1. Reliable, High Capacity, Multipoint, Wireless Information Networks by Matthew Bromberg Ph.D.

2. Problem Identification Information Networks Require High Capacity, Reliable, Data Networking Data networks require the transfer of large data files (e.g. medical imaging) Bandwidth in Hz is scarce and expensive. (Billions required for nationwide footprint.) Information transfer must be reliable, especially when human lives are at stake (e.g. military networks, emergency services, police etc.) Wired Networks are Costly and Impractical wired infrastructure is costly to build and maintain wiring is infeasible in for mobile units and temporary structures (e.g field hospitals) Wireless is the Only Solution for Soldiers in the Field Soldier becomes part of wireless network Can integrate with current Land Warrior program

3. Problem Identification Continued Wireless Network faces Severe Multipath unknown terrain effects urban environments indoor multipath Wireless Network faces Degraded Propagation indoor propagation losses canyons and urban environments Wireless Network faces Interference co-channel interference from other network nodes hostile interference from jammers interference from other, co-channel networks Wireless Network Must be Secure must have low probability of intercept (LPI) must be secure against infiltration

4. Multipath Illustration Multipath: wireless signal bouncing off of terrain buildings etc. Main path blocked causes severe reduction of signal strength

5. Advantages of Proposed Solution Maximizes Network Capacity Simulations suggest more than an order of magnitude improvement ( x 35) Exploits Multipath Can use multipath diversity to multiply capacity Mitigates Interference Multi-antenna array excises co-channel interference Optimizes Transmit Beamforming Permits inexpensive remote transceivers Offers reduced interference profile for LPI increases capacity of network Network is Optimized Locally Power control only needs local information Entire network performance is optimized Required Transmit Power is Minimized Total network transmit power can be minimized subject to a capacity constraint Dramatic reduction in required transmit power observed (factor of 40,000)

6. Network Objective Function Maximize channel capacity flows through network Optimize maximum theoretical bit rate achievable in network Minimize transmitted power subject to capacity constraint alternative network performance formulation can use arbitrary bit rate targets based on quality of service QoS requirements Maximize Information Flow into and out of Cut Sets Basestation Remote

7. Advantages of Time Division Duplex TDD alternates in time transmission and reception over the same frequencies Channel on uplink nearly the same as downlink RF components shared for transmission and reception Optimal transmit weights easily obtained

8. Multi-Antenna Receiver Reverse arrows for transmitter

9. Exploitation of Channel Reciprocity Channel Reciprocity asserts uplink channel response is the same (matrix transpose) as the downlink Can be achieved in TDD networks after transmit/receive gain compensation d 1k1 d 1k2 d 1kQ g 1k1 g g 1k2 g g 1kQ g... d 1k G      k,k)  i 2k... W 2k w 2k1 * w 2k2 * w 2kQ * d 1k1 d 1k ^ ^ d 1k2 ^ d 1kQ ^... Channel Reciprocity H 21 (k; j) = H 12 (j; k) T ( swap 1 and 2 indices above for downlink ) Remote Transmit Base Receive X 2k link k has Q sublinks Receiver Model

10. Information Theoretic Objective Function Useful metric is mutual information Represents maximum achievable throughput maximize mutual information subject to power constraints decoupled capacity metric assumes linear receiver weights easier to analyze data processing inequality Decoupled Capacity Achieves its Upper Bound Linear Beamforming is the best you can do for Gaussian other user interference Best receiver weights easily computed using local statistics

11. Reciprocity Theorem Reciprocal channels imply the Reciprocity Theorem D 21 (W,G) = D 12 (G *,W * ) uplink capacity equals downlink capacity transmit with conjugate of receiver weights uplink sum total power also equals downlink total power (alternative objective function) Transmit weights are easily obtained from receive weights. Transmit and receive weights only require local information. (No Network God) Optimizing the receiver ’globally’ optimizes the entire network! Network is stable and improves at every iteration.

12. Illustration of Reciprocity Theorem Receive Beamformer enhances signal of interest (SOI), suppresses interferer Transmit beamformer enhances signal of interest, offers minimal interference to other nodes in field of view km - 1 -0.50 1 - - - - 0.8 0.6 0.4 0.2 0 0.4 0.6 0.8 km SOI Inter1 Inter2

13. Network Optimality Using Local Information Receiver computes optimal Wiener beamforming weights using statistics observed at receiver Optimal transmit weights are proportional to receive weights: g =  w * Optimal power control only requires post-beamforming interference power estimate from other end of link L ( ,g,  )  g T  local model of sum of xmit powers)  q  Q(m) log(1 +  (q))   m  (capacity constraint) g =   f(    (gradient of total xmit power wrt target SINR)  (q) =  (q)  *(q)/   (q) (new xmit power is old power times ratio of optimal target SINR divided by achieved SINR) gradient can be computed by simply estimating post beamformer interference at both ends of link

