Analysis of Receiver Quantization in Wireless Communication Systems

Transcription

1 Analysis of Receiver Quantization in Wireless Communication Systems Theory and Implementation Gareth B. Middleton Committee: Dr. Behnaam Aazhang Dr. Ashutosh Sabharwal Dr. Joseph Cavallaro 18 April 2007 M.S. Defense

2 An Example The Effects of Quantization sin(x)

3 An Example The Effects of Quantization sin(x) Q[sin(x)]

4 An Example The Effects of Quantization sin(x) Q[sin(x)] g sin(x)

5 An Example The Effects of Quantization sin(x) Q[sin(x)] g sin(x) Q[g sin(x)]

6 An Example The Effects of Quantization sin(x) Q[sin(x)] Fill dynamic range g sin(x) Q[g sin(x)]

7 An Example The Effects of Quantization sin(x) Q[sin(x)] Fill dynamic range Nonlinear g sin(x) Q[g sin(x)]

8 Sources of this Problem Sources of Quantization Error: Channel Fading Near Far

9 Sources of this Problem Sources of Quantization Error: Channel Fading Near Far

10 Sources of this Problem Sources of Quantization Error: Channel Fading Near Far

11 Sources of this Problem Sources of Quantization Error: Channel Fading Fast A-D (Gigahertz range) Precision is expensive Near Far

12 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth

13 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with?

14 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with? Undersampling / Underquantizing tradeoff

15 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with? Undersampling / Underquantizing tradeoff Effects on OFDM

16 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with? Undersampling / Underquantizing tradeoff Effects on OFDM

17 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with? Undersampling / Underquantizing tradeoff Effects on OFDM BER = 0.34!

18 Complications of Quantization Effects on Advanced Wireless Systems High speed, MIMO systems require lots of bandwidth All this data is saturating receiver DSP! How little can we get away with? Undersampling / Underquantizing tradeoff Receiver quantization can be damaging, so we need the balance point Effects on OFDM BER = 0.34!

19 Outline 1 Introduction Motivating Example Our Contributions

20 Outline 1 Introduction Motivating Example Our Contributions 2 Exact Analysis System Setup Channel Estimation Effects Result: Minimum Quantization at High SNR Result: Effect of Quantization on SER

21 Outline 1 Introduction Motivating Example Our Contributions 2 Exact Analysis System Setup Channel Estimation Effects Result: Minimum Quantization at High SNR Result: Effect of Quantization on SER 3 Hardware System Description Medium-Low SNR Results WARP AGC Implementation Performance

22 Outline 1 Introduction Motivating Example Our Contributions 2 Exact Analysis System Setup Channel Estimation Effects Result: Minimum Quantization at High SNR Result: Effect of Quantization on SER 3 Hardware System Description Medium-Low SNR Results WARP AGC Implementation Performance 4 Conclusions

23 Quantization Error Floors Middleton & Sabharwal, Allerton 2006 System configuration: SIMO Single carrier QAM Uniform quantizer Fading channel No AGC BER Modulation Order and Quantization: 16 and 64 QAM, 1 Antenna 16 QAM 64 QAM Full 12 bits SNR

24 Quantization Error Floors Middleton & Sabharwal, Allerton 2006 System configuration: SIMO Single carrier QAM Uniform quantizer Fading channel No AGC BER Modulation Order and Quantization: 16 and 64 QAM, 4 Antennas 16 QAM 64 QAM Full 12 bits SNR

25 Quantization Error Floors Middleton & Sabharwal, Allerton 2006 System configuration: SIMO Single carrier QAM Uniform quantizer Fading channel No AGC BER Modulation Order and Quantization: 16 and 64 QAM, 4 Antennas 16 QAM 64 QAM Full 12 bits SNR Theorem: Non-zero probability of deep fades causes error floors!

26 Correcting this Problem AGC is Required r AGC Q[ ] Sig. Proc.

27 Correcting this Problem AGC is Required r Requires magnitude A AGC Q[ ] Sig. Proc.

28 Correcting this Problem AGC is Required r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc.

29 Correcting this Problem AGC is Required r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc.

30 Correcting this Problem AGC is Required r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc. AGC is not a new problem, why did we embark on this research?

31 Correcting this Problem AGC is Required r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc. AGC is not a new problem, why did we embark on this research? Analysis is missing: What is A, how to choose g? Requires understanding of quantization

32 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels?

33 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels? How do we instantiate an AGC which chooses g accordingly, using the received signal r?

