## 1 Introduction  
There is a growing need for wireless implantable neural recording systems that can simultaneously acquire neural signals from a large number of channels. Recording from hundreds of neurons may allow neurophysiologists to study brain function in freely-behaving animals, and in future will provide the signals necessary to control neural prosthetic devices [1]. Compared to wired systems, wireless neural recording devices provide a number of benefits: reduction of motion artifacts and freedom of animal movements in neuroscience experiments, as well as reduced infection risks and higher patient mobility in neuroprosthetic applications. However, these systems entail severe technical challenges, such as the robustness of the wireless link and the need of a large data transmission band, coupled to low-power dissipation and small size in case of brain-implantable devices. The main issue is related to the huge amount of data associated with a large number of recording channels: in a \(64\) channel system featuring a \(20\) kHz sampling frequency (the neural signal band extends to about \(7\)-\(10\) kHz) with \(8\) bit resolution, the required data rate of the wireless link is \(10.24\) Mbit/s. Achieving such a high bit rate is not straightforward either in fully implantable devices where power consumption is limited to about \(10\) mW to avoid tissue necrosis [2] and in battery-powered systems for maintaining a reasonable battery life. Hence, most integrated circuits (ICs) reported in the literature that simultaneously support neural recording and wireless telemetry must trade-off power consumption against the amount of data to be wirelessly sent. Data compression was adopted to solve this problem in earlier systems. For example, since in a typical extracellular electrode trace most of the useful information is contained in spikes (or action potentials, APs), [PERSON] _et al._[3] enable only the transmission of the spike occurrence information, achieving a low bit rate of \(330\) kbit/s for \(100\) channels. However, since the examination of the raw traces may improve the selection of the spike detection threshold, the system reported in [4] allows to collect raw data from \(2\) out of \(64\) channels present in the system, while only spike occurrence times are sent for the remaining \(62\) channels via a \(2\) Mbit/s wireless link. On the other hand, spike waveforms are used in neuroprosthetic applications to assign spikes to specific neurons improving the prediction of an intended movement [5]. Hence, during the last four years, wireless systems capable of sending all raw data have been reported. In [6], [PERSON] _et al._ describe a \(128\) channel system able to transmit all raw data using an impulse-radio ultra-wide band (IR-UWB) transmitter with up to \(90\) Mbit/s rate. In such system, problems may arise from skull and skin absorption at high frequencies (signal spectrum is in the \(3.5\)-\(4.5\) GHz range) and from pulse distortion and the need of an external broadband antenna. As a matter of fact, no _in vivo_tests are reported for this kind of system. In [7], [PERSON] _et al._ report a system that transmits raw data from \(32\) channels, encoded in a pulse-width modulated (PWM) signal via a \(640\) kS/s frequency-shift keying (FSK) wireless link. In this system, the transmitted information relies on the time width of each symbol, making this transmission prone to the noise of the wireless link and of the receiver. Moreover, the system in [7] requires a relatively large bandwidth (\(38\) MHz), which means higher probability of RF interferences, and does not meet the band requirements of any medical communication standard. We propose here a solution that is intermediate to the two extremes described above.