Wireless Multiple Access Schemes in a Class of Frequency Selective Channels with Uncertain Channel State Information Christopher Steger February 2, 2004

Outline Introduction and Motivation Problem Formulation Analysis Simulations Conclusions

Outline Introduction and Motivation Problem Formulation Analysis Simulations Conclusions

Introduction: What is 4G? We know that we desire data rates far exceeding existing systems. We know that our PHY layer design depends heavily on our choice of multiple access scheme. We still don’t know what 4G will be.

How do we choose? We determine that there are four basic candidates:  OFDM  TDMA  MC-CDMA  DS-CDMA We contend that spectral efficiency is an essential metric. f t t t OFDM TDMA CDMA

How do we measure? Observe that spectral efficiency is proportional to mutual information. Mutual information can be determined without fixing a particular bandwidth. Fewer assumptions are better

PREAMBLE DATA How can we add realism? Two important aspects are missing from previous analyses:  Frequency selective channels  Estimation-based channel state information.

Outline Introduction and Motivation Problem Formulation  Channel Model  System Models Analysis Simulations Conclusions

Problem Formulation This is a first step in several directions. We need to stay simple.  The simplest frequency selective channels.  The simplest versions of our multiple access schemes

Channel Model The simplest multipath channel: 2 paths. The simplest frequency domain channel: 2 subcarriers. Discrete in time and frequency. Block fading. f1f1 f2f2 h1h1 h2h2 DFT

Channel Model We define channels in both time and frequency to assure fairness. Fading is complex Rayleigh or Ricean. We vary correlation in one domain by varying variances in the other.

System Models Simplest broadcast scenario: 2 users. Avoid giving any system an unfair advantage. All systems form channel estimates from a preamble signal. Frame of Length L Symbols Preamble of Length  L(1-  )L Data Symbols

Common Assumptions Gaussian signaling No feedback.  No power control. Fixed resource allocation.  Size and number of subcarriers is constant.  Time slot and spreading code allocations are constant. Nonlinear interference cancellation.  “Genie-aided” LMMSE equalization.

OFDM System Two subcarrier OFDM is indistinguishable from FDMA. Each user gets one subcarrier  Flat fading.  Frequency allocation is independent of power allocation. 0B/2B User 1User 2 0 t2t

OFDM Block Diagram Estimate Channel Equalize User 1 Data User 2 Data ChannelFFT Detect and Decode Output IFFT

TDMA System Each user receives half of the frame and the full bandwidth.  Users can resolve both multipath Time allocation is independent of power allocation. Nonlinear ISI cancellation.  Cancel edge effects as well. s 0 h 1 s 0 h 2 s 1 h 1 s 1 h 2 s 2 h 1 s 2 h 2 Interval of Interest

TDMA Block Diagram Estimate Channel Equalize User 1 Data User 2 Data Channel ISI Cancellation Detect and Decode Output

MC-CDMA System Complex orthogonal spreading codes.  Length 2  Spread over two subcarriers. Both users use full bandwidth and full frame. Each subcarrier is flat fading Code allocation and spreading length is independent of power allocation. s 1 c 11 f 1 s 1 c 12 f 2 s 2 c 21 f 1 s 2 c 22 f 2 Full Bandwidth Half Bandwidth User 1 User 2 First Subcarrier Second Subcarrier

MC-CDMA Block Diagram Estimate Channel FFT Despread Spread IFFT  Channel Interference Cancellation Equalize Detect and Decode User 1 Data User 2 Data Output

DS-CDMA System Complex, orthogonal spreading codes.  Length 2 Synchronous transmission Users can resolve both multipath components. Nonlinear interference cancellation  ISI  Other user Code assignment and spreading length are independent of power allocation. s 1 c 11 hs 1 c 12 h s 2 c 21 hs 2 c 22 h Symbol Interval Chip Interval User 1 User 2

DS-CDMA Channel Interval of Interest s 10 c 11 h 1 s 10 c 12 h 1 User 2 Signal User 1 Signal s 10 c 11 h 2 s 10 c 12 h 2 s 11 c 11 h 1 s 11 c 12 h 1 s 11 c 11 h 2 s 11 c 12 h 2 s 12 c 11 h 1 s 12 c 12 h 1 s 12 c 11 h 2 s 12 c 12 h 2 s 20 c 21 h 1 s 20 c 22 h 1 s 20 c 21 h 2 s 20 c 22 h 2 s 21 c 21 h 1 s 21 c 22 h 1 s 21 c 21 h 2 s 22 c 21 h 1 s 21 c 22 h 2 s 22 c 22 h 1 s 22 c 21 h 2 s 22 c 22 h 2

DS-CDMA Block Diagram Estimate Channel Despread Detect and Decode User 1 Data User 2 Data Spread  Channel Interference Cancellation Equalize Output

Outline Introduction and Motivation Problem Formulation Analysis  Sketch of Derivation  Calculating Achievable Rate Regions  Results Simulations Conclusions

Analysis We are deriving a lower bound on mutual information using a method developed by Medard in It is a lower bound because it assumes that uncertain CSI yields an additional AWGN term. The bound depends on the variance of our LMMSE equalizer.

Sketch of Derivation First, we find the LMMSE equalizer [Anderson and Moore, Optimal Filtering]. Then we find the variance of the equalizer. We lower bound our mutual information by finding the difference between the entropy of the signal and the entropy of Gaussian noise with variance equal to that of the equalizer.

Calculating Achievable Regions To find average mutual information, take expectation over all channel states. To define the region, find the average mutual information for all divisions of transmit power between the two users.

Results: Equations

Results: Achievable Rate Regions

Recall that in order to achieve correlation in time we have made one subcarrier much stronger than the other. Therefore, one FDMA user is favored.

Outline Introduction and Motivation Problem Formulation Analysis Simulations  Methods  Results Conclusions

Simulations Try an alternative evaluation method for our multiple access schemes. Verify our analytical results.  Verify that we have calculated lower bounds.  Assess the tightness of the bounds.  Verify convergence to analytical results with perfect CSI.

Methods Perform actual channel estimation, interference cancellation and equalization. Determine the SNR of the output. Use that SNR to determine mutual information. Average over many (10000) channel states.

Simulation Block Diagram Estimate Channel Equalize Generate Signal 1 Generate Signal 2 Channel Cancel Interference Process Calculate SNR Process Multiplex Calculate Mutual Info Generate Fading Generate Noise

Simulation Results

Recall that in order to achieve correlation in time we have made one subcarrier much stronger than the other. Therefore, one FDMA user is favored.

Outline Introduction and Motivation Problem Formulation Analysis Simulations Conclusions  Evaluating Schemes  Our Tools

Conclusions: Evaluating Schemes In several cases, we did not achieve a clear differentiation between schemes. In the cases where we were able to see strong trends:  TDMA and MC-CDMA often had nearly identical performance.  When FDMA performs well, DS-CDMA tends to do badly.  It makes a large difference whether fading is defined in time or frequency.  The difference between Ricean and Rayleigh fading is also a strong indicator of performance. All 4 schemes were best and worst at least once.

Conclusions: Tools Our analytical solutions don’t scale well for future work. The agreement between our analytical and simulation results is mutually validating. Simulations scale much more easily to more challenging channels. Lower bound analysis is not always accurate. Simulations are the best method.