Uplink Throughput in a Single-Macrocell/Single-Microcell CDMA System, with Application to Data Access Points

1. Uplink Throughput in a Single-Macrocell/Single-Microcell CDMA System, with Application to Data Access Points Shalinee Kishore (Lehigh University) skishore@lehigh.edu Stuart C. Schwartz (Princeton University) Larry J. Greenstein (WINLAB-Rutgers University) H. Vincent Poor (Princeton University) VTC Fall 2003

2. Two-Tier Cellular CDMA System • Macrocell serves NM (large number) users at fixed data rate RM. • Microcell serves n (small number) users one-at-a-time at higher data rate, Rm, resembles a Data Access Point (DAP). • Both base stations employ CDMA in the same frequency channel  cross-tier interference. • Microcell user can vary its spreading gain according to path gain and interference conditions. Macrocell with embedded microcell (used to enhance data capabilities)

3. Goal: Analyze achievable uplink throughputs for DAP. Per-user throughput Total DAP throughput Per-user Throughput: Uplink throughput for a single DAP user. Total DAP Throughput: Uplink throughput over all n DAP users.

4. Problem Statement Given: • Single-Macrocell/Single-Microcell CDMA System with system bandwidth W and fixed chip rate 1/W. • Probability distribution of user locations • Transmission gain model between user j and base station i (i = M,m)

5. Problem Statement (Cont’d) • N total users who are assigned base stations according to path gains. • User j elects macrocell when TjM > dTjm, otherwise it elects DAP. d= desensitivity factor d 1  small DAP coverage area • NM macrocell users who simultaneously transmit with rate RM= W/G • (G is fixed macrocell processing gain) and achieve minimum SINR GM. • Remaining n = N - NM DAP users who transmit one-at-a-time and can • adapt their processing gain (thus their data rate, Rm). Objective: Determine Rm for DAP users with minimum SINR of Gm.

6. Calculation of DAP Single-User Data Rate Using the SINR requirements, it can be shown for n random DAP users, Normalized interference at macrocell due to DAP user random variables Normalized interference at DAP due to macrocell users Our results show that the distribution of IMIm can be well modeled as lognormal.

7. Calculation of DAP Single-User Data Rate(Cont’d) • Consequently, cumulative distribution function (CDF) of r given n DAP • users, F(r|n), is that of a truncated lognormal random variable. • The distribution of r is: where pn is the probability that there are n DAP users. • Thus, distribution of r can be well-approximated using weighted sum of • CDF’s of truncated lognormal random variables. • Single-user data rates can be used to compute data throughputs.

8. Data Throughputs: Time-Averaged Data Rates Per User Throughput, tu, takes into account time-limited access when more than one DAP user in the system. Distribution can be computed as: E{tu} can be computed from this distribution. Total DAP Throughput, t, measure of DAP utilization. For a given n, t is the sum of throughputs for the n users. Average value can be computed as where E{r|n} can be approximated assuming a truncated lognormal distribution.

9. Accuracy of Truncated Lognormal Approximation CDF tu/W, Normalized Per-User Throughput (K=26, Gm=7, NM=25, HM / Hm = 10)

10. Normalized Average Throughput (E{ t / W }) Versus d Total DAP Throughput Normalized Average Throughput Per-User Throughput d,Desensitivity (K=26, Gm=7, NM=25, HM / Hm = 10)

11. Conclusion • Demonstrated that by controlling the desensitivity factor, a microcell • can be converted to a DAP. • Analyzed uplink data rate for a single DAP user and demonstrated • that it can be well-approximated as a truncated lognormal • random variable. • Developed throughput statistics for both single DAP users and overall • DAP users. • Found the value of desensitivity for which per-user throughput and • total DAP throughput are both high. • Future work: multiple DAP’s, downlink throughputs, effect of mobility • (time-varying channel conditions), etc.