Fundamental Limits of Noncoherent Massive Random Access Networks

This paper studies the capacity of massive random-access networks modeled as a multiple-input multiple-output fading channel with infinitely many interfering users. The network is assumed to operate in a noncoherent regime, where transmitters and receivers know the fading statistics but not their realizations. Users access the network via random activation with a given probability. To characterize the symmetric sum rate, a random-coding argument is invoked together with the assumption that users and interferers draw their codebooks according to the same distribution. For this channel model, rigorous upper and lower bounds on the network capacity are derived. The behavior of these bounds depends critically on the spatial decay of the large-scale fading statistics from interfering users. In particular, if the large-scale fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly, then the capacity is bounded in the transmit power. This occurs because the aggregate interference scales with the transmit power, and reveals an inherent saturation effect in interference-limited networks. Moreover, in this regime, random user activity cannot fundamentally eliminate the resulting capacity ceiling. In contrast, if the large-scale fading coefficients of the interferers decay faster than double-exponentially, then the capacity becomes unbounded in the transmit power. Note that proving an unbounded capacity is nontrivial even if the number of interfering users is finite, since the condition that the users’ codebooks follow the same distribution prevents interference-avoiding strategies such as time-, frequency-, or code-division multiple access, and cooperation among users associated with different access nodes is not allowed. An unbounded coding rate is achieved by using bursty signaling together with treating interference as noise.