## 3 Multiple-Access Reservation Receiver Initiation MAC (MAR-RiMAC)
### \"Request to Transmit\" (RtT) Signaling
(**d**) Cross-correlating with a non-matched CSS does not produce spike values. support 127 CSSs with minimal misdetections (practically none). Another alternative is the large set of Kasami sequences with 255 symbols per sequence, which can support 4011 CSSs with similar performance (e.g., [48]). If the number of devices is very high, instead of extending the length of the CSS sequences to support a unique sequence for each device, which increases the transmission overhead even under light loads, we can reuse CSSs. Specifically, since the devices usually send reports only occasionally, not all the devices in the neighborhood are expected to transmit a report at the same time, and only a subset of devices is expected to transmit simultaneously; the number of required CSSs can be reduced based on this expected number, i.e., devices will not receive unique CSSs and they will have to choose from a common CSS pool. Obviously, reducing the number of CSSs also reduces the sequence length, i.e., transmission duration. However, since multiple devices utilize the same CSS pool and multiple devices can use the same CSS, we need to find a mechanism to associate a received CSS with the device that sent it. If the number of CSSs is much higher than the expected number of devices that may transmit simultaneously, we can let each device choose which CSS to use at each transmission opportunity randomly by relying on the low probability that different devices will choose the same CSS (e.g., with 127 CSSs and five devices transmitting simultaneously, the probability that each device will choose a different CSS is over 0.92). In this case, the sink will pool the devices based on the CSSs used (i.e., the index or some other CSS identification will be included in the polling message). Note that if two devices choose the same CSS, there will be a collision while transmitting their reports, yet the rest of the devices that chose a unique CSS will have no problem in sending their reports; the colliding devices will resolve the collision according to the collision resolution mechanism described below after randomly choosing a different CSS. Another option is to define a small contention interval starting right after the RtR message, such that each device randomly chooses the CSS and the timing (minislot) with which it transmits its reservation request. The sink will pool the device based on the CSS and the timing; now, collision will occur only if two devices choose the same CSS and the same time slot. An illustration of a contention interval with five minislots is given in Figure 5.  
Figure 4: A sender conveys information to the receiver via a pre-defined CSS. For each newly acquired sample, \(y(k+\Delta)\), the receiver computes the signal’s correlation with a local copy of a particular CSS, \(C(\Delta)=\sum_{k=0}^{L-1}s^{*}(k)y(k+\Delta)\), where \(s^{*}\) denotes the complex conjugate of the target CSS: \(s\). The correlation value spikes every time a pre-defined CSS is received. **(a)** Signal correlation of seven repetitions of a 127-symbol-length Gold-code codeword under background interference, generated by random OFDM transmissions of a potential background interference (received signal to interference and noise ratio (SINR) is \(-6\) dB). **(b)** Cross-correlation values of a specific CSS when an additional 10 different CSSs were sent. The figure depicts the cross-correlation values with each of the 11 CSSs. The correlator spikes when the designated CSS is received. It is low for all ten other CSSs. Note that the cross-correlation values stay low until \(y(\Delta)\) is aligned with the beginning of \(s\). Aggregated Signal Collection (ASC): The second mechanism that can be utilized relies on group testing [54]. It also relies on each device transmitting a unique binary predefined sequence after receiving the RtR signal. Specifically, each device is assigned a unique sequence of ones and zeroes of length \(T\) (the value of \(T\) will be determined later).