LTE Related Simulations

In this subsection we consider SINR based simulations. The system setup is in accordance with the LTE specifications [3GP09b] and summarized in Table 3.1. The simulation setup

0 10 20 30 40 50 60 0 20 40 60 80 100 120 140 SNR [dB]

spectral efficiency [bits/sec/Hz]

cellular max. SINR; number iter. 10 min. out−of−cell int. leak.; number iter. 10 cellular max. SINR; number iter. 100 min. out−of−cell int. leak.; number iter. 100 cellular max. SINR; number iter. 10000 min. out−of−cell int. leak.; number iter. 10000 max. slope d=9

local zero forcing

Figure 3.6: (3, 5)_{× (3, 5)}cellular system; spectral efficiency vs. SNR; comparison of the minimum out-of-cell interference algorithm and the cellular max SINR algo- rithm for different number of iterations. Both algorithms achieve the maximal degrees of freedom.

is essentially similar to the setup used in Section 2.5.2. The channels are modeled using the SCME [BSM+_{05]. The cluster of cooperating base stations comprises three base stations}

which are located at different sites but have the same network area. Figure 2.9 shows the average SINR distribution over the network area. The three peaks are close to the base station locations. Channel state information is assumed to be averaged over one scheduling block. One scheduling block comprises of 12 adjacent subcarriers. Therefore, the transmit precoders and receive filters are computed per scheduling block.

We compare the SINR maximization algorithm with user selection (Subsection 3.3.3) with two baseline schemes. The first baseline is given by local zeroforcing and block diag- onalization with greedy user selection. Using local zeroforcing each base station nulls all intra-cell interference but takes no steps to minimize the out-of-cell interference. The user selection is performed in a greedy fashion [TBT07]. The second baseline is block diagonal- ization. When using block diagonalization each scheduled user is connected to all (three) base stations. The detailed algorithm is described in [SSH04]. Block diagonalization is a joint transmission scheme and therefore requires data sharing between the base stations.

In Figure 3.8 we assume perfect channel state information and compare the system spectral efficiency of the proposed SINR maximization algorithm with local zeroforcing

0 10 20 30 40 50 60 0 5 10 15 20 25 SNR [dB]

spectral efficiency [bits/sec/Hz]

local zero forcing

cellular max. SINR; number iter. 10 min. out−of−cell int. leak.; number iter. 10 cellular max. SINR; number iter. 100 min. out−of−cell int. leak.; number iter. 100

Figure 3.7:(3, 4)_{× (2, 2)} cellular system with µ = 1; spectral efficiency vs. SNR; com- paring the proposed algorithms with local zeroforcing beamforming.

and block diagonalization. We observe that block diagonalization performs about 10 bit/s/Hz better than the proposed scheme which performs about 15 bit/s/Hz better than local zeroforcing. We conclude that with perfect channel state information we can observe a significant cooperation gain.

Now we consider quantized channel state information at the base stations. Assume each user quantizes its channel in the time-domain; an approach proposed for LTE in [Wil10]. To do so, we assume that most significant np = 6 channel taps lie within the first ncp= 100

samples. The real and imaginary parts of each of the np channel taps is quantized using

nB bits. Further, we assume that a user reports a feedback message every TF B = 0.5 ms.

Thus, the feedback rate is RF B =

ntnr

TF B

(log₂(ncp) + 2npnB) bit/s/user.

Figure 3.9 shows the mean spectral efficiency of the feedback rate. We observe that at a relevant feedback rate (i.e. RF B < 5 Mbit/s/user) the proposed max SINR algorithm

performs close to block diagonalization. This is a remarkable result since the requirements on the backhaul network are significantly smaller than with block diagonalization which requires data sharing. In the regime of very small feedback rates the rate approximation scheme discussed in Chapter 2 gives the best performance.

Table 3.1: Summary of simulation parameters.

Parameter Description

Scenario FDD Downlink

Number BS 3

Number UE 30

Antenna configuration BS: 4 Tx Ant.; MS: 2 Rx Ant. uniform linear array (λ/2 spacing) Carrier Frequency 2.1 GHz, 10 MHz bandwidth Scheduling block size 1 PRB

Number streams per user 1

Modulation and Coding ideal link adaptation Pilot/control overhead not taken into account

Feedback per scheduling block

Channel model SCME: urban macro (3 km/h, high angular spread) Scheduling frequency selective SDMA.

Max. users per SB 4 (MU-MIMO mode)

Receiver linear receiver with ideal channel state information Intra-cell/Out-of-cell interference fully modeled

3.5 Summary and Conclusions

We considered cellular systems which are a natural extension of the interference channel. The degrees of freedom of certain cellular systems and under different assumptions on the channel statistics have been derived. Conditions for the feasibility of interference alignment for systems with symbol extension have been found. The insights obtained in the analysis motivated us to propose different algorithms for the optimization of beamforming vectors and receive filters. One of the algorithms includes a greedy user selection, which exploits the multi-user diversity of cellular systems. In the simulations we showed that in certain scenarios the optimal degrees of freedom can be achieved with the proposed algorithms. We demonstrated that even if the optimal degrees of freedom can not be achieved – in some scenarios – an interference free transmission can be guaranteed. For other scenarios, we saw that even if an interference free transmission can not possible the proposed algorithms have huge advantages, in terms of sum rate, over uncoordinated schemes. We demonstrated by LTE related simulations that – in a practical scenario – the proposed algorithms performs very close to joint transmission schemes that require data sharing. In Chapter 4 we will further evaluate the performance degradation of coordinated transmit strategies due quantized channel state information feedback.

20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

net spectral efficiency [bits/sec/Hz]

cdf of spectral efficiency [bits/sec/Hz]

ideal CSIT; max SINR (10 iterartions) (64.20 bits/s/Hz) ideal CSIT; Block Diag. (75.97 bits/s/Hz)

ideal CSIT; local ZF (51.46 bits/s/Hz)

cooperation gain

Figure 3.8: CDF of system spectral efficiency; ideal channel state information; comparing the proposed max SINR algorithm with local zeroforcing and block diagonal- ization. 0 1 2 3 4 5 6 7 8 20 30 40 50 60 70 80

feedback load [Mbit/s/user]

mean speceff [bit/sec/Hz] partial CSIT; local ZF

perfect CSIT; local ZF Rate Approximation

ideal CSIT; fixed codebook (LTE 4 bit) partial CSIT; block diag.

perfect CSIT; block diag. partial CSIT; max SINR (10 iter.) ideal CSIT; max SINR (10 iter.)

Figure 3.9: Mean spectral efficiency vs. feedback load [Mbit/sec/user]; comparison of dif- ferent transmit strategies.

3.6 Proofs