34 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels? How do we instantiate an AGC which chooses g accordingly, using the received signal r? Our Results Conditions to determine the minimum A for any modulation, at high SNR

35 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels? How do we instantiate an AGC which chooses g accordingly, using the received signal r? Our Results Conditions to determine the minimum A for any modulation, at high SNR Results on minimum A for M-PSK and M-QAM

36 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels? How do we instantiate an AGC which chooses g accordingly, using the received signal r? Our Results Conditions to determine the minimum A for any modulation, at high SNR Results on minimum A for M-PSK and M-QAM Use of the platform as a tool for extending results to medium-low SNR regimes

37 Our Contributions Questions How do we choose the target signal magnitude value A? To what SNR regimes do these results apply for fading channels? How do we instantiate an AGC which chooses g accordingly, using the received signal r? Our Results Conditions to determine the minimum A for any modulation, at high SNR Results on minimum A for M-PSK and M-QAM Use of the platform as a tool for extending results to medium-low SNR regimes Instantiation of AGC for the WARP platform

38 Connecting AGC and Quantization Intertwined Problems Equivalent at high SNR: Changing q for fixed A. Changing A for fixed q. A = 1 q = 1 3

39 Connecting AGC and Quantization Intertwined Problems Equivalent at high SNR: Changing q for fixed A. Changing A for fixed q. A = 3 q = 1

40 Quantization: Previous Work Context for Our Results Much work has been done on Optimal Quantizers: Lloyd & Max (Optimal quantizer design) Gray (Rate distortion for quantizers) Neuhoff (Quantization noise models)

41 Quantization: Previous Work Context for Our Results Much work has been done on Optimal Quantizers: Lloyd & Max (Optimal quantizer design) Gray (Rate distortion for quantizers) Neuhoff (Quantization noise models) Areas of Research Not much work on signals passed through hard-limiting, well-defined quantizers.

42 Quantization: Previous Work Context for Our Results Much work has been done on Optimal Quantizers: Lloyd & Max (Optimal quantizer design) Gray (Rate distortion for quantizers) Neuhoff (Quantization noise models) Areas of Research Not much work on signals passed through hard-limiting, well-defined quantizers. Our Contribution We will study the effects of defined quantizers on real world signals.

43 Outline 1 Introduction 2 Exact Analysis System Setup Channel Estimation Effects Result: Minimum Quantization at High SNR Result: Effect of Quantization on SER 3 Hardware 4 Conclusions

44 Analysis Reduced System Model SISO Single carrier Pilot symbol channel estimation Arbitrary Modulation (though we ll only study results for PSK and QAM)

45 Analysis Reduced System Model SISO Single carrier Pilot symbol channel estimation Arbitrary Modulation (though we ll only study results for PSK and QAM) Channel Assumptions 1-tap fading with perfect AGC (rotation only): we will change q instead of input magnitude. High SNR Uniform hard-limiting quantizer, even number of levels

46 Analysis Reduced System Model SISO Single carrier Pilot symbol channel estimation Arbitrary Modulation (though we ll only study results for PSK and QAM) Goal: For this system, what is A? Equivalently, what is q? Channel Assumptions 1-tap fading with perfect AGC (rotation only): we will change q instead of input magnitude. High SNR Uniform hard-limiting quantizer, even number of levels

47 Quantized Constellation Points Effects of A-D on Modulation Q I(cos) and Q(sin) quantize in time such that symbols quantize in the I Q plane I

48 Illustrative Example QPSK with 2 Bit Resolution Blue circles are received from the channel Light-blue squares are the quantized symbols presented to the receiver

49 Phase Estimation with Quantization Channel Effects Quantizer becomes our source of trouble: Pilot symbols are quantized Channel estimation error results Error Estimated Phase

50 Phase Estimation with Quantization Maximum Phase Error at High SNR We can bound the phase estimation error to ˆθ [ θ emax, θ emax ] c i q θ emax π 4

51 Phase Estimation with Quantization Maximum Phase Error at High SNR We can bound the phase estimation error to ˆθ [ θ emax, θ emax ] c i q θ emax = tan 1 ( Im[ci ] + q 2 Re[c i ] q 2 ) π 4 θ emax π 4

52 Phase Estimation with Quantization Maximum Phase Error at High SNR We can bound the phase estimation error to ˆθ [ θ emax, θ emax ] c i q θ emax = tan 1 ( Im[ci ] + q 2 Re[c i ] q 2 Outermost symbols must be used for phase estimation ) π 4 π 4 θ emax

