1 Introduction
1.1 Related works
1.2 Contributions
1.3 Paper outline and notation
2 Signal model
2.1 UL channel estimation
2.2 UL data transmission
2.3 DL data transmission
3 UL receive combing and power allocation
3.1 UL receive combining
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The NC only has to invert a \(K \times K\) matrix in (17) instead of the \(LN \times LN\) matrix in (15). However, this requires that each AP inverts an \(N \times N\) matrix to compute \({\textbf{X}}_{l}\), where the necessary local matrices can be precomputed and kept fixed as long as the transmit powers \({\textbf{p}}\) remain unchanged.
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If the in-network sums in step 2 are computed efficiently exploiting the available network topology, this will reduce the network signaling strongly compared to the transmission of all NL signals.
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The method is also robust against link failures: if the data (\({\textbf{x}}_{l}\) and \({\textbf{X}}_{l}^{H} \hat{{\textbf{H}}_{l}}\)) from a certain AP l is not received as a term in the in-network sums, the obtained estimate will still be optimal for a network setup with AP l removed.
3.2 UL power allocation preliminaries
Symbol | Meaning | Place of computation |
---|---|---|
\(\gamma _{k}\) | \(E\{ {\textbf{v}}^{H}_{k} \hat{{\textbf{h}}}_{k}\}\) | NC |
\(\upsilon _{ki}\) | \(E\{ |{\textbf{v}}^{H}_{k} \hat{{\textbf{h}}}_{i}|^{2} \}\) | NC |
\(\xi _{ki}\) | \(E\{ {\textbf{v}}^{H}_{k} {\textbf{C}}_{i} {\textbf{v}}_{k}\}\) | NC |
\(\nu _{k}\) | \(E\{ {\textbf{v}}^{H}_{k} {\textbf{R}}^{\mathrm{UL}}_{{\textbf{n}} {\textbf{n}}} {\textbf{v}}_{k}\}\) | NC |
\(\mu _{k}\) | \(E\{ {\textbf{v}}^{H}_{k} {\textbf{v}}_{k}\}\) | NC |
\(\xi ^{l}_{ki}\) | \(E\{ {\textbf{v}}^{H}_{kl} {\textbf{C}}_{il} {\textbf{v}}_{kl}\}\) | AP |
\(\nu ^{l}_{k}\) | \(E\{ {\textbf{v}}^{H}_{kl} {\textbf{R}}^{\mathrm{UL}}_{{\textbf{n}}_{l} {\textbf{n}}_{l}} {\textbf{v}}_{kl}\}\) | AP |
\(\mu ^{l}_{k}\) | \(E\{ {\textbf{v}}^{H}_{kl} {\textbf{v}}_{kl}\}\) | AP |
3.3 UL receive combining and power allocation
4 DL transmit precoding and power allocation
4.1 DL power allocation preliminaries
4.2 UL–DL duality
4.3 DL transmit precoding and power allocation
5 Further considerations
5.1 Examples of power allocation strategies
5.2 Network topologies
Channel estimation | UL signal estimation | UL power allocation | DL data transmission | DL power allocation | |
---|---|---|---|---|---|
Network-wide SEPA and DTPA | \(B \tau _{p} N L\) | \(B \tau _{u} N L\) | – | \(B (\tau _{d} K + N L)\) | – |
D-UL-SEPA and D-DL-DTPA | – | \(B (\tau _{u} K + K^{2})\) | \(K^{2} + K\) | \(B \tau _{d} K + K^{2}\) | \(K^{2} + K\) |
6 Numerical simulations
Parameter | Value |
---|---|
Network area | 1 km \(\times\) 1 km |
Number of APs | \(L = 50\) |
Number of antennas per AP | \(N = 2, 4, 8, 16\) |
Frounthaul communication gain \({\mathcal{O}}(\frac{NL}{K})\) | \({\mathcal{O}}(2),{\mathcal{O}}(4),{\mathcal{O}}(8),{\mathcal{O}}(16)\) |
Bandwidth | 20 MHz |
Noise model | \({\textbf{R}}^{\mathrm{UL}}_{{\textbf{n}} {\textbf{n}}} = \sigma ^{2} {\textbf{I}}_{M}\), \(\sigma ^{2,{\mathrm{DL}}}_{k} = \sigma ^{2} \ \forall k\) |
Noise power | \(\sigma ^{2} = -94\) dBm |
Maximum UL transmit power | 100 mW |
Maximum DL transmit power | \(P_{t} = 1000\) mW |
Samples per coherence block | \(\tau _{c} = 200\) |
Channel gain at 1 km | − 140.6 dB |
Pathloss exponent | 3.67 |
Height difference between AP and UE | 10 m |
Standard deviation of shadow fading | 4 |
Number of coherence block | \(B = 100\) |
Number of Monte Carlo simulations | 50 |
6.1 Numerical simulations UL
6.1.1 Estimation method
6.1.2 Convergence behavior
6.1.3 Performance
L = 50, N = 8, K = 50 | L = 50, N = 16, K = 50 | L = 100, N = 8, K = 50 | ||||
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SEUL,2 | SEUL,1 | SEUL,2 | SEUL,1 | SEUL,2 | SEUL,1 | |
MR | 42.5|55.1 | – | 82.0|104.1 | – | 89.2|121.3 | – |
LMMSE | 122.3|129.3 | 127.7|135.0 | 184.7|197.4 | 187.0|199.7 | 195.5|206.6 | 198.3|209.7 |
MMSE | 248.0|285.2 | 257.7|295.4 | 371.6|417.8 | 375.0|421.2 | 389.0|441.3 | 393.4|447.0 |
L = 50, N = 8, K = 50 | L = 50, N = 16, K = 50 | L = 100, N = 8, K = 50 | ||||
---|---|---|---|---|---|---|
SEUL,2 | SEUL,1 | SEUL,2 | SEUL,1 | SEUL,2 | SEUL,1 | |
MR | 0.0|0.8 | – | 0.0|1.4 | – | 0.0|1.6 | – |
LMMSE | 0.7|2.3 | 0.7|2.4 | 2.0|3.4 | 2.1|3.4 | 2.2|3.7 | 2.3|3.7 |
MMSE | 1.2|4.0 | 1.3|4.0 | 3.2|6.4 | 3.2|6.4 | 3.5|7.0 | 3.5|7.1 |
6.2 Numerical simulations DL
6.2.1 Convergence behavior
6.2.2 Performance
L = 50, N = 8, K = 50 | L = 50, N = 16, K = 50 | L = 100, N = 8, K = 50 | |
---|---|---|---|
MR | 59.8|65.7 | 111.3|124.2 | 124.4|145.0 |
LMMSE | 162.0|128.0 | 297.2|197.4 | 325.9|216.3 |
MMSE | 214.3|278.0 | 336.0|412.5 | 369.7.0|453.2 |
L = 50, N = 8, K = 50 | L = 50, N = 16, K = 50 | L = 50, N = 16, K = 50 | |
---|---|---|---|
MR | 0.4|0.8 | 0.9|1.4 | 1.0|1.5 |
LMMSE | 0.4|2.4 | 1.4|3.5 | 1.6|3.9 |
MMSE | 0.9|4.0 | 2.6|6.5 | 2.8|7.2 |