14. Locally Enabled, Globally Optimized (LEGO) Compute Weights w 2 = R x 2 x 2 - 1 R x 2 s Estimate Transfer Power h 2 =| w 2 H R x 2 s / R ss | 2 /  1 Estimate Interference Power i 2 =R y 2 y 2 -  1 h 2 R ss Set gradient: g(k)=i 2 (k)i 1 (k)/h 2 Optimize local model   =arg min  L( , g,  )  1 =i 1   /h  2 =i 2   Base Station (User 2 Node) Subscriber Unit (User 1 Node) Compute Weights w 1 = R x 1 x 1 R x 1 s Estimate Transfer Power h 2 =| w 1 H R x 1 s / R ss | 2 /  2 Estimate Interference Power i 1 =R y 1 y 1 -  2 h 2 R ss   i 1 InterferingSUs InterferingBSs Patented Technique Computations can be concentrated at basestation

15. Convergence to Theoretical Maximum Capacity Simulation Parameters: 19 Cells, 1 km radius, 1800 MHz, Hata cost 231 path loss model, Rayleigh fading, statistically independent antennas, 128 sample block processing, non-blind max-SINR beamform weights, 4 antennas at base, 2 antennas at remote. 1 remote in network. Rapid convergence to theoretical maximum capacity

16. Convergence Example 19 Cell network 1 remote per cell (per band) Each remote has links to 2 basestations 8 antennas at each basestation 2 antennas at each remote 2 independent channels -5-4-3-2012345 -4 -3 -2 0 1 2 3 4 km

17. LEGO Convergence Easily achieves 5 bps per Hz (could have achieved a lot more) Converges in 15 iterations (40 msec or so) Node transmit power < 20 dBm (Well under unlicensed band spec.) 01020304050607080 0 10 20 30 40 50 dBm Forward Link Xmit Gains 01020304050607080 -5 0 5 10 15 20 Iterations dBm Reverse Link Xmit Gains 01020304050607080 0 5 10 15 Bits per Sample Reverse Link Capacity 01020304050607080 0 5 10 15 20 Bits per Sample Forward Link Capacity Iteration 5 bps/Hz = 10 bits/samp * 50 ksamps/100kHz Minimize power subject to capacity constraint metric

18. Multiplying Capacity by Exploiting Diversity 7 Cell Network.(Reuse pattern of 3). Max Xmit pow. = 15 dBm. Equal number of antennas per base and remote. Number of antennas varied. LEGO Exploits Multipath, vs Single Path Transmission, Conventional Power Management 024681012 0 5 10 15 20 25 Number of antennas Bits per Sample Capacity vs Num. antennas LEGO Single Mode Equal Power Channel rank allowed to grow LEGO never uses more than 5 modes

19. Multiplying Capacity by Optimal Power Management 19 cell network. Number of users per cell varied. Maximum achievable worst-case capacity plotted. 012345 1 2 3 4 5 6 7 8 9 10 Capacity, Bits Per Sample Users Per Cell (1/Reuse) Channel Capacity vs. Cell Capacity LEGO Const. Power Single antenna 2.5 × capacity of standard power management and 35 × an algorithm that does not exploit reciprocity

20. Multiplying Capacity Using MultiPoint Networks 4 Cell Network Max Xmit Power 53 dBm Star and Ad-Hoc Topologies 8 antennas at base, 2 at each remote km -2012 -2.5 -2 -1.5 -0.5 0 0.5 1 km -2012 -2.5 -2 -1.5 -0.5 0 0.5 1 km 0 5 10 15 20 25 30 35 Bits Per Sample Star Topology Ad-Hoc Topology 65% capacity increase (100% Asymptotic increase) Increased connectivity multiplies capacity.

21. Minimizing Transmit Power Experiment Setup 5 Antennas at each base station * 2 Antennas at each remote unit  3 Basestations, 6 Remotes, 2 links per remote LEGO power control, vs Standard vs 1 antenna comparison Transmit power varied, max remote bit rate plotted 6 independent (50 kHz) frequency channels -2.5-2-1.5-0.500.51 -2.5 -2 -1.5 -0.5 0 0.5 km Standard power control: Constant link transmit power and constant link receive power at basestation. (similar to CDMA) 1 Antenna case can only use a single link at each remote, and FDMA for co-channel interference LEGO is 40,000 times better.

22. Reducing Required Transmit Power To achieve 8.6 bps per Hz requires 25.3 dB or 339 times more power for Standard Power Management To achieve 2.9 bps per Hz requires 46.1dB or 41 thousand times more power for the single antenna case. Cost of power amplifiers increases by the power squared. Compared to LEGO Performance

23. COTS Implementation LEGO permits network operation in the presence of co-channel interference Network could operate in unlicensed band, at 2.4 GHz 5 GHz and 900 MHz are other possibilities A large amount of commercial off the shelf hardware (COTS) exists for the unlicensed bands. Hardware costs can be kept down, following the philosophy of the Army’s Land Warrior program.