Compressive Sensing has well boosted massive random access protocols over the last decade. In this paper we apply an orthogonal FFT basis as it is used in OFDM, but subdivide its image into so-called sub-channels and let each sub-channel take only a fraction of the load. In a random fashion the subdivision is consecutively applied over a suitable number of time-slots. Within the time-slots the users will not change their sub-channel assignment and send in parallel the data. Activity detection is carried out jointly across time-slots in each of the sub-channels. For such system design we derive three rather fundamental results: i) First, we prove that the subdivision can be driven to the extent that the activity in each sub-channel is sparse by design. An effect that we call sparsity capture effect. ii) Second, we prove that effectively the system can sustain any overload situation relative to the FFT dimension, i.e. detection failure of active and non-active users can be kept below any desired threshold regardless of the number of users. The only price to pay is delay, i.e. the number of time-slots over which cross-detection is performed. We achieve this by jointly exploring the effect of measure concentration in time and frequency and careful system parameter scaling. iii) Third, we prove that parallel to activity detection active users can carry one symbol per pilot resource and time-slot so it supports so-called one-shot messaging. The key to proving these results are new concentration results for sequences of randomly sub-sampled FFTs detecting the sparse vectors "en bloc". Eventually, we show by simulations that the system is scalable resulting in a coarsely 20-fold capacity increase compared to standard OFDM.

翻译：压缩感知在过去十年中极大地推动了大规模随机接入协议的发展。本文采用OFDM中使用的正交FFT基，但将其图像细分为所谓的子信道，并让每个子信道仅承担部分负载。这种细分以随机方式在适当数量的时隙上连续应用。在时隙内，用户不改变其子信道分配，并并行发送数据。活动检测在各子信道中跨时隙联合执行。针对这种系统设计，我们推导出三个基本结果：i) 首先，我们证明细分可以推进到每个子信道中的活动在设计中是稀疏的程度，我们将这种效应称为稀疏捕获效应。ii) 其次，我们证明该系统实际上能够承受相对于FFT维度的任意过载情况，即无论用户数量如何，活跃和非活跃用户的检测失败率均可保持在任意期望阈值以下。唯一的代价是延迟，即执行交叉检测所需的时隙数量。我们通过联合探索时间和频率中测度集中效应以及系统参数的精心缩放来实现这一点。iii) 第三，我们证明在与活动检测并行的情况下，活跃用户可以在每个导频资源和时隙上携带一个符号，从而支持所谓的单次消息传输。证明这些结果的关键是针对随机子采样FFT序列的新集中性结果，这些FFT能够"整体"检测稀疏向量。最后，我们通过仿真表明该系统具有可扩展性，与标准OFDM相比，其容量大约提升20倍。