53 Channel Rotation Correcting Phase What do we do about channel phase?

54 Channel Rotation Correcting Phase What do we do about channel phase? Unrotate symbols using ˆθ

55 Channel Rotation Correcting Phase What do we do about channel phase? Unrotate symbols using ˆθ Apply usual decision regions

56 Channel Rotation Correcting Phase What do we do about channel phase?

57 Channel Rotation Correcting Phase What do we do about channel phase? Rotate the decision regions

58 Phase Estimation Error Limiting Decision Region Rotation Ideally, we rotate by ˆθ = θ Quantization causes ˆθ [ θ emax, θ emax ] We may rotate the decision regions by any amount in this range

59 Phase Estimation Error Limiting Decision Region Rotation Ideally, we rotate by ˆθ = θ Quantization causes ˆθ [ θ emax, θ emax ] We may rotate the decision regions by any amount in this range Definition: Extended Decision Region Let Ri θe specify the union of all decision regions Ri θ for symbol m i, rotated by ˆθ [ θ emax, θ emax ]

60 Extended Decision Regions For 8-PSK, θ = 0, ˆθ [ θ emax, θ emax] R θ 1 R θ 0

61 Extended Decision Regions For 8-PSK, θ = 0, ˆθ [ θ emax, θ emax] R θ 1 R θe 0

62 Extended Decision Regions For 8-PSK, θ = 0, ˆθ [ θ emax, θ emax] R θe 1 R θe 0

63 Extended Decision Regions For 8-PSK, θ = 0, ˆθ [ θ emax, θ emax] Overlapping Extended Decision regions R θe 1 R θe 0

64 Errors from Quantization Incorrect Symbol Mapping R θe 1 R θe 0

65 Errors from Quantization Incorrect Symbol Mapping R θe 1 R θe 0

66 Errors from Quantization Incorrect Symbol Mapping R θe 1 R θe 0

67 Errors from Quantization Incorrect Symbol Mapping Potential Error! R θe 1 R θe 0

68 Errors from Quantization Incorrect Symbol Mapping Potential Error! Rˆθ 1 Rˆθ 0

69 Result Quantizing with Zero Error Intuition: Quantizer shouldn t: move constellation points into ambiguous decision regions create too much ambiguity through phase uncertainty

70 Result Quantizing with Zero Error Intuition: Quantizer shouldn t: move constellation points into ambiguous decision regions create too much ambiguity through phase uncertainty Theorem If Q[m i ] do not fall into disputed decision regions for all constellation points m i and all channel phases θ, the quantized system will operate without error at high SNR.

71 Intuition Behind the Proof Consider extreme (1-bit) quantization! For any high order modulation, communication is impossible.

72 Intuition Behind the Proof Consider extreme (1-bit) quantization! For any high order modulation, communication is impossible. As q 0, the phase estimate converges i.e. ˆθ θ

73 Intuition Behind the Proof Consider extreme (1-bit) quantization! For any high order modulation, communication is impossible. As q 0, the phase estimate converges i.e. ˆθ θ Extended decision regions Ri θe converge to regular regions, i.e. Ri θe Ri θ

74 Intuition Behind the Proof Consider extreme (1-bit) quantization! For any high order modulation, communication is impossible. As q 0, the phase estimate converges i.e. ˆθ θ Extended decision regions Ri θe converge to regular regions, i.e. Ri θe Ri θ Quantizer affects symbols less: Q[m i ] m i

75 Intuition Behind the Proof Consider extreme (1-bit) quantization! For any high order modulation, communication is impossible. As q 0, the phase estimate converges i.e. ˆθ θ Extended decision regions Ri θe converge to regular regions, i.e. Ri θe Ri θ Quantizer affects symbols less: Q[m i ] m i Balance Point At some q, the combination of convergent decision regions and convergent points results in the condition being met, guaranteeing zero error.

