are neglectable. In the heterogeneous scenario a
“per RB” feedback provides additional sum spectral efficiency improvement of approximately 3 bit/s/Hz.