Summary

Chapter 20 Summary: Resource Allocation and Scheduling

Key Points

• 1.

  Multiuser diversity transforms fading from an impairment into a resource. By scheduling the user with the best channel in each time slot, the opportunistic scheduler achieves a sum-rate capacity that scales as $\log_2(\ln K)$ — a double-logarithmic growth with the number of users $K$. The expected maximum of $K$ i.i.d. Rayleigh channel gains grows as $\ln K + \gamma_{\text{EM}}$, following Gumbel extreme-value statistics.

• 2.

  Proportional fair scheduling maximises $\sum_k \ln \bar{T}_k$ by serving user $k^{\star} = \arg\max_k R_k[t]/\bar{T}_k[t]$. This gradient-ascent interpretation (Kushner--Whiting 2004) guarantees convergence to the log-utility optimum. The $\alpha$-fair utility family parameterises the entire throughput--fairness frontier: $\alpha = 0$ (max-rate), $\alpha = 1$ (PF), $\alpha \to \infty$ (max-min).

• 3.

  OFDMA resource allocation exploits frequency-selective fading by assigning subcarriers to users and distributing power. For unconstrained sum-rate maximisation, the greedy assignment (each subcarrier to its strongest user) followed by water-filling is globally optimal due to the orthogonality of subcarriers. Per-user rate constraints make the problem NP-hard in general.

• 4.

  Link adaptation (AMC) closes the gap between channel capacity and practical throughput by dynamically selecting the MCS based on CQI feedback. The target BLER of $\sim$10% for initial transmission, combined with HARQ retransmissions, maximises effective throughput. Outer-loop link adaptation (OLLA) tracks bias errors from CQI quantisation and feedback delay.

• 5.

  Inter-cell interference coordination (ICIC) manages the dominant impairment for cell-edge users. Frequency reuse with factor $\Delta$ improves cell-edge SINR by $\Delta^{\alpha/2}$ at the cost of $1/\Delta$ bandwidth per cell. Fractional frequency reuse (FFR) preserves cell-centre throughput (reuse-1) while protecting cell-edge users (reuse-$\Delta$).

• 6.

  Cross-layer design integrates the MAC scheduler, link adaptation, HARQ, and buffer management into a unified control loop. Modern systems (5G NR) operate this loop at sub-millisecond granularity with QoS-differentiated scheduling for URLLC, eMBB, and mMTC traffic classes.