Automatic Gain Control Response Delay and Acquisition in Direct- Sequence Packet Radio Communications Sure 2007 Stephanie Gramc Dr. Noneaker

Research Motivation Direct-sequence (DS) spread-spectrum modulation – Use of bandwidths much wider than minimum required for simple point-to-point communication at the same data rate – Resistance to jamming – Resistance to detection – Sharing of channels among multiple users Applications – Cellular code-division multiple-access networks – Tactical military radio networks – Wireless local area networks with high data rate

Research Purpose Focus on acquisition of a DS packet – Timing uncertainty of arriving signal – Must achieve synchronization to demodulate data – Can be limiting factor in communication system performance Model the delay caused by an AGC System’s delay in responding to change in signal power Analyze the effect of the AGC delay on acquisition performance

a M-1 a3a3 a2a2 a1a1 a0a0 Packet Transmission Format Preamble sequence – Not modulated – Known a priori at receiver – Frequently changed for security – Let M = preamble length in chips – Preamble transmitted over time [0, MT c ) – Values of +1, -1, j, or -j Preamble SequenceData

s(t): Transmitted signal where n(t): Additive White Gaussian Noise (AWGN) Channel with spectral density of N 0 /2 r(t): Received signal Communication System t = kT s s(t) r(t) Chip- Matched Filter Sequence- Matched Filter n(t) AGC Acquisition Algorithm Preamble Matched Filter IF Filter

Matched Filter Input convolved with local copy of preamble Example – M=7 and Sequence = (+1, -1, -1, +1, -1, +1, +1) – Preamble received at t=0 – Peaks at t = 7(T c ) = MT c Output peaks when last chip of an incoming (matched) preamble sequence is received Use an acquisition threshold to detect end of arriving preamble sequence Noise Free Matched Filter Output

Matched Filter (Alternate Representation) Chip-Matched Filter: – Convolve incoming signal with one chip of local preamble Discrete time sequence matched filters – Sample chip-matched filter output at times t = kT c, k =0 to M-1 – Apply weight of a k to each output – Produces a group of independent Gaussian random variable (sum represents matched filter output) t = kT s Chip- Matched Filter Sequence- Matched Filter

Automatic Gain Control (AGC) Gain is the increase in power of the received signal AGC automatically adjusts the gain based on the strength of the input signal Designed to keep average power constant into subsequent electronics Weaker signals are amplified more: higher gain Stronger signals are amplified less: lower gain time Gain levels for s(t) + n(t) Idealized AGC Behavior Gain levels for n(t )

Automatic Gain Control Response Delay Practical AGC has delayed response to signal-level change Effects input to matched filter  effects acquisition algorithm Model response as linear with response delay t agc: More Realistic AGC Behavior t agc time A 0 = Gain levels for n(t) A 1 = Steady state gain levels for s(t) + n(t)

Accounting for Channel Attenuation Old approximation of idealized AGC system gain levels with Develop gain approximations for AGC system with response delay Adjust statistics to model linear delay in AGC system

Preamble Signal-to-noise Ratio Noise power spectral density in received signal is: Energy in received signal is: SNR

Mean of Matched Filter Output AGC system with idealized instantaneous response β is measure of IF filter bandwidth C A (i) measures characteristics of preamble sequence

Mean of Matched Filter Output AGC system with response delay

Variance of Matched Filter Output AGC system with idealized instantaneous response

Variance of Matched Filter Output AGC system with response delay

Acquisition Algorithm Let acquisition threshold = η i If X i > η i – Declare hit – Enter verification mode to check if synchronization has occurred If verified, enter data-detection mode If verification fails, return to acquisition mode Let verification interval = Q – Amount of time required for receiver to determine if false alarm occurred and return to acquisition mode

Probability of Not Acquiring a Packet Probability of a miss – Acquisition fails because matched-filter output does not exceed acquisition threshold when the end of the preamble is received Probability of a false alarm – Acquisition fails because algorithm in in verification mode when the end of the preamble is received and acquisition threshold is exceeded P (not acquiring) = P (miss) + P (false alarm)

Simulate Matched Filter Output Generate two independent Gaussian random variables with unit variance and zero mean: U i and V i Scale U i and V i by standard deviation and mean expressions corresponding to current time in the simulation Form test statistic: X i =U i 2 + V i 2

Simulation Times of Receiver System i = 0 corresponds to time start of packet’s preamble is received {X i, i<0} correspond to time before packet’s arrival {X i, … X tagc } correspond to time during reception of preamble effected by delay in AGC system {X tagc, … X M-1 } correspond to time during reception of preamble with completely adjusted gain X M corresponds to reception of full preamble sequence

Probability of Not Acquiring in AGC System with Idealized AGC Response for M=26, Q=65 Probability SNR (db) P(fa) P(miss)

Probability of Not Acquiring Probability of Not Acquiring in AGC System with Response Delays for M=26, Q=65 SNR (db)

Probability of Not Acquiring Probability of Not Acquiring in AGC System with Response Delays for M=100, Q=250

Conclusions Misses contribute to not acquiring for lower SNR values False alarms contribute to not acquiring for higher SNR values As the response delay time in the AGC system increases, probability of not acquiring increases Increase Factor of Not Acquiring with AGC Delay Compared to Ideal AGC

Acknowledgments Dr. Noneaker Javier Schlömann Dr. Xu Josh Lawrence Workshop Speakers – Dr. Hubbard – Dr. Baum – Dr. Russell – Dr. Hubing

Questions

The Effect of Automatic Gain Control on Serial Matched-Filter Acquisition in Direct-Sequence Packet Radio Communications Sure 2007 Stephanie Gramc Dr. Noneaker

IF (Intermediate-frequency) Filter IF filter rejects out of band noise power in received signal before inputting signal into AGC system (1/3): – Ratio of signal power that is passed through the IF filter – Ratio of the noise power passed through the IF filter – Measure of the ratio of IF filter’s bandwidth to the bandwidth of the DS signal

Accounting for Signal Power Power: Energy: – Per chip: – Per preamble:

t_agc = 0 t_agc = 1 t_agc = 2 t_agc = 3 t_agc = 4 t_agc = 5 SNR (db) Probability of Not Acquiring Probability of Not Acquiring in AGC System with Response Delays for M=26, Q=65

Probability of Not Acquiring Probability of Not Acquiring in AGC System with Response Delays for M=100, Q= t_agc = 0 t_agc = 1 t_agc = 5 t_agc = 10 t_agc = 15 t_agc = 20 t_agc = 25 SNR (db)