To leverage rich data distributed at the network edge, a new machine-learning paradigm, called edge learning, has emerged where learning algorithms are deployed at the edge for providing intelligent services to mobile users.While computing speeds are advancing rapidly, the communication latency is becoming the bottleneck of fast edge learning. To address this issue, this work is focused on designing a low-latency multi-access scheme for edge learning. To this end, we consider a popular privacy-preserving framework, federated edge learning (FEEL), where a global AI-model at an edge-server is updated by aggregating (averaging) local models trained at edge devices. It is proposed that the updates simultaneously transmitted by devices over broadband channels should be analog aggregated "over-the-air" by exploiting the waveform-superposition property of a multi-access channel.Such broadband analog aggregation (BAA) results in dramatical communication-latency reduction compared with the conventional orthogonal access (i.e., OFDMA). In this work, the effects of BAA on learning performance are quantified targeting a single-cell random network. First, we derive two tradeoffs between communication-andlearning metrics, which are useful for network planning and optimization. The power control ("truncated channel inversion") required for BAA results in a tradeoff between the update-reliability [as measured by the receive signalto-noise ratio (SNR)] and the expected update-truncation ratio. Consider the scheduling of cell-interior devices to constrain path loss. This gives rises to the other tradeoff between the receive SNR and fraction of data exploited in learning. Next, the latency-reduction ratio of the proposed BAA with respect to the traditional OFDMA scheme is proved to scale almost linearly with the device population. Experiments based on a neural network and a real dataset are conducted for corroborating the theoretical results. In addition, we discuss the extensions of BAA to acquire safety against adversary attacks and integrate beamforming for enhancing cell-edge links.