# Multifunction RF Systems for Naval Platforms
## 3 MFRF System Design Considerations
### Practical Limitations and Trade-Offs
#### 3.2.3 Element-Level vs. Subarray-Level Digitization/Waveform Generation  
Section 3.1 discusses the key advantages of element-level digitization and waveform generation. The main deterrents to performing these operations at the element level for an AESA are added cost and design complexity, given that there are typically several thousand elements on an array and each element, if dual-polarized, would require two DDSs and two ADCs. As a rough order-of magnitude indication of incremental per-element costs, the Analog Devices DDS is listed at about $140 USD per unit, while the Texas Instruments ADCs in Table 3 (TI, Dallas, TX, USA) are priced in order of decreasing bandwidth as $2000 USD, $850 USD, $400 USD and $20 per ADC. There is an obvious correlation of decreasing price with narrower ADC bandwidths. The alternative approach to an element-level design is to divide the AESA into fixed subarrays, with each subarray, rather than each element, serviced by a single digital receiver and/or DWG. This is illustrated in Figure 6 for the simple case of a two-element subarray on a combined Rx/Tx AESA. In a typical implementation, the waveform signal from the DWG is split and injected into the Tx channels of the subarray, while the received signals in the Rx subarray channels are summed in a combiner before digitization by the digital receiver. Note that subarray sizes for Tx and Rx operations can generally be different, even with combined Tx/Rx arrays. Also, either digitization or waveform generation may be implemented at the element level, while the other is realized at the subarray level. For a subarray-level approach, analog _be_amforming (BF) elements must be included in the Rx and Tx paths. These may be phase shifters in the case of narrowband waveforms or more complex TTD circuits for wideband signals. A waveform can be considered narrowband from a subarray viewpoint if \(L_{s}\ll c_{0}/2B\), where \(L_{s}\) is the maximum dimension of the subarray, \(c_{0}\) is the speed of light, and \(B\) is the waveform bandwidth [28]. For the waveform bandwidth of \(B=1\) GHz that must be accommodated by the EA and ES functions, the subarray dimensions must therefore be much less than 15 cm to meet this narrowband criterion. However, these subarray dimensions would be comparable to the actual element spacing, given the frequency ranges of operation in Table 1, so larger subarrays with TTD beamforming elements must be used. TTD formation of Tx beams with maximum array gain is then accomplished by employing the DWGs to introduce relative waveform time delays between subarrays, and the TTD beamforming elements to generate additional relative waveform time delays between radiating elements within each subarray. For TTD formation of Rx beams, the TTD beamforming elements impose relative time delays between signals received from different elements within each \begin{table}
\begin{tabular}{c c c} \hline \hline
**Device** & **Number of Bits** & **Sampling Rate (GSPS)** \\ \hline Texas Instruments ADC12 DJ3200 & 12 & 6.4 \\ Texas Instruments ADC32 RF45 & 14 & 3.0 \\ Texas Instruments ADS54J60 & 16 & 1.0 \\ Texas Instruments ADS1675 & 24 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Representative specifications for ADCs. subarray, and after combining and digitization at the subarray level, relative time offsets between the subarrays are added in the digital domain before coherent summation. Compared to an element-level implementation, subarray-level digitization/waveform generation results in less flexibility to dynamically configure the AESA. Since the subarrays assigned to DWGs and/or digital receivers in a subarray-level implementation are essentially fixed in size by the hardware design, the RAM is restricted to partitioning the AESA into areas that are multiples of this smallest subarray size. If these subarrays are relatively large, this constraint may have an adverse effect on the ability of the AESA to accommodate multiple RF functions.