76 Applying This Result We can compute θ emax we can compute R θe i

77 Applying This Result We can compute θ emax we can compute R θe i We can determine minimum distance between quantized points

78 Applying This Result We can compute θ emax we can compute R θe i We can determine minimum distance between quantized points Choose q such that all points are just farther apart than this minimum distance

79 Numerical Results M-PSK Applying this condition, we compute minimum q for different modulations System operating over fading channel, with normalized radius, requires this many bins Error floor disappears for quantizers with this minimum number of bits M Bins Required Bits

80 Numerical Results M-PSK Applying this condition, we compute minimum q for different modulations System operating over fading channel, with normalized radius, requires this many bins Error floor disappears for quantizers with this minimum number of bits M-QAM M Bins Required Bits M Bins Required Bits

81 Results Numerical Simulations Probability of Error for 16 QAM under Quantization 1 Tap Rayleigh Fading with Pilot Symbol Estimation 10 Bins 12 Bins 10 4 p(e) SNR

82 Results 12 Bins for 16-QAM (Minimum for Zero Error)

83 Results 10 Bins for 16-QAM (Inadequate)

84 Clipping Error What happens if we over-amplify? Under-amplification introduces serious quantization error, destroys both phase and magnitude information Over-amplification destroys only magnitude information

85 Clipping Error What happens if we over-amplify? Under-amplification introduces serious quantization error, destroys both phase and magnitude information Over-amplification destroys only magnitude information Theorem Modulations encoding information only in phase can withstand arbitrary amounts clipping, while those encoding any information on magnitude suffer when clipping occurs

86 Clipping Error What happens if we over-amplify? Under-amplification introduces serious quantization error, destroys both phase and magnitude information Over-amplification destroys only magnitude information Theorem Modulations encoding information only in phase can withstand arbitrary amounts clipping, while those encoding any information on magnitude suffer when clipping occurs M-PSK survives arbitrary amounts of ideal gain, provided the quantizer has the minimum resolution required to recover phase.

87 Where are We? We have found minimum quantization resolution for fading channels at high SNR.

88 Where are We? We have found minimum quantization resolution for fading channels at high SNR. How do we incorporate noise?

89 Where are We? We have found minimum quantization resolution for fading channels at high SNR. How do we incorporate noise? Densities of quantized channel phase in the presence of noise are analytically intractable. Assume zero channel phase for now.

90 Additive Noise Are All Modulations Equal? Decision regions for 8 PSK, 18 bins of quantization

91 Additive Noise Are All Modulations Equal? Decision regions for 8 PSK, 18 bins of quantization PSK and QAM respond differently to additive noise

92 Additive Noise Computing SER Gaussian density falling within decision region: 18 bins for 8 PSK

93 Additive Noise Computing SER Gaussian density falling beyond decision region: 18 bins for 8 PSK

94 Additive Noise Effects of Q[ ] on PSK Symbol Error 10 0 SER for 8 PSK, 18 levels of Quantization 10 0 SER for 8 PSK, 28 levels of Quantization SER m 0 m SNR SNR

95 Additive Noise Effects of Q[ ] on PSK Symbol Error 10 0 SER for 8 PSK, 18 levels of Quantization 10 0 SER for 8 PSK, 28 levels of Quantization SER m 0 m SNR SNR Theorem: SER Probabilities under Quantization For QAM modulation with sufficient bins, SER probabilities are equal across symbols regardless of quantization resolution For any other modulation, SER probabilities are unequal across symbols, converging as q 0.

96 Conclusions Analytical Results Computed minimum q for high SNR

97 Conclusions Analytical Results Computed minimum q for high SNR This gives the minimum amplitude for the input signal: Removes Error Floor

98 Conclusions Analytical Results Computed minimum q for high SNR This gives the minimum amplitude for the input signal: Removes Error Floor Examined how quantization affects symbol error rate

99 Conclusions Analytical Results Computed minimum q for high SNR This gives the minimum amplitude for the input signal: Removes Error Floor Examined how quantization affects symbol error rate The Next Step Relax the High SNR assumption Turn to implementation!

100 Outline 1 Introduction 2 Exact Analysis 3 Hardware System Description Medium-Low SNR Results WARP AGC Implementation Performance 4 Conclusions

101 System Configuration Using WARP Hardware Channel Emulator WARP Tx Q[ ] WARP Rx 64 subcarrier SISO-OFDM, 48 data bearing QPSK subcarriers

102 System Configuration Using WARP Hardware Change SNR Channel Emulator WARP Tx Q[ ] WARP Rx 64 subcarrier SISO-OFDM, 48 data bearing QPSK subcarriers

103 System Configuration Using WARP Hardware Change SNR Channel Emulator Change resolution WARP Tx Q[ ] WARP Rx 64 subcarrier SISO-OFDM, 48 data bearing QPSK subcarriers

104 System Configuration Using WARP Hardware Change SNR Channel Emulator Change resolution WARP Tx Q[ ] WARP Rx BER 64 subcarrier SISO-OFDM, 48 data bearing QPSK subcarriers

