# Uplink Throughput in a Single-Macrocell/Single-Microcell CDMA System, with Application to Data Access Points Shalinee Kishore (Lehigh University)

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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

Two-Tier Cellular CDMA System Macrocell serves N M (large number) users at fixed data rate R M. Microcell serves n (small number) users one-at-a-time at higher data rate, R   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)

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.

Problem Statement 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,  ) Given:

N total users who are assigned base stations according to path gains. User j elects macrocell when T jM >  T j , otherwise it elects DAP. Problem Statement (Cont’d)  = desensitivity factor   1  small DAP coverage area N M macrocell users who simultaneously transmit with rate R M = W/G (G is fixed macrocell processing gain) and achieve minimum SINR  M. Remaining n = N - N M DAP users who transmit one-at-a-time and can adapt their processing gain (thus their data rate, R  ). Objective: Determine R  for DAP users with minimum SINR of  .

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

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 p n 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.

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

Accuracy of Truncated Lognormal Approximation CDF  u /W, Normalized Per-User Throughput (K=26,   =7, N M =25, H M / H  = 10)

Normalized Average Throughput (E{  / W }) Versus  Normalized Average Throughput  Desensitivity Total DAP Throughput Per-User Throughput (K=26,   =7, N M =25, H M / H  = 10)

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.

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