105 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR bits Pe

106 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR bits 6 bits 10 3 Pe

107 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR Pe bits 6 bits 7 bits

108 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR Pe bits 6 bits 7 bits 8 bits

109 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR Pe bits 6 bits 7 bits 8 bits 10 bits

110 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR Pe bits 6 bits 7 bits 8 bits 10 bits bits

111 Medium-Low SNR Performance BER as a Function of Resolution for SISO System SNR Pe bits 6 bits 7 bits 8 bits 10 bits bits 12 bits

112 Hardware Results Hardware Results In the medium-low SNR regimes, error floors appear for low precision, as we predict Above 12 bits, error floors disappear! Hardware has filled in the gaps between high SNR analysis and real world operating regimes.

113 Hardware Results Hardware Results In the medium-low SNR regimes, error floors appear for low precision, as we predict Above 12 bits, error floors disappear! Hardware has filled in the gaps between high SNR analysis and real world operating regimes. Pushing Down the Error Floor To get the most precision from our quantizers, we need to fill their range! Automatic Gain Control

114 Building the AGC r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc. We have gained an understanding of Q[ ] How do we design an AGC to choose g such that minimum resolution is met?

115 Building the AGC r Chooses g(r, A) Requires magnitude A AGC Q[ ] Sig. Proc. We have gained an understanding of Q[ ] How do we design an AGC to choose g such that minimum resolution is met?

116 Implementation Challenges Two Problems Problem: We don t know what I/Q magnitudes to expect from the transmitter! Solution: Track the envelope of the transmission instead. Specifically, track the power.

117 Implementation Challenges Two Problems Problem: We don t know what I/Q magnitudes to expect from the transmitter! Solution: Track the envelope of the transmission instead. Specifically, track the power. Problem: We can t predict spikes in the signal, and feedback loop is too slow! Solution: Choose target gain to minimize expected distortion.

118 Challenge: Multi-Antenna Gain Control Coupled AGC? On multi-antenna systems, choose target gains across multiple radios! Choosing g for MIMO AGC min g A (g + E[r 2 ]) 2

119 Challenge: Multi-Antenna Gain Control Coupled AGC? On multi-antenna systems, choose target gains across multiple radios! Choosing g for MIMO AGC min g A (g + E[r 2 ]) 2 note the absence of vector products min g i A i (r i ) (g i + E[r 2 i ]) 2

120 Challenge: Multi-Antenna Gain Control Coupled AGC? On multi-antenna systems, choose target gains across multiple radios! Choosing g for MIMO AGC min g A (g + E[r 2 ]) 2 note the absence of vector products min g i A i (r i ) (g i + E[r 2 i ]) 2 Result: MIMO AGC operation decouples into L SISO AGC operations However, packet preambles must be designed differently for multi-transitter systems to avoid interference effects

121 SISO AGC Implementation on WARP Algorithm cos(2πf t) G RF RSSI G BB I Q

122 SISO AGC Implementation on WARP cos(2πf t) Algorithm 1 Estimate signal strength from RSSI G RF RSSI G BB I Q

123 SISO AGC Implementation on WARP Algorithm cos(2πf t) 1 Estimate signal strength from RSSI G RF RSSI I 2 Choose RF gain and estimate BB gain G BB Q

124 SISO AGC Implementation on WARP Algorithm cos(2πf t) 1 Estimate signal strength from RSSI G RF RSSI G BB I Q 2 Choose RF gain and estimate BB gain 3 Compute digital signal power V IQ

125 SISO AGC Implementation on WARP Algorithm cos(2πf t) 1 Estimate signal strength from RSSI G RF RSSI G BB I Q 2 Choose RF gain and estimate BB gain 3 Compute digital signal power V IQ 4 Update BB gain such that V IQ = A

126 SISO AGC Implementation on WARP Algorithm cos(2πf t) 1 Estimate signal strength from RSSI G RF RSSI G BB I Q 2 Choose RF gain and estimate BB gain 3 Compute digital signal power V IQ 4 Update BB gain such that V IQ = A Converges within 4µs

127 SYSGEN Implementation Today s Dual-Core AGC

128 Computational Complexity Cost of Implementation Attr. AGC-1 Slices 5350 FF 7399 LUT 7377 Mult 18 AGC-1: Original implementation (Jan 2006)

129 Computational Complexity Cost of Implementation Attr. AGC-1 AGC-2 Slices FF LUT Mult AGC-1: Original implementation (Jan 2006) AGC-2: Reused arithmetic (Mar 2006)

130 Computational Complexity Cost of Implementation Attr. AGC-1 AGC-2 AGC-2H Slices FF LUT Mult AGC-1: Original implementation (Jan 2006) AGC-2: Reused arithmetic (Mar 2006) AGC-2H: Reused arithmetic, polyphase decimation (May 2006)

131 Computational Complexity Cost of Implementation Attr. AGC-1 AGC-2 AGC-2H AGC-2H + MIMO Slices FF LUT Mult AGC-1: Original implementation (Jan 2006) AGC-2: Reused arithmetic (Mar 2006) AGC-2H: Reused arithmetic, polyphase decimation (May 2006) AGC-2H+MIMO: Reused arithmetic, polyphase decimation, dual core (Sep 2006)

132 System Performance Testbench Deviation between exact gain and AGC-chosen gain, A = 19 dbm. db P IN

133 System Performance Wireless Environment AGC Chosen Baseband Gain Value for Select Target Magnitudes Rx Power = 24 dbm, Trials 5 dbm 10 dbm 15 dbm 20 dbm 25 dbm p(g) Baseband Gain Value (db)

134 System Performance Wireless Environment 0.35 Variance of AGC Baseband Gain Values: Rx power = 24 dbm Variance (db 2 ) dbm 10 dbm 15 dbm 20 dbm 25 dbm

135 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings AGC Trigger times The signal V IQ is a function of time: if the AGC starts at a different point during the packet, it will use varying V IQ values.

136 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings DC Offset DC Offset can introduce itself in the gain calculation r = hx

137 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings DC Offset DC Offset can introduce itself in the gain calculation r = hx = g 1 hx + d 1

138 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings DC Offset DC Offset can introduce itself in the gain calculation r = hx = g 1 hx + d 1 = g 2 g 1 hx + g 2 d 1 + d 2

139 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings DC Offset DC Offset can introduce itself in the gain calculation r = hx = g 1 hx + d 1 = g 2 g 1 hx + g 2 d 1 + d 2 = g 2 g 1 hx + g 2 d 1 + d 2 d e

140 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings DC Offset DC Offset can introduce itself in the gain calculation r = hx = g 1 hx + d 1 = g 2 g 1 hx + g 2 d 1 + d 2 = g 2 g 1 hx + g 2 d 1 + d 2 d e = g 2 g 1 hx

141 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings Gain Settings AGC can only set gains in increments of 2 db

142 Sources of Variance Differing AGC trigger times DC Offset during gain calculations Non-continuous gain settings Gain Settings AGC can only set gains in increments of 2 db 4dB dB

143 Outline 1 Introduction 2 Exact Analysis 3 Hardware 4 Conclusions

144 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements

145 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool

146 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool Efficient AGC Implementation

147 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool Efficient AGC Implementation Bottom Line New theoretical results have been derived

148 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool Efficient AGC Implementation Bottom Line New theoretical results have been derived Hardware brought these results closer to realistic situations

149 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool Efficient AGC Implementation Bottom Line New theoretical results have been derived Hardware brought these results closer to realistic situations Error floors from quantization can be removed with proper handling of receiver gain.

150 Tying it All Together Theory and Implementation Fundamental Idea: Platforms filled gaps in analysis Contributions High SNR quantization requirements High SNR AGC requirements Medium-Low SNR results from the platform, our tool Efficient AGC Implementation Bottom Line New theoretical results have been derived Hardware brought these results closer to realistic situations Error floors from quantization can be removed with proper handling of receiver gain. Gain Control is the preferred method to guard against quantization errors

151 Continuing Work Where can we go from here? Robust modeling of quantization to come down from high SNR

152 Continuing Work Where can we go from here? Robust modeling of quantization to come down from high SNR More complete understanding of MIMO-AGC, namely settling times

153 Continuing Work Where can we go from here? Robust modeling of quantization to come down from high SNR More complete understanding of MIMO-AGC, namely settling times Tighter feedback in AGC implementation

154 Continuing Work Where can we go from here? Robust modeling of quantization to come down from high SNR More complete understanding of MIMO-AGC, namely settling times Tighter feedback in AGC implementation Better understanding of clipping error in multi-carrier systems (PAPR)

155 Continuing Work Where can we go from here? Robust modeling of quantization to come down from high SNR More complete understanding of MIMO-AGC, namely settling times Tighter feedback in AGC implementation Better understanding of clipping error in multi-carrier systems (PAPR) among many others...

156 Thank You Any further questions?